Arithmetic with Negative Numbers
(KS2, Year 5)
- 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
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:
Question
What is 2 + −1?Question
What is 2 − −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:
Question
What is 2 × −2?Question
What is −2 × −2?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:Worksheet
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