Year Five Maths

OPERATIONS ON NUMBERS

Whole Number Addition, Subtraction, Multiplication and Division

Infogrid Pacific Pte. Ltd.

Unit 1: Year Five Maths. Operations on Numbers

©2012-13 Infogrid Pacific Pte. Ltd. All rights reserved

The included ALL-IN™ and AZARDI Interactive Engine™ Javascript software are trademarks and the Intellectual property of Infogrid Pacific.  This software is licensed to the end-user for use in a single downloaded copy of this e-book only and for no other purpose.

The ALL-IN and AZARDI Interactive Engine software is explicitly NOT licensed for reuse in any form for any purpose and cannot be reused, copied or be used to create derivative products without written permission from Infogrid Pacific.

For more information on Infogrid Pacific visit:

http://www.infogridpacific.com

Technical Information

This document has been prepared as XHTML5 using IGP:Digital Publisher – an advanced content authoring, editing and production application. The output is available simultaneously in multiple print PDF editions and specification compliant ePub3 formats. It can be viewed online in AZARDI. The International ePub Reader.

Contact Information

Email: sales@infogridpacific.com

AZARDI Help and Shortcuts

INFORMATION

This is an experimental ePub3 fixed-layout forced scrolling page (Spine property layout:rendition-scrolling). Do not adjust your personalization setting for this page.

Learn the features and accessibility shortcut  of AZARDI to get the most out of your reading experience. AZARDI Desktop is designed to empower you to get the best reading experience for any type of content on your monitor.

Application Keyboard Shortcut Keys

BUTTON

WIN/LIN KEYS

MAC KEYS

DESCRIPTION

F11

F11

View in Fullscreen

Right Arrow or PgUp

Right Arrow or PgUp

Navigates to next page

Left Arrow or Pg Dn

Left Arrow or Pg Dn

Navigates to previous page

-

Shift Right Arrow or Shift PgUp

Shift Right Arrow or Shift PgUp

Navigates to next section/chapter

-

Shift Left Arrow or Shift PgDn

Shift Left Arrow or Shift PgDn

Navigates to previous section/chapter

Alt+L

Ctrl+L

Close Reading mode, Save settings and goes to Library

Alt+U

Ctrl+U

Shows the reading personalization options

Alt+P

Ctrl+P

Opens the Default Settings dialog

-

Alt+R

Alt+R

Resets the book to the Default Settings

F1

F1

Opens the Help file in new viewport

-

-

View Print Page numbers

-

ALT+H

ALT+H

View fixed layout spine Properties in ePub3.

SMIL Audio with Overlay

BUTTON

WIN/LIN KEYS

MAC KEYS

DESCRIPTION

-

-

The audio icon is unmuted when a page contains SMIL Audio overlays. The following controls can then be used.

Ctrl+Spacebar

Command+Spacebar

Audio play/pause (Toggle)

Shift+Spacebar

Shift+Spacebar

Stop audio

-

Click paragraph in Stop mode

Click paragraph in Stop mode

Play paragraph

-

Click paragraph in Play mode

Click paragraph in Play mode

Continue from paragraph

Personalization Interface

Personalization tools are available for standard re-flowing ePubs. They are not available for Fixed Layout ePubs.

Personalization Alt+U to show the Personalization options.

Audio Icon  Available when a document section contains SMIL audio overlays. Click to show Play/Pause/Stop buttons.

Font size.  Click the +/- buttons to change the font size.

Margins.  Click the +/- buttons to change the margins.

Line-height.  Click the +/- buttons to change the line-height

Text-alignment.  Toggles text alignment between justified and align-left.

Hyphenation.  Toggles hyphenation on and off. Does not work on all browsers.

Page flow.  Scroll mode, single page, two column page, three column page, four column page.

Column Rules.  Toggle column rules on and off.

Reset.  Alt+R Resets to the application default presentation.

Fixed Layout Interface

The Fixed Layout (FLO) buttons are available when a fixed-layout book is loaded. These are looping multi-click buttons.

BUTTON

WIN/LIN KEYS

MAC KEYS

DESCRIPTION

-

-

Change FLO Background tone (multiclick)

-

-

Change FLO Chrome option (multiclick)

© Copyright 2005-2012 Infogrid Pacific Pte. Ltd. All rights reserved.

Introduction

PURPOSE OF THIS BOOK

This is a Mathematics interactive content demonstration book using standard long-arithmetic.

It uses the ALL-IN (AZARDI Learning Library-Interactive Now!) arithmetic module for the instant implementation of long forms of addition, subtraction, multiplication and division.

It's purpose is to allow education publishers to understand and evaluate the potential of ePub3 for creating education textbooks in a standard format rather than proprietary packages.

This book must currently be used with the AZARDI ePub3 reading system as it has and uses ePub3 features not supported by any other ePub3 reading system.

WHAT YOU WILL SEE

This book shows the use of advanced presentation and interactive arithmetic as available from the standard IGP:Digital Publisher production application using straight-forward tagging patterns and "built-in" interactive options. This book is a fully valid ePub3 book.

Arithmetic Presentation

This book uses highly structured presentation arithmetic to ensure clear and consistent presentation of the arithmetic in every context.

Accessibility is always important with our production and delivery systems so all equations and the body text fonts can be resized and the screen layout optimized for any requirement.

Tutorial Interactivity

Sliding panels are used for the Guided Practice tutorial exercises. This approach allows focus on the problem one step at a time with more detail that can generally be done in a print book, and  with easy back and forward navigation to review the tutorial steps. These could also be animated and have audio included.

Exercise Interactivity

There are Exercises linked from each Guided Practice. Exercise pages can be of any size or quantity as print page limitations do not exist. They can also be graded for learning targets. The student can do the exercises mentally or on paper and immediately check the answer in the actual equation. There is no "turning to the answer page".

In addition the Exercise pages can be downloaded as PDFs and printed for personal or classroom use. The Exercises have the answers on each print sheet.

Interactive Practice

Each of the four operation on numbers concepts (addition, subtraction, multiplication and division) has an independent "fixed-layout" practice page. Here sums are generated automatically and the student can practice as much as they like or need.

Test Yourself

In a similar manner to the Interactive Practice, the independent Test Yourself fixed layout pages give 10 problems and then a mark. The fully module (not provided in this demonstration) allows review and reattempt of the wrong answers as a student works through their learning steps.

PRODUCTION ADVANTAGES

Mathematics is always regarded as "challenging" in production; and it is. Even more so with digital content than print. The IGP:Digital Publisher approach delivers a suite of advantages not available in any other production system.

It is built on rock-solid, tested, tagging patterns that can be shaped with CSS, enhanced with images and actioned with Javascript.

The approach is designed for the world. Any and all languages. Any and all locale requirements.

Because the content is always managed in IGP:Digital Publisher new publishing solutions are presented. Books can be incrementally updated with additional interactivity at any time.

IN THIS BOOK

This book has a number of icon blocks that contain special information or resources.

INFORMATION

Information blocks contain production guidelines or instructions. These give information about the tools, content and interactions. These information blocks are not designed to be included in a final book.

WATCH THE VIDEO

Name and link to online resource. (12:26min).

In AZARDI this opens in a new controlled reader window (without URL bar) to control Internet access to online video resources.

EXERCISE: TRY IT YOURSELF

A link to an exercises with interactive answers for the student to try.

There is also a link to the printable PDF Exercise download page.

There are links to online printable PDFs for each exercise if a teacher/student would like to have a printed version of any exercise.

EPUB3 FEATURES USED IN THIS BOOK

This is a fixed layout ePub3 book using a full set of fixed layout spine properties. It uses reflowable and fixed layout pages as well as landscape only pages so will not work in iBooks or Readium.

- Lesson narratives and frontmatter are reflowable sections. They can be adjusted and optimized for your monitor and reading preferences with the AZARDI personalization tools.

- Interactive Practice and Interactive Test pages are fixed-layout landscape. They cannot be modified or changed by the user.

- Exercise pages are non-linear in the spine and not in the TOC. The reader skips these pages with previous/next navigation. They can only be entered and exited with page navigation links (or the return-button).

- Exercise pages and the AZARDI Help page use the experimental ePub3 spine property rendition:layout-scrolling. This instructs the reading system to present the pages in scrolling mode even if other sections have been customized for a multi-column view. Page Up and Page Down work on scrolling pages.

Unit 1

Operations on Numbers

Whole Number Addition, Subtraction, Multiplication and Division

INTRODUCTION

The mathematic lessons in this set of books is divided into learning units.

Students can use the interactive tutorials to view and learn multiple levels of maths problem solving. The advantage of these books is they can be downloaded and used off-line. They are accessible to students around the world in regions where there is little or no Internet connectivity.

In addition to the linear and interactive lessons the book contains multiple and comprehensive Interactive Exercises that can also be printed for personal or classroom use.

The lessons contain links to online interactive video resources for additional tuition.

Each chapter has highly interactive Practice and Test Yourself modules that allow any student to create their own learning experience.

This first unit contains four chapters addressing the following concepts:

Whole number long-addition

Whole number long-subtraction

Whole number long-multiplication

Whole number long-division.

Lesson 1

Whole Number Addition

Here you'll learn how to add whole numbers.

Vocabulary

Here are the vocabulary words found in this Concept.

