Open Math›Year 7›Computation with integers›Multiplying and dividing integers

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

-4 \times 3

Identify the signs of both numbers.

-4

is negative and

3

is positive. The signs are different.

When the signs are different, the result is negative. Multiply the absolute values.

4 \times 3 = 12

Apply the negative sign to the result.

-4 \times 3 = -12

Answer

-12

Multiplying two negative integers

Moderate

Problem

Calculate

-6 \times (-5)

Identify the signs of both numbers.

Both

-6

and

-5

are negative. The signs are the same.

When the signs are the same, the result is positive. Multiply the absolute values.

6 \times 5 = 30

The result is positive.

-6 \times (-5) = 30

Answer

30

Multi-step expression with mixed operations

Challenging

Problem

Calculate

3 \times (-4) + (-2) \times 5

Apply order of operations: perform all multiplications before addition.

There are two multiplications:

3 \times (-4)

and

(-2) \times 5

Calculate the first multiplication. The signs are different, so the result is negative.

3 \times (-4) = -12

Calculate the second multiplication. The signs are different, so the result is negative.

(-2) \times 5 = -10

Add the two results.

-12 + (-10) = -12 - 10 = -22

Answer

-22

Practise

Q1·Straightforward

Calculate

-4 \times 3

Explanation

The signs are different (negative and positive), so the result is negative.
Multiply the absolute values:

4 \times 3 = 12

Apply the sign:

-4 \times 3 = -12

Q2·Straightforward

Calculate

-15 \div 3

Explanation

The signs are different, so the result is negative.
Divide the absolute values:

15 \div 3 = 5

Apply the sign:

-15 \div 3 = -5

Q3·Straightforward

Calculate

6 \times (-5)

Explanation

The signs are different, so the result is negative.
Multiply the absolute values:

6 \times 5 = 30

Apply the sign:

6 \times (-5) = -30

Q4·Straightforward

Calculate

20 \div (-4)

Explanation

The signs are different, so the result is negative.
Divide the absolute values:

20 \div 4 = 5

Apply the sign:

20 \div (-4) = -5

Q5·Moderate

Calculate

-6 \times (-5)

Explanation

Both signs are negative, so the result is positive.
Multiply the absolute values:

6 \times 5 = 30

Apply the sign:

-6 \times (-5) = 30

Q6·Moderate

Calculate

-18 \div (-3)

Explanation

Both signs are negative, so the result is positive.
Divide the absolute values:

18 \div 3 = 6

Apply the sign:

-18 \div (-3) = 6

Q7·Moderate

Calculate

-8 \times (-7)

Explanation

Both signs are negative, so the result is positive.
Multiply the absolute values:

8 \times 7 = 56

Apply the sign:

-8 \times (-7) = 56

Q8·Moderate

Calculate

-24 \div (-6)

Explanation

Both signs are negative, so the result is positive.
Divide the absolute values:

24 \div 6 = 4

Apply the sign:

-24 \div (-6) = 4

Q9·Challenging

Calculate

(-3) \times 4 \div (-6)

Explanation

Work from left to right:

(-3) \times 4 = -12

Then divide:

-12 \div (-6) = 2

(Two negatives give a positive result.)

Q10·Challenging

Calculate

(-2) \times (-3) \times (-4)

Explanation

Work from left to right:

(-2) \times (-3) = 6

(Two negatives give a positive.)
Then:

6 \times (-4) = -24

(Positive times negative gives a negative.)

Q11·Challenging

Calculate

3 \times (-4) + (-2) \times 5

Explanation

Perform the multiplications first:

3 \times (-4) = -12

(-2) \times 5 = -10

Then add:

-12 + (-10) = -12 - 10 = -22

Q12·Challenging

Calculate

(-15) \div 3 \times (-2)

Explanation

Work from left to right:

(-15) \div 3 = -5

Then multiply:

-5 \times (-2) = 10

(Two negatives give a positive result.)

Open Math

Multiplying and dividing integers

Number · MA4-INT-C-01

Name:

Date:

Q1Straightforward

Calculate

-4 \times 3

Q2Straightforward

Calculate

-15 \div 3

Q3Straightforward

Calculate

6 \times (-5)

Q4Straightforward

Calculate

20 \div (-4)

Q5Moderate

Calculate

-6 \times (-5)

Q6Moderate

Calculate

-18 \div (-3)

Q7Moderate

Calculate

-8 \times (-7)

Q8Moderate

Calculate

-24 \div (-6)

Q9Challenging

Calculate

(-3) \times 4 \div (-6)

Q10Challenging

Calculate

(-2) \times (-3) \times (-4)

Q11Challenging

Calculate

3 \times (-4) + (-2) \times 5

Q12Challenging

Calculate

(-15) \div 3 \times (-2)

Worked solutions and answers at openmath.au/year-7/computation-with-integers/multiplying-and-dividing-integers