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How to multiply and divide positive and negative numbers

Part of MathsPositive and negative numbers

Key points

  • Multiplication is . This means that the order in which you multiply a pair of numbers does not make a difference, eg 3 x 5 = 5 x 3
  • The is the answer when two or more numbers are multiplied together.
  • Calculations can be written with brackets around negative numbers because this can make a calculation easier to read, eg -3 × -1 is the same calculation as (-3) × (-1)
  • Learning about positive and negative numbers will help when multiplying and dividing negative numbers.
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Multiplying positive and negative numbers

When multiplying negative numbers it is often useful to complete the calculation using positive numbers initially.Then remember that:

  • multiplying two numbers together with the same sign gives a positive answer
  • multiplying two numbers together with different signs gives a negative answer

Examples: multiplying positive and negative numbers

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  1. Positive multiplied by positive equals a positive. Negative multiplied by negative equals a positive. Positive multiplied by negative equals a negative. Negative multiplied by positive equals a negative.

    Start by completing the calculation using positive numbers first, then use the sign rules to find the sign of the answer.

Dividing positive and negative numbers

When dividing negative numbers it is often useful to complete the calculation using positive numbers initially.Remember that:

  • dividing two numbers with the same sign gives a positive answer
  • dividing two numbers with different signs gives a negative answer

Examples: dividing positive and negative numbers

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  1. Positive divided by positive equals a positive. Negative divided by negative equals a positive. Positive divided by negative equals a negative. Negative divided by a positive equals a minus.

    Start by completing the calculation using positive numbers first, then use the sign rules to find the sign of the answer.

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Question

Calculate the following. You might need a pen and paper to note down the answers.

  1. (-6) × 3

  2. (-4) × (-2)

  3. (-6) ÷ 2

  4. (-6) ÷ (-2)

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Practise multiplying and dividing negative numbers

Remember that negative numbers are sometimes written in brackets. This can make the calculation easier to read.

Activity

Try this ordering activity to practise calculating with positive and negative numbers. You might need a pen and paper to help with your working out.

Quiz

Practise multiplying and dividing positive and negative numbers in this quiz.

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Real-world maths

Magnifying glass focused an invoice with negative numbers.
Businesses use negative numbers to represent expenses or money paid out.

  • Negative numbers are used in everyday life, especially in business when making financial decisions and forecasting future profits.

  • Accountants and businesses use negative numbers to represent when money has already been or is going to be spent. Eg a regular outgoing of £300 per month on expenses is calculated as 12 x (-£300) over the next year.

Magnifying glass focused an invoice with negative numbers.
Businesses use negative numbers to represent expenses or money paid out.
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Using your maths skills, help to build bridges and bring light back to the islands in this free game from tv Bitesize.

Play the Divided Islands game!
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More on Positive and negative numbers

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