Addend  The numbers being added

Sum  The answer to an addition problem

Place value  Writing each number in order according to the decimal place value it has.

Carry digit  A value carried from one column to another to maintain place values

Horizontally  Across or left to right

Vertically  Up and down

INFORMATION

A general concept overvew statement or word problem exercise can be placed in the concept introduction section.

Depending on the monitor size and orientation this page should be adjusted for optimal reading using Alt-U to select columns or scrolling and to adjust the text size.

GUIDANCE

You are already used to adding whole numbers and have been using addition for some time. We are now going to move your addition skills further forward with this learning module on long-addition.

We are assuming you are comfortable with a familiar problem like this:

4

+

5

=

In this problem, we are adding four and five. There are four whole things plus five whole things and this gives an answer of  nine things.

4

+

5

=

9

The numbers that we are adding together are called addends. The answer to an addition problem is the sum.

This first problem was written horizontally or left to right across the page.

In this lesson you will be learning how to write your problems vertically on your own.

How do we do this?

We can add whole numbers by writing them vertically according to place value.

Place value is when you write the numbers in order according to the decimal value that it has. These can be Units, Tens, Hundreds, Thousands and more.

This place value table shows the abbreviations we use in this lesson. Note that "Units" is also called "Ones" in some countries.

Ten Thousands

Thousands

Hundreds

Tens

Units

TTh

Th

H

T

U

5

4

3

2

1

This number is 54,321. In words this is said, fifty-four thousand, three hundred and twenty-one.

It can also be shown as an arithmetic sum which highlights how the place values work together.

50,000

+

4,000

+

300

+

20

+

1

Adding whole numbers

When you add whole numbers, it is easier to understand the problem and solve it by writing them vertically according to place value. We started with this very simple example.

4

+

5

=

9

To write this vertically it is important to line up the digits vertically. Because they are both in the units place value they are placed directly in-line vertically.

U

4

+

5

9

GUIDED TUTORIAL 1

Now that was too simple. Just mental arithmetic. But what happens when there are more digits in an addition problem?

4

5

6

+

2

7

=

When we have more digits we line up the place values vertically. Here we have 456 which is 4 Hundreds, 5 tens and 6 units being added to 27 which is 2 tens and 7 units.

Remember we have to vertically align all place values. So here they are:

H

T

U

4

5

6

+

2

7

Remember H is Hundreds, T is Tens and U is Units place values.

Now use this Guided Tutorial to see how to line up the place values, and how keeping the place values lined up makes long-addition easy. Don't just look at the tutorial. Practice writing your own sums on paper.

STEP 1. PLACE VALUES ALIGNED

H

T

U

4

5

6

+

2

7

We are going to add 456 and 27.

The biggest place value in 456 is 4. That is  a Hundreds place value.

The biggest place value in 27 is 2. A Tens place-holder.

It is best to put the biggest number at the top. Then it is easy to line the shorter numbers under that.

See how the Units (U), Tens (T) and Hundreds (H) are all each lined up vertically in their correct column.

STEP 2. READY TO START

4

5

6

+

2

7

We are going to add  456 and 27 together.

Remember our vocabulary terms. The big number 456 is an addend and the smaller number 27 is also an addend.

When we have added them together the result is the sum.

Notice we have a carry-forward area at the top of the vertical problem. We will be learning how to use this.

STEP 3. ADD THE UNITS

1

4

5

6

+

2

7

3

First we add the Units column.  That is:

6 + 7 = 13

The number 13 has 1 Tens and 3 Units.

The unit value 3 is placed in the Units answer line and the 1 is carried forward to the tens column.

That means you write the carry-forward value above the Tens column as shown here.

STEP 4. ADD THE TENS

1

4

5

6

+

2

7

8

3

Now we add the Tens column.

The 1 that was carried forward in the Tens column must also be added into the total. So the Tens sum is:

1 + 5 + 2 = 8

There is only the single digit so it is written into the Tens place value in the answer row.

There is no carry forward value.

STEP 5. ADD THE HUNDREDS

1

4

5

6

+

2

7

4

8

3

The last step is to add the Hundreds place value column.

There is only one value 4 in this column.

The 4 can be put directly into the answer line in the Hundreds place value position.

STEP 6. FINISHED

1

4

5

6

+

2

7

4

8

3

Here is our final answer.

The sum of 27 added to 456 is 483

As you get better at long-addition, try keeping the carry forward value for each column in your memory rather than writing it down.

◄ SLIDE FOR MORE ►

EXERCISE: TRY IT YOURSELF

Exercise 1-1. Simple Long-Addition ►

Download the Exercise as a printable PDF ►

GUIDED TUTORIAL 2

So far in this lesson we have learnt how to add numbers with up to three digits. We can add numbers having five digits or more the same way. So let's see what happens when we add this huge looking sum:

9

8

9

4

5

6

+

7

5

9

2

7

=

It may look hard, but once you get the place values aligned and work steadily through the problem it is easy to learn and do.

STEP 1. ARRANGE PLACE VALUES

HTh

TTh

Th

H

T

U

8

8

9

4

5

6

+

7

5

9

2

7

We are going to add 889,456 and 75,927 together.

First set the sum up vertically being careful to line up the place values.

This time we have Hundred-Thousands (HTh), Ten-Thousands (TTh), Thousands (T), Hundreds (H), Tens (T) and Units (U) place values.

All numbers are carefully placed into their correct place value column.

STEP 2. ADD THE UNITS

1

8

8

9

4

5

6

+

7

5

9

2

7

3

First we add the Units column.  7 is added to 6.

7 + 6 = 13

The number 13 has 1 Tens and 3 Units.

The Units value 3 is placed in the answer line in the Units column.

The 1 is carried forward to the Tens column.

When doing this by writing make sure you keep the place values lined-up.

STEP 3. ADD THE TENS

1

8

8

9

4

5

6

+

7

5

9

2

7

8

3

Now we add the Tens column. That is:

1 + 5 + 2 = 8

The total for the Tens column is 8. We put it in the answer line.

This time there is no carry forward number.

STEP 4. ADD THE HUNDREDS

1

1

8

8

9

4

5

6

+

7

5

9

2

7

3

8

3

We now move across to add the Hundreds column. Here the sum is:

4 + 9 = 13

The total is 13.

This is the total for the Hundreds column so we put 3 into the answer line.

The 1 is carried forward to the Thousands column

STEP 5. ADD THE THOUSANDS

1

1

1

8

8

9

4

5

6

+

7

5

9

2

7

5

3

8

3

We are now up to adding the Thousands column. The sum is:

1 + 9 + 5 = 15

Remember to include the carry forward number from the Hundreds column.

We place the five into the answer line.

The 1 is carried forward into the Ten-thousands column.

STEP 6. ADD THE TEN-THOUSANDS

1

1

1

1

8

8

9

4

5

6

+

7

5

9

2

7

6

5

3

8

3

We are now adding the Ten-thousands column. The sum is:

1 + 8 + 7 =16

We repeat the steps as before. The six is placed in the answer-line in the Ten-thousands column.

The 1 is carried-forward to the Hundred-thousands column.

STEP 7. ADD THE HUNDRED-THOUSANDS

1

1

1

1

8

8

9

4

5

6

+

7

5

9

2

7

9

6

5

3

8

3

We are now up to the last column, the Hundred-thousands. Here the sum is easy:

1 + 8 = 9

We put the 9 in the answer-line in the Hundred-thousands column.

There is nothing to carry forward so the problem is finished.

STEP 8. THE ANSWER

1

1

1

1

8

8

9

4

5

6

+

7

5

9

2

7

9

6

5

3

8

3

The final answer is:

889,456 + 75,927 = 965,383.

In words that is Nine-hundred and sixty-five thousand, three-hundred and eighty-three.

You can see adding big numbers is the same as smaller numbers and you just move carefully across the place value columns.

◄ SLIDE FOR MORE ►

EXERCISE: TRY IT YOURSELF

Exercise 1-2. Very Long-Addition ►

Download the Exercise as a printable PDF ►

GUIDED TUTORIAL 3

An addition problem can have more than two addends. We just have to take more care as we arrange the digits into vertical columns. So we are going to take this very large looking problem and arrange it into vertical columns.

8

7

6

8

+

3

2

4

3

+

4

7

9

+

6

6

1

5

=

The horizontal problem becomes this vertical layout. It looks more organized already.

Th

H

T

U

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

Now go though the guided practice to see how this is added together:

STEP 1. PLACE VALUES

TTh

Th

H

T

U

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

1

9

1

0

5

The first step is to arrange the numbers vertically with the place value columns correctly aligned.

In this sum we have Thousands (Th), Hundreds (H), Tens (T), and Units (U) place value columns.

The vertical alignment is very important when your sum has multiple addends.

STEP 2. ADD THE UNITS COLUMN

2

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

5

First we add the Units column.

That is 8+3+9+5 = 25

25 = 20 + 5

The 5 is placed in the Units column and  the 2 (representing 20) is carried forward into the Tens column.

STEP 3. ADD THE TENS COLUMN

2

2

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

0

5

Next we add the Tens column. We have to remember to include the 2 that was carried forward.

2 + 6 + 4 +7 + 1 = 20

The 0 is placed into the answer-line in the Tens position and the 2 is carried forward into the Hundreds column.

