Year 6: Multiplying decimals by whole numbers
Part of the Year 6 decimals chapter. Chapter overview · whole chapter on one page
Multiplying decimals by whole numbers
Many problems use decimals with money and measures: 4 notebooks at £2.35 each, or 9 jugs of 0.75 litres. Multiplying a decimal by a whole number works like multiplying whole numbers, with one extra step at the end.
First, ignore the decimal point and multiply the digits as a whole number. Then count the decimal places in the decimal number in the question. The answer has the same number of decimal places, so put the point back in that place.
Key ideas
- Multiply as if there were no decimal point, then put the point back.
- The answer has the same number of decimal places as the decimal number in the question.
- Estimate first. 3.46 × 7 is about 3 × 7 = 21, so an answer of 2.422 or 242.2 would be wrong.
- Carry the tens in the usual way, column by column, from the right.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
3.46 × 7 ----- 24.22
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.6 × 7 = 42, write 2 and carry 4
4 × 7 = 28 + 4 carried = 32, write 2 and carry 3
3 × 7 = 21 + 3 carried = 24, write 4 and carry 2
write 2 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.346 × 7 = 2422, and 2422 → 24.22
Check. About 3 × 7 = 21, and 24.22 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
2.35 × 4 ---- 9.40
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 4 = 20, write 0 and carry 2
3 × 4 = 12 + 2 carried = 14, write 4 and carry 1
2 × 4 = 8 + 1 carried = 9, write 9 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.235 × 4 = 940, and 940 → 9.40
Check. About 2 × 4 = 8, and 9.40 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
1.8 × 9 ---- 16.2
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.8 × 9 = 72, write 2 and carry 7
1 × 9 = 9 + 7 carried = 16, write 6 and carry 1
write 1 - Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.18 × 9 = 162, and 162 → 16.2
Check. About 2 × 9 = 18, and 16.2 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Watch out
Do not forget the decimal point in the answer. If you ignore it, 3.46 × 7 = 2422 looks like 2422, but the answer is 24.22. Count the places in the question.
Exam tip
Exam tip. Always check the size of your answer with an estimate. If the estimate and the answer do not match, look for a missing decimal point.
Exercise 5C Multiplying decimals by whole numbers
Non-calculatorKey words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
3.46 × 7 ----- 24.22
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.6 × 7 = 42, write 2 and carry 4
4 × 7 = 28 + 4 carried = 32, write 2 and carry 3
3 × 7 = 21 + 3 carried = 24, write 4 and carry 2
write 2 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.346 × 7 = 2422, and 2422 → 24.22
Check. About 3 × 7 = 21, and 24.22 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
0.85 × 6 ---- 5.10
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 6 = 30, write 0 and carry 3
8 × 6 = 48 + 3 carried = 51, write 1 and carry 5
write 5 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.85 × 6 = 510, and 510 → 5.10
Check. About 1 × 6 = 6, and 5.10 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
4.5 × 3 ---- 13.5
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 3 = 15, write 5 and carry 1
4 × 3 = 12 + 1 carried = 13, write 3 and carry 1
write 1 - Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.45 × 3 = 135, and 135 → 13.5
Check. About 4 × 3 = 12, and 13.5 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
2.7 × 8 ---- 21.6
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.7 × 8 = 56, write 6 and carry 5
2 × 8 = 16 + 5 carried = 21, write 1 and carry 2
write 2 - Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.27 × 8 = 216, and 216 → 21.6
Check. About 3 × 8 = 24, and 21.6 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
1.24 × 4 ---- 4.96
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.4 × 4 = 16, write 6 and carry 1
2 × 4 = 8 + 1 carried = 9, write 9
1 × 4 = 4, write 4 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.124 × 4 = 496, and 496 → 4.96
Check. About 1 × 4 = 4, and 4.96 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
6.08 × 5 ----- 30.40
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.8 × 5 = 40, write 0 and carry 4
0 × 5 = 0 + 4 carried = 4, write 4
6 × 5 = 30, write 0 and carry 3
write 3 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.608 × 5 = 3040, and 3040 → 30.40
Check. About 6 × 5 = 30, and 30.40 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
0.6 × 9 --- 5.4
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.6 × 9 = 54, write 4 and carry 5
write 5 - Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.6 × 9 = 54, and 54 → 5.4
Check. About 1 × 9 = 9, and 5.4 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
3.15 × 2 ---- 6.30
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 2 = 10, write 0 and carry 1
1 × 2 = 2 + 1 carried = 3, write 3
3 × 2 = 6, write 6 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.315 × 2 = 630, and 630 → 6.30
Check. About 3 × 2 = 6, and 6.30 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
0.85 × 6 ---- 5.10
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 6 = 30, write 0 and carry 3
8 × 6 = 48 + 3 carried = 51, write 1 and carry 5
write 5 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.85 × 6 = 510, and 510 → 5.10
Check. About 1 × 6 = 6, and 5.10 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
2.35 × 4 ---- 9.40
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 4 = 20, write 0 and carry 2
3 × 4 = 12 + 2 carried = 14, write 4 and carry 1
2 × 4 = 8 + 1 carried = 9, write 9 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.235 × 4 = 940, and 940 → 9.40
Check. About 2 × 4 = 8, and 9.40 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
1.25 × 7 ---- 8.75
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 7 = 35, write 5 and carry 3
2 × 7 = 14 + 3 carried = 17, write 7 and carry 1
1 × 7 = 7 + 1 carried = 8, write 8 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.125 × 7 = 875, and 875 → 8.75
Check. About 1 × 7 = 7, and 8.75 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
0.75 × 9 ---- 6.75
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 9 = 45, write 5 and carry 4
7 × 9 = 63 + 4 carried = 67, write 7 and carry 6
write 6 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.75 × 9 = 675, and 675 → 6.75
Check. About 1 × 9 = 9, and 6.75 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
1.45 × 5 ---- 7.25
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 5 = 25, write 5 and carry 2
4 × 5 = 20 + 2 carried = 22, write 2 and carry 2
1 × 5 = 5 + 2 carried = 7, write 7 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.145 × 5 = 725, and 725 → 7.25
Check. About 1 × 5 = 5, and 7.25 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. First find the total cost. Then take it away from the £10 note.
