1F Adding and subtracting integers

Learning intentions

By the end of this topic you will be able to … ✔ solve problems involving addition and subtraction of positive and negative numbers.

Adding and subtracting positive integers

• When adding a positive integer, move to the right on the number line. For example, to calculate 4 + 5, start at − 4 and move 5 steps to the right.

• When subtracting a positive integer, move to the left on the number line. For example, to calculate 1 2, start at –1 and move 2 steps to the left.

Adding and subtracting negative integers

• When adding a negative integer, move to the left on the number line. For example, to calculate 4 + ( 3), start at 4 and move 3 steps to the left.

• When subtracting a negative integer, move to the right on the number line. For example, to calculate 2 ( 5), start at −2 and move 5 steps to the right.

• Adding a negative number can be simplified to subtracting its value.

• Subtracting a negative number can be simplified to adding its value.

Example 1F.1 Adding and subtracting positive numbers

Use the number line to calculate: a 6 + 8

THINK a 1 Draw a number line. b 1 Draw a number line.

2 Start at the first number, then add the second number by moving right.

2 Start at the first number, then subtract the second number by moving left.

4 8

Example 1F.2 Adding and subtracting negative numbers

Use the number line to calculate: a 4 + ( 7)

THINK a 1 Simplify the calculation. Remember that + ( ) = b 1 Simplify the calculation. Write the problem in a simpler equivalent form by replacing − (−) with +.

2 Draw a number line.

3 Start at the first number, then subtract the value by moving left.

2 Draw a number line.

3 Start at the first number, then add the value by moving right.

Helpful hints

✔ The negative sign is identical to the minus sign. The function of the symbol depends on its context. Example

8 Indicates the number is less than zero in value

2 8 Indicates the operation of subtraction eight’ minus eight’ 8 + 2 Indicates the number is less than zero in value eight plus two’

✔ Don’t make assumptions about the sign of the answer – subtraction can produce positive numbers and addition can produce negative numbers!

✔ When simplifying calculations involving negative numbers, only combine the signs located in between the numbers.

1F.1 1F.2