[ Remember we are actually adding Tens shortened for convenience. We actually added:

20 + 60 + 70 + 10 = 200 ]

STEP 4. ADD THE HUNDREDS COLUMN

2

2

2

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

1

0

5

Now it is time to add the Hundreds column. The sum is:

2 + 7 + 2 + 4 + 6 = 21

The one is placed in the answer line in the Hundreds position and the 2 is carried forward to the Thousands Column.

[ Remember we are actually adding 100s shortened for convenience. We actually added:

200 + 700 + 200 + 400 + 600 = 2100 ]

STEP 5. ADD THE THOUSANDS COLUMN

1

2

2

2

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

1

9

1

0

5

The last step is to add the digits in the Thousands column. The sum is:

2 + 8 + 3+ 6 = 19

Put the 9 in the answer line Thousands column.

The 1 is carried forward to the Ten-thousands column.

Because there is no other numbers in the Ten-thousands column you can just write  the 1 into the answer-line.

STEP 6. THE ANSWER

1

2

2

2

8

7

6

8

3

2

4

3

4

7

9

+

6

6

1

5

1

9

1

0

5

Here is the final answer. 19,105.

In words that is Nineteen Thousand, One Hundred and Five.

◄ SLIDE FOR MORE ►

EXERCISE: TRY IT YOURSELF

Exercise 1-3.Vertical Long-Addition

Download the Exercise as a printable PDF ►

VIDEO REVIEW

These videos may help you with learning how to add whole numbers.

WATCH THE VIDEO

Khan Academy Basic Addition. (12:26min).

WATCH THE VIDEO

Adding Whole Numbers. (1:13min).

INTERACTIVE PRACTICE AND TEST

INTERACTIVE PRACTICE

Practice your addition here.

Interactive Practice will keep on generating long-addition problems for you to solve for as long as you want to keep on practicing.

INTERACTIVE TEST

Test your addition here.

You will be presented with 10 sums. Solve each one as fast as you can.

Your final score will be saved.

Take the time to complete all the Exercises and use the Practice and Test Interactive tools to make sure addition becomes your friend. Learn to enjoy the numbers. They are fun and these exercises let you do it all at your own speed anytime you want.

ADDITION PRACTICE

CORRECT

WRONG

6900 123

NEXT

RETURN

ADDITION TEST

TYPE:

STATUS:

6900 123

NEXT

TEST YOURSELF ADDITION

INSTRUCTIONS

1. Click or Tap on Start button to get started

2. 10 random test sets are presented in a single loop

3. Key in answer values on each cells, always start from the right

4. As you key you will be navigated through to the right input cell to enter the  right value

5. When all cells are filled the answer will be checked automatically, and it will navigate to the next test set

6. When all 10 sets are completed, it will show your result

7. You can restart your test session again by clicking or tapping Reply button.

8. Or you can return to test home screen by click or tapping on Home button

9. Or you can navigate to different section

Start

CONGRATULATIONS!

Try Again...

Correct Score:

Wrong Score:

Total frame set:

Your progress meter:

Home

HOME

Lesson 2

Whole Number Subtraction

INTRODUCTION

Here you’ll learn how to subtract whole numbers using vertically arranged subtraction problems.

Vocabulary

Here are the vocabulary words that are found in this Concept.

Subtrahend the number being subtracted. IE minuend - subtrahend = difference

Minuend the number being subtracted from.

Difference  the answer to a subtraction problem

Regroup when you need to borrow from the next column in subtraction and reduce the corresponding minuend digit. Used with the subtractive method.

Borrow  when you need to borrow a digital from the next column. Used with the additive method.

Payback  when you need to return a borrowed digit to the next column's subtrahend.Used with the additive method.

INFORMATION

A general concept overvew statement or word problem exercise can be placed in the concept introduction section.

Depending on the monitor size and orientation this page should be adjusted for optimal reading using Alt-U to select columns or scrolling and to adjust the text size.

GUIDANCE

You have a lot of experience with subtraction of whole numbers. Let's just think about what subtraction is for a short time.

Subtraction is the opposite of addition.

What does that mean exactly? It means that if you can add two numbers and get the sum of the numbers, then you can subtract one of those numbers from that total and end up with the difference and the difference will be the other starting number.

In other words, Subtraction is the opposite of addition. When you add two numbers you get a sum, when you subtract two numbers, you get the difference. Let's look at that in a little more detail.

6

+

9

=

14

That is easy. So if we subtract 9 from 14 we have the following:

14

−

9

=

6

In the same way we can subtract the 6 from 14 and get this:

14

−

6

=

9

So while 6 + 9 and 9 + 6 give the same result - 14, subtraction lets us get two values and that is very useful.

So now we need to get down to learning how to put the problem into vertical form just as we did with long-addition.

1

4

−

9

0

6

You can easily do this simple subtraction using mental arithmetic. But what happens if you had more digits? Look at this:

12456

−

237

=

?

That is not so easy understand and solve so we arrange the numbers vertically being very careful to arrange them in their place values.

What does this look like in a place value table? Here it is. All we have to do is include the minus sign to make this a subtraction problem.

Ten Thousands

Thousands

Hundreds

Tens

Units

TTh

Th

H

T

U

1

2

4

5

6

2

3

7

INFORMATION

Subtraction Teaching Methods

There are two international methods of teaching long-subtraction, arguable one of the more difficult arithmetic concepts to learn.

The regroup or the subtractive method is common in the U.S. and many other places. The  additive method is still used in some countries. Both are presented here as Guided Practice options to show that the required teaching method can easily be accomodated for any locale.

This module is middle-school maths so it is assumed the basic concepts of addition and subtraction have already been taught and reasonably understood, and that the concept is being extended to more complicated numerical expressions.

By design the IGP:Digital Publisher construction, ALL-IN Interactive Learning Library and AZARDI:Content Fulfilment delivery system support all languages and localization needs for education publishers in any country and any language.

GUIDED TUTORIAL 1. SUBTRACTIVE METHOD

Let's do it. You can see it step by step in this tutorial. Remember to make sure you understand each step and slide back and forwards if you need to.

STEP 1. PLACE VALUES

TTh

Th

H

T

U

1

7

5

5

6

−

5

3

7

We are going to Subtract 537 from 17,556.

The minuend is 17,556. It has a Ten-thousands place value. The minuend must go on the top.

The subtrahend is 537 and is the smaller number. It has a Hundreds place value. The subtrahend must go on the bottom.

See how the Units (U), Tens (T) and Hundreds (H) are lined up vertically in their correct column.

STEP 2. THE VOCABULARY

1

2

4

5

6

−

1

5

3

7

We are now ready to start the subtraction.

We have set the sum up vertically.

Remember the top number is the minuend.

The bottom smaller number is the subtrahend.

We are subtracting the subtrahend from the minuend. The result will be the difference.

STEP 3. SUBTRACT THE UNITS

4

16

1

2

4

5/

6/

−

2

4

7

9

First we are going to subtract the Units column. Subtracting  7 from 6 is not possible.

We borrow 1 from the Tens to make the minuend 16. 7 can now be subtracted from 16.

The answer 9 is placed in the Units answer line.

Now we regroup the Tens column by subtracting the 1 that was borrowed.  5 minus 1 is 4.

Strike out the 5 and write 4 above.

STEP 4 SUBTRACT THE TENS

4

16

1

2

4

5/

6/

−

2

3

7

1

9

Next we subtract in the Tens column.

We regrouped the Tens so we are now subtracting 3 from 4.

The answer is 1. We place this into the difference line.

STEP 5. SUBTRACT THE HUNDREDS

1

1

2

4

5

6

−

2

3

7

2

1

9

We now subtract in the Hundreds column.

Here we are subtracting 2 from 4.

Because the minuend was bigger than the subtrahend we don't have to borrow in this column.

The result is 2 and that is added to the difference line.

STEP 6. SUBTRACT THE THOUSANDS

1

1

2

4

5

6

−

2

3

7

1

2

2

1

9

We have now run out of numbers in the bottom (subtrahend) line. They are effectively zero.

For clarity, 2 minus nothing is 2.

The 2 in the Thousands column can be placed directly into the difference line in the Thousands place value column.

STEP 7. SUBTRACT THE TEN-THOUSANDS

1

1

2

4

5

6

−

2

3

7

1

2

2

1

9

We have now run out of numbers in the bottom (subtrahend) line. They are effectively zero.

For clarity, 1 minus nothing is 1.

The 1 in the Ten-thousands column can be placed directly into the difference line in the Ten-thousands place value column.

STEP 8. THE ANSWER

1

1

7

5

5

6

−

2

4

7

1

2

2

1

9

Here is the final answer 12,219.

The difference of 12,345 minus 237 is 12,219.

Remember the terms for subtraction.

We subtracted the subtrahend 237 from the minuend 12,456 to get the difference 12,219.

= END OF TUTORIAL =

◄ SLIDE FOR MORE ►

EXERCISE: TRY IT YOURSELF

Exercise 2-1. Long-Subtraction Interactive

Download the Exercise as a printable PDF ►

PRODUCTION NOTE

Sliding panel interactive tutorials have been set to 500px width. Their size cannot be changed. Make sure you Adjust your monitor/viewport appropriately (Alt-U). If you are using a desktop or projector two column view is recommended. Use full-screen (F-11). If you are on a mobile device, scrolling page portrait orientation is recommended.

