Year 6 Arithmetic (SATs): Multiplying and dividing decimals, and the equals sign
Part of the Year 6 Arithmetic (SATs) multiplication and division chapter. Chapter overview · whole chapter on one page
Multiplying and dividing decimals, and the equals sign
Rule
Multiplying by 10, 100 or 1000 moves every digit one, two or three places to the left. Dividing moves them to the right.
To multiply a decimal by a whole number, multiply as if there were no point, then put the point back so the answer has the same number of decimal places.
The equals sign means "the same as": both sides have the same value.
Key ideas
- ×10, ×100, ×1000 move digits to the left; ÷10, ÷100, ÷1000 move them to the right.
- The answer to a decimal × whole number has the same number of decimal places as the decimal.
- Write a decimal division to two places, adding zeros after the point if needed.
- Both sides of an equals sign must have the same value.
Method. Multiply by 100: each digit moves two places to the left.
- Move each digit two places left. The digit 4 moves to the hundreds, 5 to the tens, 6 to the ones.4.56 → 456
- Check the point. There are no decimal places left, so the answer is a whole number.456
- Write the answer. The answer is 456.456
- Write the answer. 456
Check. 456 ÷ 100 = 4.56. ✓
Watch out. Do not add zeros after the point for ×100 here: 4.56 × 100 is 456.
Method. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 345 by 6, as whole numbers.345 × 6 = 2070
- Put the decimal point back. 3.45 has 2 decimal places, so the answer has 2 decimal places.2070 → 20.70
- Write the answer. 20.70
Check. 3.45 is about 3.5, and 3.5 × 6 = 21, close to 20.70. ✓
Watch out. 3.45 has two decimal places, so 20.70 has two decimal places too.
Method. Divide the whole number, then continue with a decimal point and zeros.
- Divide the whole number first. 4 goes into 27 6 times, with a remainder of 3.27 ÷ 4 = 6 remainder 3
- Write a decimal point, add a 0 and keep dividing. The remainder 3 becomes 30, and 4 goes into 30 7 times.30 ÷ 4 = 7 remainder 2
- Write a decimal point, add a 0 and keep dividing. The remainder 2 becomes 20, and 4 goes into 20 5 times.20 ÷ 4 = 5 remainder 0
- Write the answer. 6.75
Check. 4 × 6.75 = 27. ✓
Exercise 2E Practice: decimals, powers of 10 and the equals sign
Non-calculatorMethod. Multiply by 10 moves each digit one place to the left.
- Move each digit one place left. The 7 moves to the tens and the 5 moves to the ones.7.5 → 75
- Write the answer. 75
Check. 75 ÷ 10 = 7.5. ✓
Method. Multiply by 100 moves each digit two places to the left.
- Move each digit two places left. The 4 moves to the tens and the 6 to the ones.0.46 → 46
- Write the answer. 46
Check. 46 ÷ 100 = 0.46. ✓
Method. Divide by 10 moves each digit one place to the right.
- Move each digit one place right. The 3 moves to the tenths column and the 4 to the hundredths.3.4 → 0.34
- Write the answer. 0.34
Check. 0.34 × 10 = 3.4. ✓
Method. Multiply as whole numbers, then put the point back.
- Ignore the decimal point for now. Multiply the digits 236 by 4, as whole numbers.236 × 4 = 944
- Put the decimal point back. 2.36 has 2 decimal places, so the answer has 2 decimal places.944 → 9.44
- Write the answer. 9.44
Check. 2.36 is about 2.4, and 2.4 × 4 = 9.6, close to 9.44. ✓
Method. Multiply as whole numbers, then put the point back.
- Ignore the decimal point for now. Multiply the digits 185 by 6, as whole numbers.185 × 6 = 1110
- Put the decimal point back. 1.85 has 2 decimal places, so the answer has 2 decimal places.1110 → 11.10
- Write the answer. 11.10
Check. 1.85 is about 2, and 2 × 6 = 12, close to 11.10. ✓
Method. Divide, then continue with a decimal point and zeros.
- Divide the whole number first. 8 goes into 14 1 times, with a remainder of 6.14 ÷ 8 = 1 remainder 6
- Write a decimal point, add a 0 and keep dividing. The remainder 6 becomes 60, and 8 goes into 60 7 times.60 ÷ 8 = 7 remainder 4
- Write a decimal point, add a 0 and keep dividing. The remainder 4 becomes 40, and 8 goes into 40 5 times.40 ÷ 8 = 5 remainder 0
- Write the answer. 1.75
Check. 8 × 1.75 = 14. ✓
Method. Divide, then continue with a decimal point and zeros.
- Divide the whole number first. 4 goes into 19 4 times, with a remainder of 3.19 ÷ 4 = 4 remainder 3
- Write a decimal point, add a 0 and keep dividing. The remainder 3 becomes 30, and 4 goes into 30 7 times.30 ÷ 4 = 7 remainder 2
- Write a decimal point, add a 0 and keep dividing. The remainder 2 becomes 20, and 4 goes into 20 5 times.20 ÷ 4 = 5 remainder 0
- Write the answer. 4.75
Check. 4 × 4.75 = 19. ✓
Method. Work out the right-hand side first.
- Work out the right-hand side. 96 ÷ 3 = 32.96 ÷ 3 = 32
- Find the missing number. 4 × 8 = 32, so the box is 8.4 × 8 = 32
- Write the answer. 8
Check. 4 × 8 = 32 = 96 ÷ 3. ✓
Method. The right-hand side must equal the left-hand side.
- Work out the right-hand side. 12 × 5 = 60.12 × 5 = 60
- Find the missing divisor. 240 ÷ 4 = 60, so the box is 4.240 ÷ 4 = 60
- Write the answer. 4
Check. 240 ÷ 4 = 60 = 12 × 5. ✓
Method. Multiply the length of one roll by 6.
- Ignore the decimal point for now. Multiply the digits 235 by 6, as whole numbers.235 × 6 = 1410
- Put the decimal point back. 2.35 has 2 decimal places, so the answer has 2 decimal places.1410 → 14.10
- Write the answer. 14.10 m
Check. 2.35 × 6 is about 2.4 × 6 = 14.4, close to 14.10. ✓
Method. Divide the money by 4.
- Divide the whole number first. 4 goes into 27 6 times, with a remainder of 3.27 ÷ 4 = 6 remainder 3
- Write a decimal point, add a 0 and keep dividing. The remainder 3 becomes 30, and 4 goes into 30 7 times.30 ÷ 4 = 7 remainder 2
- Write a decimal point, add a 0 and keep dividing. The remainder 2 becomes 20, and 4 goes into 20 5 times.20 ÷ 4 = 5 remainder 0
- Write the answer. £6.75
Check. 4 × £6.75 = £27. ✓
Method. Multiplying by 10 moves digits to the left.
- Move the digit. The 5 in the tenths column moves to the units column.0.5 → 5
- Check the answer. 5 ÷ 10 = 0.5, so the answer 5 is right.0.5 × 10 = 5
- Write the answer. No, 0.5 × 10 = 5, because multiplying by 10 moves each digit one place to the left.
Check. 5 ÷ 10 = 0.5. ✓