- Write £10 with two decimal places. This makes the subtraction easy to line up.10.00 − 7.25
- Subtract, column by column. Borrow from the column on the left when you need to.10.00 − 7.25 = 2.75
- Write the answer. The change is the amount left over.2.75
Check. 7.25 + 2.75 = 10.00. ✓
Watch out. Line up the decimal points before you subtract.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.
Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.
- Set out the layout. The number being divided goes inside the bracket. The answer goes above it.
4.6 6 ) 27.6 0 - 27 24 -- 36 36 -- 0 - Start with the first digit, 2. 6 does not go into 2, so this digit of the answer is 0.2 ÷ 6 = 0, remainder 2
- Bring down the next digit, so we have 27. How many 6s go into 27? 4, because 4 × 6 = 24.27 ÷ 6 = 4, remainder 3
- Bring down the next digit, so we have 36. Write the decimal point in the answer now, above the point. How many 6s go into 36? 6, because 6 × 6 = 36.36 ÷ 6 = 6, remainder 0
- Write the answer. Keep going until the remainder is 0, or until you have the places you need.4.6
Check. 4.6 × 6 = 27.6. ✓
Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.
Key words. In long division, the dividend is the number being divided, the divisor is the number we divide by, and the remainder is what is left over. Bring down a 0 after the decimal point to keep going.
Method. Share the number out one digit at a time. Put the decimal point in the answer when you reach it in the number.
- Set out the layout. The number being divided goes inside the bracket. The answer goes above it.
3.4 4 ) 13.6 0 - 13 12 -- 16 16 -- 0 - Start with the first digit, 1. 4 does not go into 1, so this digit of the answer is 0.1 ÷ 4 = 0, remainder 1
- Bring down the next digit, so we have 13. How many 4s go into 13? 3, because 3 × 4 = 12.13 ÷ 4 = 3, remainder 1
- Bring down the next digit, so we have 16. Write the decimal point in the answer now, above the point. How many 4s go into 16? 4, because 4 × 4 = 16.16 ÷ 4 = 4, remainder 0
- Write the answer. Keep going until the remainder is 0, or until you have the places you need.3.4
Check. 3.4 × 4 = 13.6. ✓
Watch out. Do not forget the decimal point in the answer. Bring down zeros only after you have used all the digits of the number.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 1 decimal place.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
3.6 × 5 ---- 18.0
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.6 × 5 = 30, write 0 and carry 3
3 × 5 = 15 + 3 carried = 18, write 8 and carry 1
write 1 - Count the decimal places and put the point back. The decimal number has 1 decimal place, so the answer has 1 decimal place.36 × 5 = 180, and 180 → 18.0
Check. About 4 × 5 = 20, and 18.0 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Estimate first, then check the working.
- Estimate. 3.46 is a little more than 3, and 3 × 7 = 21.3 × 7 = 21
- Compare with the answer. The answer 24.22 is a little more than 21, which matches the estimate.24.22 is a little more than 21
- Decide. The answer is the right size.Yes, 24.22 is sensible.
Check. 3.46 × 7 is about 3.5 × 7 = 24.5, which is close to 24.22. ✓
Watch out. An estimate tells you the size of the answer. It does not give the exact answer.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
0.45 × 8 ---- 3.60
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.5 × 8 = 40, write 0 and carry 4
4 × 8 = 32 + 4 carried = 36, write 6 and carry 3
write 3 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.45 × 8 = 360, and 360 → 3.60
Check. About 0 × 8 = 0, and 3.60 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.
Key words. A decimal place is a digit after the decimal point. The answer to a multiplication has the same number of decimal places as the decimal number in the question.
Method. Multiply as if there were no decimal point. Then put the point back so the answer has 2 decimal places.
- Write the numbers in columns. Line up the numbers on the right. Ignore the decimal point for now.
0.36 × 60 ----- 21.60
- Multiply each digit, starting from the right. Write the last digit of each answer and carry the tens to the next column.6 × 60 = 360, write 0 and carry 36
3 × 60 = 180 + 36 carried = 216, write 6 and carry 21
write 21 - Count the decimal places and put the point back. The decimal number has 2 decimal places, so the answer has 2 decimal places.36 × 60 = 2160, and 2160 → 21.60
Check. About 0 × 60 = 0, and 21.60 is close to that. ✓
Watch out. Count the decimal places in the question. Do not count the zeros you carry.