Arithmetic with Negative Numbers
What Is Arithmetic with Negative Numbers?
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.

Subtracting a negative number.

Multiplying by a negative number.

Dividing by a negative number.
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