The Lesson

Arithmetic means adding, subtracting, multiplying and dividing numbers. Arithmetic becomes trickier when it involves negative numbers and needs extra care. In this lesson, we are going to look at:

Adding a Negative Number

Adding a negative number is equivalent to subtracting the (positive) number.

Question

What is 2 + −1?
Adding −1 becomes subtracting +1.
2 + −1 = 2 − (+1) = 2 − 1 = 1

Subtracting a Negative Number

Subtracting a negative number is equivalent to adding the (positive) number. 2 negatives make a positive!

Question

What is 2 − −1?
Subtracting −1 becomes adding +1.
2 − −1 = 2 + (+1) = 2 + 1 = 3

Multiplying By a Negative Number

Multiplying by a negative number gives different results depending on the sign of the number it is multiplied with.

Multiplying a Positive Number with a Negative Number

Multiplying a positive number with a negative number creates a negative number.

Question

What is 2 × −2?
2 × −2 = −(2 × 2) = −4

Multiplying a Negative Number with a Negative Number

Multiplying a negative number with a negative number creates a positive number. 2 negatives make a positive!

Question

What is −2 × −2?
−2 × −2 = −−(2 × 2) = +(2 × 2) = +4 = 4

Dividing By a Negative Number

Dividing by a negative number gives different results depending on the sign of the number it divides.

Dividing a Positive Number with a Negative Number

Dividing a positive number with a negative number creates a negative number.

Question

What is 4 ÷ −2?
4 ÷ −2 = −(4 ÷ 2) = −2

Dividing a Negative Number with a Negative Number

Dividing a negative number with a negative number gives a positive number. 2 negatives make a positive!

Question

What is −4 ÷ −2?
−4 ÷ −2 = −−(4 ÷ 2) = +2 = 2

Top Tip

Rules For Signs: Addition and Subtraction

Same signs give a plus: Different signs give a minus:

Rules For Signs: Multiplication and Division

Same signs give a plus: Different signs give a minus: