Multiplying and dividing integers
Multiply and divide positive and negative integers, including pairs of negatives.
Worked examples
Multiplying integers with different signs
Straightforward
Problem
Calculate .
1
Identify the signs of both numbers.
is negative and is positive. The signs are different.
2
When the signs are different, the result is negative. Multiply the absolute values.
3
Apply the negative sign to the result.
Answer
Multiplying two negative integers
Moderate
Problem
Calculate .
1
Identify the signs of both numbers.
Both and are negative. The signs are the same.
2
When the signs are the same, the result is positive. Multiply the absolute values.
3
The result is positive.
Answer
Multi-step expression with mixed operations
Challenging
Problem
Calculate .
1
Apply order of operations: perform all multiplications before addition.
There are two multiplications: and .
2
Calculate the first multiplication. The signs are different, so the result is negative.
3
Calculate the second multiplication. The signs are different, so the result is negative.
4
Add the two results.
Answer
Practise
Q1·Straightforward
Calculate .
Explanation
The signs are different (negative and positive), so the result is negative.
Multiply the absolute values:
Apply the sign:
Multiply the absolute values:
Apply the sign:
Q2·Straightforward
Calculate .
Explanation
The signs are different, so the result is negative.
Divide the absolute values:
Apply the sign:
Divide the absolute values:
Apply the sign:
Q3·Straightforward
Calculate .
Explanation
The signs are different, so the result is negative.
Multiply the absolute values:
Apply the sign:
Multiply the absolute values:
Apply the sign:
Q4·Straightforward
Calculate .
Explanation
The signs are different, so the result is negative.
Divide the absolute values:
Apply the sign:
Divide the absolute values:
Apply the sign:
Q5·Moderate
Calculate .
Explanation
Both signs are negative, so the result is positive.
Multiply the absolute values:
Apply the sign:
Multiply the absolute values:
Apply the sign:
Q6·Moderate
Calculate .
Explanation
Both signs are negative, so the result is positive.
Divide the absolute values:
Apply the sign:
Divide the absolute values:
Apply the sign:
Q7·Moderate
Calculate .
Explanation
Both signs are negative, so the result is positive.
Multiply the absolute values:
Apply the sign:
Multiply the absolute values:
Apply the sign:
Q8·Moderate
Calculate .
Explanation
Both signs are negative, so the result is positive.
Divide the absolute values:
Apply the sign:
Divide the absolute values:
Apply the sign:
Q9·Challenging
Calculate .
Explanation
Work from left to right:
Then divide:
(Two negatives give a positive result.)
Then divide:
(Two negatives give a positive result.)
Q10·Challenging
Calculate .
Explanation
Work from left to right:
(Two negatives give a positive.)
Then:
(Positive times negative gives a negative.)
(Two negatives give a positive.)
Then:
(Positive times negative gives a negative.)
Q11·Challenging
Calculate .
Explanation
Perform the multiplications first:
Then add:
Then add:
Q12·Challenging
Calculate .
Explanation
Work from left to right:
Then multiply:
(Two negatives give a positive result.)
Then multiply:
(Two negatives give a positive result.)