GUIDED TUTORIAL 2. ADDITIVE METHOD

The additive method of subtraction involves borrowing a digit from the next column when required and then paying it back.

It is borrowed into the subtrahend and adds 10 to the number. It is paid back into the minuend and added to the minuend before the subtraction takes place.

That means there is a borrow row at the top and a payback row under the subtrahend.

Let’s put that into action and write it vertically into our arithmetic subtraction. You can see this in action in this tutorial. Go steadily and make sure you understand each step.

STEP 1. PLACE VALUES

TTh

Th

H

T

U

1

2

4

5

6

−

1

5

3

7

We are going to Subtract 537 from 17,556.

The minuend is 17,556. It has a Ten-thousands place value. The minuend must go on the top.

The subtrahend is 537 and is the smaller number. It has a Hundreds place value. The subtrahend must go on the bottom.

See how the Units (U), Tens (T) and Hundreds (H)  are all each lined up vertically in their correct column.

STEP 2. SUBTRACTION VOCABULARY

1

2

4

5

6

−

1

5

3

7

We are now ready to start the subtraction.

We have set the sum up vertically.

Remember the top number is the minuend.

The bottom smaller number is the subtrahend.

We are subtracting the subtrahend from the minuend. The result will be the difference.

STEP 3. SUBTRACT THE UNITS

1

1

2

4

5

6

−

1

5

3

7

9

First we are going to subtract the Units column.

Subtracting 7 from 6 is not possible.

We borrow 1 from the Tens to make the minuend 16. 7 can now be subtracted from 16.

The answer 9 is placed in the Units position on the difference line.

STEP 4. SUBTRACT THE TENS

1

1

2

4

5

6

−

1

5

3

7

1

1

9

Next we subtract in the Tens column.

We borrowed a 1 from  the Tens column to use in the Units column.

We payback the 1 by writing it under/next to the subtrahend.

We add the payback 1 to the subtrahend 3. That is 4. Now we subtract 4 from the 5 in the minuend.

The result for the Tens column is 1.

STEP 5. SUBTRACT THE HUNDREDS

1

1

1

2

4

5

6

−

1

5

3

7

1

9

1

9

We now subtract in the Hundreds column.

Subtracting 5 from 4 is not possible.

Again we must borrow 1 from the Thousands column.

14 - 5 = 9

We write 9 in the Hundreds difference line.

STEP 6. SUBTRACT THE THOUSANDS

1

1

1

2

4

5

6

−

1

5

3

7

1

1

1

0

9

1

9

Next we subtract in the Thousands column.

We borrowed a 1 from  the Thousands column to use in the Hundreds column.

We payback the 1 by writing it under/next to the subtrahend.

We add the payback 1 to the subtrahend 1. That is 2. Now we subtract 2 from the 2 in the minuend.

The Thousands column is 0.

STEP 7. SUBTRACT THE TEN-THOUSANDS

1

1

1

2

4

5

6

−

1

5

3

7

1

1

1

0

9

1

9

Next we subtract in the Ten-Thousands column.

We have now run out of numbers in the bottom (subtrahend) line. They are zero.

The 1 in the Ten-Thousands column can be placed directly into the difference line in the correct place position.

STEP 8. THE ANSWER

1

1

1

2

4

5

6

−

1

5

3

7

1

1

1

0

9

1

9

Here is the final answer 10,919.

The difference for 12,456 minus 1,537 is 10,919.

Remember the terms for subtraction.

We subtracted the subtrahend 1,537 from the minuend 12,456 to get the difference 10,919.

= END OF TUTORIAL =

◄ SLIDE FOR MORE ►

EXERCISE: TRY IT YOURSELF

Exercise 2-2. Long-Subtraction Interactive

Download the Exercise as a printable PDF ►

VIDEO REVIEW

These videos will help you with your whole number subtraction if you have Internet access.

Watch the video.

Khan Academy Basic Subtraction (8:32).

Watch the video.

James Sousa Example of Subtracting Whole Numbers (1:41).

INTERACTIVE PRACTICE

Practice your subtraction here

INTERACTIVE TEST

Test your subtraction here

Take the time to complete all the Exercises and use the Practice and Test Interactive tools to make sure subtraction becomes your friend. Learn to enjoy the numbers. They are fun and these exercises let you do it all at your own speed anytime you want.

SUBTRACTION PRACTICE

CORRECT

WRONG

6900 123

NEXT

RETURN

SUBTRACTION TEST

TYPE:

STATUS:

6900 123

NEXT

TEST YOURSELF SUBTRACTION

INSTRUCTIONS

1. Click or Tap on Start button to get started

2. 10 random test sets are presented in a single loop

3. Key in answer values on each cells, always start from the right

4. As you key you will be navigated through to the right input cell to enter the  right value

5. When all cells are filled answer will be checked automatically, and it will navigate to the next test set

6. When all 10 sets are completed, it will show your result

7. You can restart your test session again by clicking or tapping Reply button.

8. Or you can return to test home screen by click or tapping on Home button

9. Or you can navigate to different section

Start

CONGRATULATIONS!

Try Again...

Correct Score:

Wrong Score:

Total frame set:

Your progress meter:

Home

HOME

Lesson 3

Whole Number Multiplication

INTRODUCTION

Here you’ll learn how to multiply whole numbers.

Vocabulary

Here are the vocabulary words used with whole number multiplication.

Factor the numbers being multiplied in a multiplication problem

Product the answer to a multiplication problem

Multiplier the number you multiply with (also a factor)

Multiplicand the num ber being multiplied (also a factor)

INFORMATION

A general concept overvew statement or word problem exercise can be placed in the concept introduction section.

Depending on the monitor size and orientation this page should be adjusted for optimal reading using Alt-U to select columns or scrolling and to adjust the text size.

Guidance

It is time to move forward and learn about multiplying whole numbers.

Addition and multiplication are related. Understanding that will help you understand what you doing when carrying out long-multiplication.

5

×

6

=

You can easily use your times tables to complete this problem using mental arithmetic, but let’s try to understand what this problem of multiplying 5 and  6 actually means.

5 × 6 means that we can have five groups of six items. Here we have five groups of six different shapes. Count them and you will see there are 30 shapes.

▲▲▲▲▲▲

■■■■■■

◇◇◇◇◇◇

●●●●●●

▼▼▼▼▼▼

So this is six added together five times. Think of it like this:

6

+

6

+

6

+

6

+

6

=

We can also think of this another way too. We could arrange it as six groups of  five shapes. There are still 30 shapes. You can count them if you want.

▲▲▲▲▲

■■■■■

◇◇◇◇◇

●●●●●

♦♦♦♦♦

▼▼▼▼▼

5

+

5

+

5

+

5

+

5

+

5

=

However all that horizontal addition is just too much work which is why we have the times-tables and why you learnt them in your early school years. We all know the answer to this.

5

×

6

=

30

So it would appear that multiplication is way to make really long addition problems short. And that is what it is and does.

The multiplication Vocabulary

5 and 6 are factors in this problem.

So what is a factor ?

A factor is the name give to  each of any two values being multiplied. In our example above 5 and 6 are factors.

When we multiply two factors together we get the product of those numbers. In our simple problem above the product of the factors 5 and 6 is 30.

That means the product is the answer to a multiplication problem.

Now let’s take what we have learned and look at how to apply it to a few more challenging problems.

Arranging Multiplication Vertically

Let's take a look at this problem:

567

×

3

=

If you think about this like addition, it is 567 added three times. That is a lot of work, so we use our long multiplication short cut and rearrange it vertically taking care to get our place values correct.

H

T

U

5

6

7

×

3

When we arrange our problem vertically we also get two new vocabulary terms based on the way we organize the problem. Look at this:

Multiplicand

× Multiplier

Product

The top row is the biggest number and is called the multiplicand or the number being multiplied.

The middle row is usually the smaller number and is called the multiplier or, the number doing the multiplying.

The result of the problem is the product as we have already learnt.  Now let us see this in action!

GUIDED TUTORIAL 1. VERTICAL-MULTIPLICATION

This guided practice will show you how to set up your multiplication problem and use your simple times table knowledge to get the correct answer.

STEP 1. PLACE VALUES

H

T

U

5

6

7

×

3

We are now going to multiply 567 by 3.

First set the sum up vertically in their correct place values.

The big number on the top multiplicand and the smaller number on the bottom is the multiplier.

Both can also be called factors.

STEP 2 MULTIPLY THE UNITS

2

5

6

7

×

3

1

The multiplicand 567 is multiplied by the first multiplier digit which is 3.

When we multiply 7 by 3, we get 21. So 1 is placed in the product line.

We carry the 2 forward to the Tens column.

STEP 3 MULTIPLY THE TENS

2

2

5

6

7

×

3

0

1

Now we are now going to multiply 6 by 3.

We get the result 18.

Now must remember to add the 2 which we carried forward. The result is 20.

So 0 is placed in the product line and we carried the 2 forward to the Hundreds column.

STEP 4 MULTIPLY THE HUNDREDS

1

2

2

5

6

7

×

3

7

0

1

Now we multiply 5 x 3 and the answer is 15.

