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Maths · Fractions, Decimals & Percentages

Decimals × and ÷

Multiply and divide decimals by whole numbers and decimals.

Not startedCAMBRIDGE · 7CBSE · VIIIB · MYP-1

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Multiplying Decimals by Whole Numbers

When you multiply a decimal by a whole number, treat it like normal multiplication first. Count how many decimal places are in the original decimal. Put the same number of decimal places in your answer. For example, 3.4 × 5 = 17.0, which we write as 17.

Dividing Decimals by Whole Numbers

To divide a decimal by a whole number, keep the decimal point in the same place. Divide as normal, bringing the decimal point straight up into your answer. For example, 8.4 ÷ 2 means sharing 8.4 into 2 equal groups, giving 4.2 in each.

Multiplying Decimals by Decimals

Multiply the numbers as if they were whole numbers, ignoring the decimal points. Count the total decimal places in both numbers. Put that many decimal places in your final answer. So 0.3 × 0.4 becomes 3 × 4 = 12, then add 2 decimal places to get 0.12.

Dividing by a Decimal

Dividing by a decimal can be tricky, so we convert it to a whole number first. Multiply both numbers by 10, 100 or 1000 until the divisor becomes whole. Then divide normally. For instance, 6 ÷ 0.2 becomes 60 ÷ 2 = 30.

Checking Your Answer

Always estimate to check if your answer makes sense. When multiplying by a number less than 1, your answer should be smaller. When dividing by a number less than 1, your answer should be larger. This quick check catches many mistakes.

Worked examples

  1. 1. Calculate 4.6 × 3

    1. Multiply as if they were whole numbers: 46 × 3 = 138
    2. Count decimal places in 4.6: there is 1 decimal place
    3. Put 1 decimal place in the answer: 13.8

  2. 2. Calculate 12.6 ÷ 3

    1. Set up the division with the decimal point in place
    2. Divide: 12 ÷ 3 = 4, and 0.6 ÷ 3 = 0.2
    3. Answer: 4.2

  3. 3. Calculate 0.5 × 0.8

    1. Multiply ignoring decimals: 5 × 8 = 40
    2. Count total decimal places: 1 + 1 = 2 places
    3. Put 2 decimal places in answer: 0.40 or 0.4

Try it yourself

Calculate 7.2 × 4

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