# Operations with decimals · Year 7

> Operations with decimals, Year 7: Multiplying decimals and more. Explanation, worked examples and free practice for the national curriculum in England.

In Operations with decimals (Year 7) you practise 6 skills: Multiplying decimals · Dividing decimals · A fraction as a decimal · Mixed operations · Estimating with decimals · Decimal word problems.

To multiply decimals, multiply as if there were no point. Then count the digits after the point in both factors together: the answer has that many digits after the point.

To divide by a decimal, multiply the number being divided and the divisor by the same number, 10 or 100, so that the divisor is a whole number. The answer does not change.

Any fraction can be written as a decimal: divide the numerator by the denominator. When the denominator is 2, 4, 5 or 10, you can expand the fraction to a denominator of 10 or 100.

Before you calculate, estimate: multiplying by a number less than 1 makes a number smaller, and dividing by a number less than 1 makes it bigger. That way you can check whether your answer makes sense.

**Tip:** When you multiply two decimals, count the digits after the point in both factors together.

## What you learn

### Multiplying decimals

- Example: Work out: 2.3 × 9
- Answer: 20.7
- Solution: Multiply without the point: 23 × 9 = 207 Together the two factors have one digit after the point, so divide by 10: 207 ÷ 10 = 20.7

### Dividing decimals

- Example: Work out: 13.5 ÷ 9
- Answer: 1.5
- Solution: Divide as with whole numbers; the point stays where it is: 13.5 ÷ 9 = 1.5

### A fraction as a decimal

- Example: Write as a decimal: 9/80
- Answer: 0.1125
- Solution: 9/80 = 1125/10000 = 0.1125

### Mixed operations

- Example: Work out: 0.25 × 5 + 0.3
- Answer: 1.55
- Solution: Multiplying and dividing first, then adding and subtracting: 0.25 × 5 + 0.3 = 1.25 + 0.3 1.25 + 0.3 = 1.55

### Estimating with decimals

- Example: Is the answer to 10.39 + 9.94 bigger or smaller than 20?
- Options: bigger than 20 · smaller than 20
- Answer: bigger than 20
- Solution: The number 10.39 is 0.39 more than 10, and the number 9.94 is 0.06 less than 10. More is added than is missing, so the sum is bigger than 20. Check: 10.39 + 9.94 = 20.33

### Decimal word problems

- Example: On Sunday they ran 1.5 kilometres, and on Monday they ran 6.7 kilometres. How many kilometres did they run on the two days altogether?
- Answer: 8.2 km
- Solution: 1.5 + 6.7 = 8.2

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

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