Now add the 2 in the Hundreds column which we carried forword. The result is 17.

The 7 is placed in the product line.

The 1 is  carried forward to the Thousands column.

STEP 5. MULTIPLY THE THOUSANDS

1

2

2

5

6

7

×

3

1

7

0

1

There are no more numbers in the multiplicand.

The 1 in the Thousands column can be put into the product line in the Thousands place value.

STEP 6. THE ANSWER

1

2

2

5

6

7

×

3

1

7

0

1

Here is our final result.

567 multiplied by 3 is equal to 1,701.

= END OF TUTORIAL =

◀ SLIDE FOR MORE ▶

EXERCISE: TRY IT YOURSELF

Exercise 3-1. Simple Long-Multiplication ►

Download the Exercise as a printable PDF ►

PRODUCTION NOTE

Sliding panel interactive tutorials have been set to 500px width. Their size cannot be changed. Make sure you Adjust your monitor/viewport appropriately (Alt-U). If you are using a desktop or projector two column view is recommended. Use full-screen (F-11). If you are on a mobile device, scrolling page portrait orientation is recommended.

GUIDED TUTORIAL 2. LONG-MULTIPLICATION

That was pretty straight-forward. Now, what happens when there is more than one digital in the multiplier. We have to arrange our problem a little differently and introduce some addition.

2

3

4

×

1

2

=

STEP 1. PLACE VALUES

H

T

U

2

3

4

×

1

2

We are going to multiply 234 x 12. We set the sum up vertically.

The big number is the multiplicand and the smaller number is the multiplier.

This time we are leaving space between the multiplier and product lines as a calculation area. There needs to be a work-line for each digit in the multiplier.

STEP 2. MULTIPLY THE UNITS

2

3

4

×

1

2

4

6

8

The multiplicand 234 is multiplied by the first digit which is 2.

As we multiply each number we place the result in the first workline in the calculation area.

The result is 468.

STEP 3. MULTIPLY THE TENS

H

T

U

2

3

4

×

1

2

4

6

8

0

We are now going to multiply 234 by the 10's digit which is 1.

Before we start the multiplication we put a 0 in the next work-line to make the result a 10× multiplication.

This is very important to understand and remember.

STEP 4. MULTIPLY THE TENS... CONTINUED

2

3

4

×

1

2

4

6

8

2,

3

4

0

We multiply 234 by 1 and put the result 234 into the work-line before the 0.

STEP 5. ADDING THE WORK LINES

2

3

4

×

1

2

1

4

6

8

2

3

4

0

2

8

0

8

The last step is to add the work-line columns. This is standard long-addition.

There is a carry-line at the top of the work-lines to let us handle any carry values that may come up.

In this example a 1 was carried into the Hundreds column.

STEP 6. THE ANSWER

2

3

4

×

1

2

1

4

6

8

2

3

4

0

2

8

0

8

We now have our final answer. The product of 234 multiplied by 12 is 2,808.

Remember the multiplication vocabulary.

= END OF TUTORIAL =

◀ SLIDE FOR MORE ▶

EXERCISE: TRY IT YOURSELF

Exercise 3-2. Long-Multiplication ►

Download the Exercise as a printable PDF ►

VIDEO REVIEW

These videos will giv e you another view and help you with multiplying whole numbers.

WATCH THE VIDEO

Khan Academy Basic Multiplication(13:20).

WATCH THE VIDEO

James Sousa Example of Multiplying Whole Numbers(1:49).

INTERACTIVE PRACTICE

Practice your Multiplication here

INTERACTIVE TEST

Test your Multiplication here

Take the time to complete all the Exercises and use the Practice and Test Interactive tools to make sure multiplication becomes your friend. Learn to enjoy the numbers. They are fun and these exercises let you do it all at your own speed anytime you want.

MULTIPLICATION PRACTICE

CORRECT

WRONG

6900 123

NEXT

RETURN

MULTIPLICATION TEST

TYPE:

STATUS:

6900 123

NEXT

TEST YOURSELF MULTIPLICATION

INSTRUCTIONS

1. Click or Tap on Start button to get started

2. 10 random test sets are presented in a single loop

3. Key in answer values on each cells, always start from the right

4. As you key you will be navigated through to the right input cell to enter the  right value

5. When all cells are filled answer will be checked automatically, and it will navigate to the next test set

6. When all 10 sets are completed, it will show your result

7. You can restart your test session again by clicking or tapping Reply button.

8. Or you can return to test home screen by click or tapping on Home button

9. Or you can navigate to different section

Start

CONGRATULATIONS!

Try Again...

Correct Score:

Wrong Score:

Total frame set:

Your progress meter:

Home

HOME

Lesson 4

Whole Number Division

INTRODUCTION

Here you'll learn how to divide whole numbers.

Vocabulary

Here are the vocabulary words used in this Concept.

Dividend  the number being divided

Divisor  the number doing the dividing

Quotient  the answer to a division problem

Remainder  the value left over if the divisor does not divide evenly into the dividend

PRODUCTION NOTE

A general concept overvew statement or word problem exercise can be placed in the concept introduction section.

Depending on the monitor size and orientation this page should be adjusted for optimal reading using Alt-U to select columns or scrolling and to adjust the text size.

GUIDANCE

You have now learned how to add, subtract and multiply. The last whole number operation that we will learn is long-division.

What does “division” actually mean. The best way to understand it is to think of splitting into groups.

We saw that  multiplication means to add groups of things together to get a product or total. Therefore division which is splitting a total into groups is the opposite of multiplication.

7

2

÷

9

=

◆◆◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆◆◆

◆◆

In this problem we are trying to discover how many groups there will be if we split 72 into groups of 9.

72 is the number being divided, it is the dividend. 9 is the number doing the dividing, it is the divisor.

We can complete this problem by thinking of our multiplication facts and working backwards. Ask yourself “What number multiplied by 9 equals 72?”

Think back to your 9 times tables. If you said “8”, you're right!

9

×

8

=

7

2

So 72 can be split into 8 groups of 9. Therefore:

7

2

÷

9

=

8

The answer to a division problem is called the quotient. Quotient is a really old word that means "how many times".

Remainders

Sometimes, a number won’t divide evenly. When this happens, we have a remainder.

1

5

÷

2

=

?

In this example we aredividing by two. Because fifteen is not an even number there is going to be a number left over. We call that the remainder. If we look at the the nearest possible multiplication solution:

7

×

2

=

1

4

+

1

We get 14 and their is an extra 1 required to get to fifteen. So when we divide and have a remainder we write it like this:

1

5

÷

2

=

7

r

1

We can use an “r” to show that there is a remainder.

Here is another example with a larger remainder value.

3

5

÷

9

=

3

r

8

How did we get that? We use our 9 times table to see to the closest value to 35.

9

×

1

=

9

9

×

2

=

1

8

9

×

3

=

2

7

9

×

4

=

3

6

Our dividend number 35 is smaller than 36 so we have to use 3 × 9 = 27.

Then the remainder is the dividend 35 minus 27. The result is 8. So in this problem our remainder is 8.

In this example we can see the remainder must always be a smaller number than the divider.

GUIDED TUTORIAL 1. SIMPLE LONG-DIVISION

Larger numbers can be divided by using a division box. This is a tool we can use to organize the problem so we can get an answer.

Lets have a look at dividing a longer number and how to present the problem so we can work it out.We are going to solve:

7

9

8

÷

7

=

?

Use this tutorial to learn how to do this step by step.

STEP 1. SETTING UP

7

7

9

8

We are going to divide 798 by 7. We set the sum up with a division box.

Division looks a little different from the other sums, but we still have to be aware of place values as we solve the problem.

The small number on the left is the divisor.

The big number on the right is the dividend.

STEP 2. HUNDREDS

1

7

7

9

8

With division we work from the biggest place value to the smallest.

The division steps start from the left and move to the right.

So we divide the first digit 7 (Hundreds) by the divider 7 and we get 1.

The 1 is put into the quotient line above the 7.

STEP 3. CHECK THE NUMBER

1

7

7

9

8

-

7

0

When we are doing long division it is good to check each step with a multiplication.

1 × 7 = 7

We put this in the first work-line in the calculation area under the division box.

Subtract the values. 7 - 7 = 0 so there is no remainder. We can see that clearly.

STEP 4. TENS

1

1

7

7

9

8

-

7

0

9

-

7

2

Next we divide the second digit 9 by the divider 7.

The answer is 1 so we put that on the quotient line above the 9.

Now we are going to do our multiplication check.

Bring down the 9 to the work-line. Multiply 7 x 1 and put that value in the next work-line.

Subtract. This gives us a tens place-value left-over of 2 Tens.

STEP 5. FIND THE UNIT VALUE

1

1

4

7

7

9

8

-

7

0

9

-

7

2

8

We have 2 left over in the tens place value. This is 20 Units. We bring-down the 8 next to the 2 and have a total of 28 Units.

We can now divide 28 by the divider 7.

Using our times tables we can easily work out the answer is 4. So we put 4 above the 8 in the quotient line.

STEP 6. FINAL CHECKS

1

1

4

7

7

9

8

-

7

0

9

7

2

8

-

2

8

0

0

Now we are going to do our last multiplication check.

