G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

Year 8 Interactive Maths - Second Edition


Addition and Subtraction of Integers

Addition of Positive Integers

Consider the addition of 2 + 3.

The plus sign, +, tells us to face the positive direction.
So, to evaluate 2 + 3, start at 2, face the positive direction and move 3 units forwards.


This suggests that:

Positive integers can be added like natural numbers.


Addition of Negative Integers

Consider the addition of (–2) + (–3).

The plus sign, +, tells us to face the positive direction.
So, to evaluate (–2) + (–3), start at –2, face the positive direction and move 3 units backwards.


Note: 

We can write (–2) + (–3) as –2 + –3


Subtracting a Positive Integer from a Negative Integer

Consider the value of (–2) – (3).

The minus sign, –, tells us to face the negative direction.
So, to evaluate (–2) – (3), start at –2, face the negative direction and move 3 units forwards.

We notice that:

That is:


This suggests that:

Adding a negative integer is the same as subtracting a positive integer.


From the above discussion, we can state that:

Negative integer are added like natural numbers; but place a minus sign, –, in front of the sum.


Example 7

Find the value of:

Solution:


Addition of a Positive Integer and a Negative Integer

Consider the addition of 3 + (–7).

The plus sign, +, tells us to face the positive direction.
So, to evaluate 3 + (–7), start at 3, face the positive direction and move 7 units backwards.


Note:

3 + (–7) is often written as 3 – 7.

To find the value of 3 – 7, first ignore the signs and subtract the smaller number, 3, from the larger number, 7, and put the sign, –, of the larger number, 7, in front of the difference.  That is:


Example 8

Find the value of:

Solution:


Subtracting a Negative Integer from a Positive Integer

Consider the subtraction of 2 – (–3).

The minus sign, –, tells us to face the negative direction.
So, to evaluate 2 – (–3), start at 2, face the negative direction and move 3 units backwards.


This suggests that:

To take away a negative integer, add its opposite which is a positive integer.


Example 9

Find the value of:

Solution:


Note:

If two minus signs are side by side, then the two minus signs become a plus sign (i.e. a positive).


| Home Page | Order Maths Software | About the Series | Maths Software Tutorials |
| Year 7 Maths Software | Year 8 Maths Software | Year 9 Maths Software | Year 10 Maths Software |
| Homework Software | Tutor Software | Maths Software Platform | Trial Maths Software |
| Feedback | About mathsteacher.com.au | Terms and Conditions | Our Policies | Links | Contact |

Copyright © 2000-2022 mathsteacher.com Pty Ltd.  All rights reserved.
Australian Business Number 53 056 217 611

Copyright instructions for educational institutions

Please read the Terms and Conditions of Use of this Website and our Privacy and Other Policies.
If you experience difficulties when using this Website, tell us through the feedback form or by phoning the contact telephone number.