Multiply 4 X 7 and place it in the last work-line of the calculation area.

Do the subtraction. The answer is 0. So there is no remainder.

STEP 7. ANSWER & REVIEW

1

1

4

7

7

9

8

-

7

0

9

7

2

8

-

2

8

0

0

We now know 798 ÷ 7 = 114.

We can check with multiplication.

114 × 7 = 798

Even though the problem was simple we did the multiplication checks at each stage.

This keeps the division tidy and we can easily review our work and spot any mistakes.

= END OF TUTORIAL =

◀ SLIDE FOR MORE ▶

EXERCISE: TRY IT YOURSELF

Exercise 4-1. Simple Division with interactive answers ►►

Download the Exercise as a printable PDF ►

PRODUCTION NOTE

Sliding panel interactive tutorials have been set to 500px width. Their size cannot be changed. Make sure you Adjust your monitor/viewport appropriately (Alt-U). If you are using a desktop or projector two column view is recommended. Use full-screen (F-11). If you are on a mobile device, scrolling page portrait orientation is recommended.

GUIDED TUTORIAL 2. LONG DIVISION WITH REMAINDERS

Now that we understand the basic long-division method we can look at another example but this time with a remainder because the divider does not go equally into the dividend.

We are also going to make the problem a little longer.

STEP 1. SETTING UP

6

4

5

8

2

We are going to divide 4582 by 6. We set the sum up with a division box.

Division looks a little different from the other sums, but we still have to be aware of place values as we solve the problem.

The small number 6 on the left is the divisor.

The big number 4,582 on the right is the dividend.

STEP 2. THOUSANDS

0

6

4

5

8

2

The division steps start from the left and move to the right.

So we divide the first digit 4 by the divider 6. This doesn't go so we put 0 into the quotient line above the 4.

STEP 3. HUNDREDS

0

7

6

4

5

8

2

-

4

2

3

Now we look at the first two digits in the dividend. They are 45 Hundreds. We use our multiplication test to find how many times 6 goes into 45.

6 × 6 = 36

6 × 7 = 42

6 × 8 = 48

So the answer is 42. We put the 42 in the work-line under the division box.

Subtract the values. 45 - 42 = 3 Hundreds is left over.

STEP 4. TENS

0

7

6

6

4

5

8

2

-

4

2

3

8

-

3

6

2

Now we have to bring down the 8 Tens next to the 3 Hundreds. That makes a value of 380 Tens.

Again we have to work out how many time 6 can go into 38. From our previous multiplication tests we can see this will be 6.

We put 6 in the quotient line in the Tens place value position above the 8.

We do our multiplication check and subtract. The left-over value for the Tens place value is 2.

STEP 5. UNITS

0

7

6

3

r

4

6

4

5

8

2

-

4

2

3

8

-

3

6

2

2

-

1

8

4

We repeat the bring down process for the units.

The dividend Unit digit 2 is brought down next to the 2 tens left-over value. This makes 22 Units.

The multiple of 6 that is closest to 22 is

3 × 6 = 18

We put 3 in the quotient line.

STEP 6. CALCULATING THE REMAINDER

0

7

6

3

r

4

6

4

5

8

2

-

4

2

3

8

-

3

6

2

2

-

1

8

4

Now we are going to do our last multiplication check.

Multiply 3 × 6. We get 18.

Place 18 in the last work-line of the calculation area.

Do the subtraction. The answer is 4. The remainder for this problem is 4.

We write the remainder into the quotient line using r4.

STEP 7. ANSWER & REVIEW

0

7

6

3

r

4

6

4

5

8

2

4

2

3

8

3

6

2

2

1

8

4

We now know 4,582 ÷ 6 = 764 with a remainder of 4.

We can check with multiplication.

764 × 6 = 4578 + 4 = 4582

Now we understand how to do long division where the divider does not go equally into the dividend.

Remember to keep your division tidy so you can easily review your work and spot any mistakes.

= END OF TUTORIAL =

◀ SLIDE FOR MORE ▶

EXERCISE: TRY IT YOURSELF

Exercise 4-1. Simple Division with interactive answers ►►

Download the Exercise as a printable PDF ►

GUIDED TUTORIAL 3. LONG-DIVISION 2-DIGIT DIVISOR

Now we are going to look at a problem with a two-digit divisor. We are also going to increase the size of the dividend to show how you can easily use your new long-division skills to solve a wide range of dividing problems.

1

7

7

8

6

8

4

That looks pretty challenging. But getting the answer is just a matter of going step by step.

STEP 1. SETTING UP

17

7

8

6

8

4

We are going to divide 78,684 by 17. We set the sum up with a division box. Look at the dividend place values.

7 Ten-thousands (TTh)

8 Thousands (T)

6 Hundreds (H)

8 Tens (T)

4 Units (U)

We are going to use place value terms in this tutorial explanation.

STEP 2. TEN-THOUSANDS

0

17

7

8

6

8

4

-

0

7

7 Ten-thousands cannot be be divided into 17 equal parts. Therefore the quotient is 0.

Write 0 on top of the 7.

Now do the multiplication check.

17 × 0 = 0

Place this into the first work-line then subtract 0 from 7.

The answer is 7 Ten-thousands remainder.

STEP 3. THOUSANDS

0

4

17

7

8

6

8

4

-

0

7

8

Now bring down the 8 Thousands.

7 Ten-thousands and 8 Thousands together make 78 Thousands.

Let's use the 17 times tables.

17 × 1 = 17

17 × 2 = 34

17 × 3 = 51

17 × 4 = 68

17 × 5 = 85

85 is greater than 78, and 68 is less than 78. Therefore the quotient will be 4.

STEP 4. THOUSANDS CONT.

0

4

17

7

8

6

8

4

-

0

7

8

-

6

8

1

0

We put the 4 into the quotient line above the 8 in the Thousands position.

4 × 17 = 68

This is placed into the next work-line.

When 68 is subtracted from 78 the remainder is 10.

Remember this is 10 Thousands.

STEP 5. HUNDREDS

0

4

6

17

7

8

6

8

4

-

0

7

8

-

6

8

1

0

6

-

1

0

2

4

We repeat the bring down process for the 6 Hundreds.

10 Thousands makes 100 Hundreds. 100 Hundreds and 6 Hundreds  together are 106 Hundreds. Let's divide 106 by 17.

17 × 6 = 102

17 × 7 = 119

119 is greater than 106, 102 is less than 106. Therefore the quotient is 6. We do the subtraction and the remainder is 4.

STEP 6. TENS

0

4

6

2

17

7

8

6

8

4

-

0

7

8

-

6

8

1

0

6

-

1

0

2

4

8

-

3

4

1

4

These 4 Hundreds make 40 Tens. We bring down the 8 Tens. We now have 48 Tens.

Again looking at our 17 times table

17 × 2 = 34

17 × 3 = 51

51 is greater than 48 and 34 is less than 48. The quotient is 2 and is placed on the quotient line in the Tens position.

We put the 34 into the work-line and subtract. The remainder is 14 Tens.

STEP 7. UNITS

0

4

6

2

8

r

8

17

7

8

6

8

4

-

0

7

8

-

6

8

1

0

6

-

1

0

2

4

8

-

3

4

1

4

4

-

1

3

6

0

0

8

These 14 Tens make 140 Units. We bring down the 4 Units from the dividend.

We now have a total 144 Units.

17 × 8 = 136

We can see immediately that 8 is the quotient, and after subtracting 144 - 136 the remainder is also 8.

We write 8 in the Units position on the quotients line. We also write r8 at the end of the answer.

STEP 8. SUMMARY

0

4

6

2

8

r

8

17

7

8

6

8

4

-

0

7

8

-

6

8

1

0

6

-

1

0

2

4

8

-

3

4

1

4

4

-

1

3

6

0

0

8

So 78,684 divided by 17 is 4,628 with a remainder of 8.

This example shows how using multiplication helps long division.

By writing down the times table for the divider at different values you can quickly work-out the correct value to go into the quotient for all place values.

Now practice with the Exercises.

= END OF TUTORIAL =

◀ SLIDE FOR MORE ▶

EXERCISE: TRY IT YOURSELF

Exercise 4-2. Simple Division with interactive answers ►

Download the Exercise as a printable PDF ►

VIDEO REVIEW

If you have an Internet connection here are some videos for you to look at that will help you learn long division.

WATCH THE VIDEO

Khan Academy Basic Division 1(17:02).

WATCH THE VIDEO

James Sousa Example of Dividing Whole Numbers (2:28).

INTERACTIVE PRACTICE

Practice your Division here

INTERACTIVE TEST

Test your Division here

Take the time to complete all the Exercises and use the Practice and Test Interactive tools to make sure division becomes your friend. Learn to enjoy the numbers. They are fun and these exercises let you do it all at your own speed anytime you want.

DIVISION PRACTICE

CORRECT

WRONG

6900 123

NEXT

RETURN

DIVISION TEST

TYPE:

STATUS:

6900 123

NEXT

TEST YOURSELF DIVISION

INSTRUCTIONS

1. Click or Tap on Start button to get started

2. 10 random test sets are presented in a single loop

3. Key in answer values on each cells, always start from the right

4. As you key you will be navigated through to the right input cell to enter the  right value

5. When all cells are filled answer will be checked automatically, and it will navigate to the next test set

6. When all 10 sets are completed, it will show your result

7. You can restart your test session again by clicking or tapping Reply button.

8. Or you can return to test home screen by click or tapping on Home button

9. Or you can navigate to different section

Start

CONGRATULATIONS!

Try Again...

Correct Score:

Wrong Score:

Total frame set:

Your progress meter:

Home

HOME

Exercise 1-1. Simple Long Addition

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Click or tap in the answer area. Enter your answer. It will be instantly checked and show right or wrong. You can edit your answer at any time.

GROUP A

(1)

3

5

+

3

(2)

9

2

+

7

(3)

6

5

+

3

(4)

8

2

+

5

(5)

4

3

+

6

(6)

5

1

+

4

(7)

2

8

+

4

(8)

4

5

+

7

(9)

6

9

+

5

(10)

8

5

+

9

(11)

3

8

+

8

(12)

7

7

+

6

(13)

3

8

+

6

(14)

6

2

+

9

GROUP B

(1)

4

4

3

+

1

4

(2)

2

3

7

+

6

2

(3)

8

6

5

+

2

4

(4)

6

2

3

+

7

4

(5)

1

7

3

+

1

3

(6)

5

5

1

+

2

6

(7)

4

2

8

+

6

4

(8)

8

4

5

+

4

7

(9)

7

6

9

+

2

5

(10)

8

8

5

+

1

9

(11)

9

5

4

+

2

8

(12)

3

8

7

+

1

6

GROUP C

(1)

3

2

3

+

4

1

4

(2)

4

2

5

+

3

7

4

(3)

8

6

3

+

1

3

6

(4)

5

2

4

+

1

7

1

(5)

5

6

4

+

2

2

5

(6)

7

5

3

+

2

1

6

(7)

8

6

7

+

1

2

4

(8)

7

5

8

+

1

3

4

(9)

5

7

8

+

1

5

1

(10)

4

2

1

+

3

9

7

(11)

3

6

4

+

2

8

4

(12)

2

9

7

+

6

8

0

(13)

3

4

7

+

1

5

7

(14)

8

5

6

+

1

3

5

(15)

2

7

8

+

4

8

2

(16)

7

8

5

+

1

8

7

(17)

3

6

8

+

4

8

7

(18)

6

8

4

+

2

5

8

Clear all

◀ RETURN TO THE LESSON

Exercise 1-2. Very Long Addition

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

4

6

6

3

2

+

2

1

4

5

(2)

6

4

2

4

+

2

4

5

3

5

(3)

3

5

4

8

5

+

4

2

0

4

(4)

3

2

4

2

+

8

4

7

5

6

(5)

9

7

5

4

5

+

1

7

5

4

(6)

8

4

6

4

+

2

4

5

7

5

(7)

4

5

8

4

5

+

3

0

6

4

(8)

7

8

5

2

4

+

1

8

6

2

(9)

5

4

6

8

8

+

3

9

5

4

(10)

9

2

4

6

4

+

2

8

6

5

GROUP B.

(1)

9

8

5

1

4

5

+

1

4

7

2

4

(2)

2

4

5

1

5

+

2

4

4

1

2

4

(3)

7

8

5

4

8

5

+

1

3

2

1

4

(4)

8

4

5

2

1

0

+

4

3

7

8

2

(5)

9

4

5

7

5

5

+

3

6

2

7

4

(6)

3

2

4

5

8

2

+

6

4

5

1

9

(7)

6

5

8

4

+

1

6

2

8

1

6

(8)

8

4

5

8

5

2

+

6

4

1

3

8

GROUP C.

(1)

8

7

5

4

5

4

1

5

+

1

1

4

2

2

3

8

4

(2)

4

8

5

4

7

5

2

2

+

3

0

4

3

2

1

6

2

(3)

2

4

5

4

1

5

4

5

+

4

2

8

2

4

2

(4)

6

5

4

8

4

5

2

1

+

2

2

5

0

2

3

7

8

(5)

4

8

5

4

5

2

1

4

+

5

2

4

5

4

5

(6)

1

5

4

2

5

4

5

2

+

4

5

1

2

5

4

5

4

(7)

7

9

5

4

7

5

4

5

+

1

0

5

4

8

4

5

1

(8)

8

7

5

8

4

5

2

4

+

4

7

8

5

4

5

5

(9)

3

5

4

2

5

1

4

2

+

5

6

4

5

1

6

1

(10)

7

8

5

4

8

5

4

5

+

2

0

6

2

2

0

8

0

(11)

1

5

4

6

2

5

4

5

+

2

9

2

7

2

5

4

5

(12)

6

3

4

5

2

4

2

5

+

3

5

6

2

8

2

9

0

Clear all

◀ RETURN TO THE LESSON

Exercise 1-3. Vertical Long Addition

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

3

2

5

1

5

8

2

5

8

+

2

0

1

(2)

7

5

8

1

2

5

4

1

4

+

3

5

4

(3)

5

4

5

2

4

5

5

4

5

+

1

7

7

(4)

4

7

5

4

5

8

1

8

7

+

1

2

5

(5)

6

8

5

3

4

1

1

2

5

+

8

7

9

(6)

9

8

5

2

5

1

5

4

8

+

3

5

4

GROUP B

(1)

4

5

2

1

9

8

7

5

6

2

4

5

3

5

2

4

+

2

4

5

2

(2)

8

5

7

5

8

7

6

5

5

4

8

2

3

6

5

4

+

7

8

5

4

(3)

8

6

2

0

9

8

5

7

2

5

4

6

9

5

0

2

+

3

6

5

4

(4)

7

8

5

2

2

0

1

4

1

4

7

5

5

4

8

2

+

2

4

8

0

(5)

2

4

8

5

5

4

7

8

9

8

2

1

1

4

5

2

+

2

5

1

2

(6)

3

2

5

4

1

2

5

4

1

0

2

4

6

8

4

5

+

1

5

4

6

GROUP C

(1)

6

3

5

1

5

4

2

1

4

5

2

1

1

2

5

2

+

1

4

2

5

(2)

8

5

6

4

2

1

5

2

7

8

5

4

4

2

1

5

+

6

0

6

0

(3)

7

8

5

4

9

8

7

5

2

3

6

4

1

4

5

1

+

1

0

1

0

(4)

1

4

5

2

4

5

2

4

1

4

5

4

7

5

4

+

1

4

8

(5)

8

7

9

5

4

5

8

2

1

4

2

5

4

8

7

5

+

7

5

4

2

(6)

2

8

7

5

1

5

4

7

8

1

8

4

5

2

9

9

5

5

+

1

9

8

8

7

(7)

5

2

3

6

5

4

5

2

5

4

5

3

1

1

4

7

5

8

+

2

1

0

0

(8)

1

5

4

8

5

9

8

5

4

9

5

8

8

7

9

9

6

+

4

9

9

9

9

(9)

5

6

0

2

4

5

2

1

3

2

5

6

4

4

7

8

5

6

+

4

5

8

(10)

7

8

9

5

7

8

9

6

4

5

6

8

7

7

8

9

6

+

8

7

5

Clear all

◀ RETURN TO THE LESSON

Exercise 2-1. Long Subtraction

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

7

8

−

1

8

(2)

9

9

−

7

7

(3)

6

5

−

3

4

(4)

4

7

−

2

3

(5)

5

5

−

5

5

(6)

3

4

−

3

3

(7)

8

3

−

5

4

(8)

6

6

−

5

9

(9)

3

7

−

9

(10)

8

6

−

6

9

(11)

7

1

−

4

5

(12)

4

4

−

3

9

GROUP B

(1)

3

4

4

−

1

4

2

(2)

7

8

6

−

4

8

5

(3)

8

5

3

−

2

4

2

(4)

3

4

7

−

1

0

2

(5)

9

7

6

−

3

6

5

(6)

6

2

1

−

4

2

1

(7)

4

7

8

−

1

8

3

(8)

6

7

7

−

2

8

7

(9)

5

2

7

−

3

6

5

(10)

7

3

8

−

6

6

7

(11)

8

6

9

−

3

7

3

(12)

4

7

2

−

2

1

8

GROUP C

(1)

7

3

6

−

5

9

8

(2)

4

0

0

−

1

9

7

(3)

7

0

1

−

3

2

5

(4)

9

3

6

−

3

6

8

(5)

6

2

1

−

5

8

2

(6)

9

0

0

−

4

5

5

(7)

3

4

8

−

2

8

9

(8)

6

3

5

−

2

8

8

(9)

9

6

8

−

1

7

9

(10)

5

0

2

−

4

1

3

(11)

3

2

2

−

2

8

4

(12)

8

2

4

−

3

9

8

(13)

3

8

4

−

1

9

7

(14)

9

8

2

−

6

2

4

(15)

6

0

0

−

1

9

9

(16)

5

3

4

−

1

7

8

(17)

8

0

0

−

1

7

5

(18)

2

2

1

−

9

9

Clear all

◀ RETURN TO THE LESSON

Exercise 2-2. Very Long Subtraction

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

7

8

5

4

−

4

5

2

4

(2)

9

8

5

2

−

2

4

5

1

(3)

6

8

7

5

−

8

7

5

(4)

3

4

5

6

−

1

3

5

6

(5)

5

7

8

9

−

4

5

4

5

(6)

9

6

8

5

−

3

3

3

3

(7)

9

8

6

7

−

5

4

4

9

(8)

6

2

4

1

−

5

1

2

8

(9)

9

8

2

3

−

3

5

1

7

(10)

7

5

8

4

−

3

2

1

8

(11)

4

5

0

0

−

3

6

0

0

(12)

7

7

7

7

−

4

5

6

9

GROUP B

(1)

1

3

4

8

5

−

2

2

4

1

(2)

3

5

8

7

4

−

1

3

4

5

1

(3)

9

8

7

5

6

−

7

5

4

3

5

(4)

8

7

3

5

4

−

3

4

0

2

1

(5)

7

5

5

4

5

−

6

2

0

0

1

(6)

9

8

7

5

4

−

4

5

2

4

8

(7)

7

4

5

2

0

−

1

2

4

0

8

(8)

5

8

7

4

5

−

4

5

2

0

8

(9)

4

8

2

5

6

−

2

4

8

7

8

(10)

3

1

2

2

4

−

1

2

5

4

8

(11)

9

0

0

0

1

−

2

5

5

6

8

(12)

7

0

2

0

0

−

2

4

5

8

5

GROUP C

(1)

1

3

5

4

5

−

2

9

9

8

(2)

4

0

0

0

−

1

9

8

7

(3)

7

8

4

5

2

−

9

9

9

(4)

3

5

4

8

8

−

1

9

8

9

9

(5)

2

4

7

5

6

−

3

8

6

7

(6)

6

0

0

0

0

−

4

9

9

9

9

(7)

5

4

5

2

3

−

2

8

9

(8)

9

2

2

2

2

−

2

9

9

9

9

(9)

4

5

2

3

1

−

2

4

5

5

6

(10)

9

8

5

2

0

−

1

2

9

8

8

(11)

9

0

0

0

0

−

7

9

9

9

9

(12)

8

8

7

7

5

−

4

4

8

8

9

(13)

3

2

1

4

1

−

8

7

5

9

(14)

2

1

3

5

4

−

9

9

8

7

(15)

3

0

0

1

0

−

1

7

7

8

9

(16)

9

8

7

6

5

−

2

9

8

7

9

(17)

8

7

5

6

7

−

7

8

6

7

9

Clear all

◀ RETURN TO THE LESSON

Exercise 3-1. Simple Long-Multiplication

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

2

4

x

8

(2)

9

9

x

9

(3)

6

5

x

4

(4)

3

7

x

7

(5)

8

6

x

6

(6)

4

8

x

7

(7)

9

7

5

x

5

(8)

4

5

2

x

9

(9)

5

3

1

x

4

(10)

7

8

5

x

8

(11)

6

8

7

x

2

(12)

7

8

5

x

1

(13)

8

8

7

x

6

(14)

9

8

7

x

7

(15)

5

5

5

x

5

(16)

2

4

2

x

3

(17)

1

4

8

x

9

(18)

3

7

6

x

2

(19)

5

0

0

x

8

GROUP B

(1)

7

8

9

x

4

5

(2)

9

9

9

x

9

9

(3)

4

7

5

x

3

4

(4)

3

6

7

x

7

5

(5)

6

9

8

x

2

6

(6)

9

8

7

x

4

6

(7)

7

4

5

x

3

7

(8)

5

8

7

x

3

9

(9)

4

8

2

x

1

9

(10)

3

1

2

x

8

7

(11)

9

0

0

x

6

4

(12)

7

0

2

x

7

6

(13)

3

5

4

x

3

1

(14)

2

4

8

x

2

2

(15)

6

7

8

x

2

4

(16)

1

4

5

x

4

4

(17)

8

1

7

x

3

2

(18)

5

2

0

x

1

5

(19)

4

3

2

x

5

3

(20)

6

4

3

x

2

6

(21)

8

3

2

x

9

9

(22)

4

7

7

x

3

0

(23)

9

2

2

x

2

1

(24)

7

7

7

x

8

8

Clear all

◀ RETURN TO THE LESSON

Exercise 3-2.Long-Multiplication

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

8

9

5

x

1

1

(2)

9

5

6

x

2

6

(3)

3

6

4

x

3

6

(4)

1

6

7

x

4

8

(5)

6

7

9

x

1

4

(6)

9

7

3

x

2

9

(7)

2

6

8

x

1

1

1

(8)

6

6

7

x

9

8

(9)

3

4

5

x

7

6

(10)

1

7

5

x

5

5

(11)

5

2

3

x

1

6

(12)

2

4

1

x

2

4

(13)

7

5

7

x

4

0

(14)

8

4

7

x

3

2

GROUP B

(1)

7

8

9

1

x

7

8

9

(2)

9

9

9

9

x

1

2

4

(3)

4

6

8

7

x

3

6

8

(4)

3

4

8

5

x

6

4

8

(5)

6

7

8

9

x

4

7

8

(6)

4

1

5

6

x

3

6

5

(7)

9

8

7

6

x

6

5

2

(8)

4

8

5

4

x

1

2

4

(9)

1

2

5

3

x

2

2

2

(10)

6

7

8

9

x

6

8

7

(11)

3

4

1

2

x

9

7

2

(12)

3

6

9

6

x

6

4

2

(13)

7

4

1

7

x

9

9

(14)

8

5

2

3

x

3

4

5

(15)

3

5

7

8

x

2

1

4

(16)

5

5

2

4

x

4

2

7

(17)

6

4

3

0

x

1

4

0

(18)

3

3

1

2

x

4

1

5

(19)

9

6

7

3

x

3

1

3

(20)

3

1

0

2

x

6

0

0

(21)

4

8

0

2

x

8

1

8

(22)

7

0

4

2

x

2

2

5

(23)

1

2

7

8

x

9

3

5

(24)

3

0

0

2

x

7

9

2

Clear all

◀ RETURN TO THE LESSON

Exercise 4-1. Simple Long Division

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

8

2

2

4

(2)

9

9

9

9

(3)

5

5

6

5

(4)

2

8

8

0

(5)

3

9

9

6

(6)

5

1

2

5

(7)

5

9

7

5

(8)

4

4

5

2

(9)

2

5

3

6

(10)

5

2

4

5

(11)

7

7

4

9

(12)

9

3

6

9

GROUP B

(1)

3

0

7

8

0

(2)

4

5

8

5

5

(3)

2

3

8

7

4

(4)

1

0

4

8

0

(5)

1

2

8

8

8

(6)

5

4

9

1

8

(7)

4

1

1

6

4

(8)

2

0

2

2

0

(9)

2

2

6

8

2

(10)

1

5

3

1

5

GROUP C

(1)

3

3

4

5

7

0

5

(2)

8

9

1

7

0

8

8

(3)

3

0

4

4

4

0

0

(4)

9

9

1

6

8

3

(5)

7

5

3

8

1

0

0

(6)

6

2

8

8

9

0

8

(7)

8

8

3

7

3

6

0

(8)

4

6

8

3

0

7

6

(9)

9

1

7

9

0

3

3

5

(10)

1

7

6

9

4

9

6

Clear all

◀ RETURN TO THE LESSON

Exercise 4-2. Long Division

◀ RETURN TO THE LESSON

You can work out each sum in your head (best) or on paper.

Click this link to download and print out this exercise sheet. (Wait for a new Window to open)

Tap or click the answer-line of any sum and the keyboard will show. You can enter your answer and it will be instantly checked.

GROUP A

(1)

8

7

6

1

(2)

9

8

4

8

(3)

5

1

5

2

(4)

3

2

9

5

(5)

5

9

9

6

(6)

4

1

2

5

(7)

6

9

7

5

(8)

9

7

7

8

(9)

2

4

5

1

(10)

5

9

4

6

(11)

9

1

3

3

(12)

8

3

3

2

GROUP B

(1)

2

0

4

8

8

(2)

5

0

3

5

2

4

(3)

3

2

7

6

5

(4)

9

9

4

8

0

(5)

3

3

8

8

8

(6)

4

0

9

1

8

(7)

2

5

1

6

4

(8)

3

2

5

1

1

6

(9)

1

2

6

8

2

(10)

2

4

3

1

5

GROUP C

(1)

4

4

4

2

2

9

(2)

8

0

1

7

0

8

8

(3)

4

5

4

4

4

4

8

(4)

3

5

4

9

0

7

(5)

2

2

1

1

2

7

(6)

5

2

1

7

3

2

(7)

2

9

6

9

3

2

(8)

4

5

4

7

3

4

(9)

1

1

1

7

1

5

(10)

2

8

9

8

2

2

Clear all

◀ RETURN TO THE LESSON

Table of Contents

UNIT ONE: Middle School Maths: Operations on Numbers

Copyright

AZARDI Help and Shortcuts

Introduction

Unit 1: Number Sense and Variable Expressions

Lesson 1: Whole Number Addition

Practice your Addition

Test yourself addition

Lesson 2: Whole Number Subtraction

Practice your Subtraction

Test yourself subtraction

Lesson 3: Whole Number Multiplication

Practice your Multiplication

Test yourself multiplication

Lesson 4: Whole Number Division

Practice your Division

Test yourself Division