GCSE Maths: Dividing (Foundation)
Part of the GCSE Maths number basics chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Dividing
Division means sharing equally, or finding how many groups of a size fit into a number. 96 ÷ 4 can mean “share 96 into 4 equal groups” or “how many 4s are in 96?” Both give 24, because division is the inverse of multiplication: 4 × 24 = 96. The number being divided is the dividend, the number you divide by is the divisor, and the answer is the quotient. Unlike multiplication, the order matters: 24 ÷ 6 = 4 but 6 ÷ 24 = 0.25.
Short division is used when the divisor is small (up to about 12). Work from the left. Divide the first digit, write the answer above, and carry any remainder in front of the next digit. To work out 1296 ÷ 8: 8 into 12 goes once, remainder 4; carry 4 to make 49; 8 into 49 goes 6 times, remainder 1; carry 1 to make 16; 8 into 16 goes twice. So 1296 ÷ 8 = 162.
Long division uses the same idea for bigger divisors, but you write out every step. First list the multiples of the divisor (× 1 to × 9). Then repeat: divide (how many times does the divisor go in), multiply, subtract, bring down the next digit. The remainder at each stage must always be smaller than the divisor.
Remainders. If a division does not come out exactly, you can write the answer with a remainder, or keep dividing by putting a decimal point and zeros after the number (5 ÷ 8 = 0.625). In a real problem, the meaning decides: 53 people in cars that hold 5 people need 11 cars (round up), but 53 sweets shared between 5 children give 10 each with 3 left over (round down).
Dividing decimals. Dividing by a whole number is the same as before; keep the decimal point in line. If you divide by a decimal, multiply both numbers by 10, 100, … until the divisor is a whole number. 7.2 ÷ 0.4 has the same answer as 72 ÷ 4 because multiplying both numbers by the same amount keeps the ratio the same. Check every division by multiplying the answer by the divisor.
Key ideas
- Dividend ÷ divisor = quotient. Check: quotient × divisor = dividend.
- Short division: divide digit by digit from the left and carry the remainder.
- Long division: divide, multiply, subtract, bring down; the remainder is always smaller than the divisor.
- To divide by a decimal, multiply both numbers by 10, 100... to make the divisor a whole number.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 1296 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.8 ) 1296
- Start with the first 2 digits, 12. 8 does not go into the first digit, so we take digits from the left until we have a number that 8 can go into.12 ÷ 8 = 1 remainder 4 (since 8 × 1 = 8)
- Bring down the next digit, 9, to make 49. The remainder 4 goes in front of the 9. This is the same as carrying the remainder to the next column.49 ÷ 8 = 6 remainder 1 (since 8 × 6 = 48)
- Bring down the next digit, 6, to make 16. The remainder 1 goes in front of the 6. This is the same as carrying the remainder to the next column.16 ÷ 8 = 2 (since 8 × 2 = 16)
- Write the answer. Read the digits along the top.162 141 8) 1296
1296 ÷ 8 = 162
Check. Multiply back: 162 × 8 = 1296. ✓
Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 34 into each number in turn, carrying the remainder to the next digit.
- Write out the 34 times table up to 34 × 9. Having the multiples ready makes it quick to see how many times 34 goes into each number.34 × 1 = 34
34 × 2 = 68
34 × 3 = 102
34 × 4 = 136
34 × 5 = 170
34 × 6 = 204
34 × 7 = 238
34 × 8 = 272
34 × 9 = 306 - Set out the division. Write 7523 under the "bus stop" and 34 outside it. The answer will be written on top, one digit above each digit we divide.34 ) 7523
- Start with the first 2 digits, 75. 34 does not go into the first digit, so we take digits from the left until we have a number that 34 can go into.34 goes into 75 2 times: 34 × 2 = 68
Subtract: 75 − 68 = 7 - Bring down the next digit, 2, to make 72. The remainder 7 goes in front of the 2. This is the same as carrying the remainder to the next column.34 goes into 72 2 times: 34 × 2 = 68
Subtract: 72 − 68 = 4 - Bring down the next digit, 3, to make 43. The remainder 4 goes in front of the 3. This is the same as carrying the remainder to the next column.34 goes into 43 1 time: 34 × 1 = 34
Subtract: 43 − 34 = 9 - Write the answer. Read the digits along the top.221 34) 7523 68 -- 72 68 -- 43 34 -- 9
7523 ÷ 34 = 221 remainder 9
Check. Multiply back: 221 × 34 = 7514, then add the remainder 9: 7514 + 9 = 7523. ✓
Watch out. If 34 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 100 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.8 ) 100
- Start with the first 2 digits, 10. 8 does not go into the first digit, so we take digits from the left until we have a number that 8 can go into.10 ÷ 8 = 1 remainder 2 (since 8 × 1 = 8)
- Bring down the next digit, 0, to make 20. The remainder 2 goes in front of the 0. This is the same as carrying the remainder to the next column.20 ÷ 8 = 2 remainder 4 (since 8 × 2 = 16)
- There is a remainder of 4, so add a 0 on the end and bring it down to make 40. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.40 ÷ 8 = 5 (since 8 × 5 = 40)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.12.5 12 4 8) 100.0
100 ÷ 8 = 12.5
Check. Multiply back: 12.5 × 8 = 100. ✓
Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.
- Make the number you are dividing by a whole number. Multiplying both numbers by 10 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.7.2 ÷ 0.4 = 72 ÷ 4
(7.2 × 10 = 72 and 0.4 × 10 = 4) - Set out the division. Write 72 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.4 ) 72
- Start with the first digit, 7. Work from the left. We ask how many times 4 goes into 7.7 ÷ 4 = 1 remainder 3 (since 4 × 1 = 4)
- Bring down the next digit, 2, to make 32. The remainder 3 goes in front of the 2. This is the same as carrying the remainder to the next column.32 ÷ 4 = 8 (since 4 × 8 = 32)
- Write the answer. Read the digits along the top.18 3 4) 72
72 ÷ 4 = 18
Check. Multiply back: 18 × 4 = 72. ✓
Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Watch out
When the divisor is bigger than the first digit, you do not skip it. Use the first two digits (for 936 ÷ 24 start with 93), and always write a 0 in the answer if the divisor does not go into a number.Exercise 1D Dividing whole numbers and decimals
Non-calculatorKey words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 56 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.7 ) 56
- Start with the first 2 digits, 56. 7 does not go into the first digit, so we take digits from the left until we have a number that 7 can go into.56 ÷ 7 = 8 (since 7 × 8 = 56)
- Write the answer. Read the digits along the top.8 5 7) 56
56 ÷ 7 = 8
Check. Multiply back: 8 × 7 = 56. ✓
Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 9 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 81 under the "bus stop" and 9 outside it. The answer will be written on top, one digit above each digit we divide.9 ) 81
- Start with the first 2 digits, 81. 9 does not go into the first digit, so we take digits from the left until we have a number that 9 can go into.81 ÷ 9 = 9 (since 9 × 9 = 81)
- Write the answer. Read the digits along the top.9 8 9) 81
81 ÷ 9 = 9
Check. Multiply back: 9 × 9 = 81. ✓
Watch out. If 9 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 12 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 132 under the "bus stop" and 12 outside it. The answer will be written on top, one digit above each digit we divide.12 ) 132
- Start with the first 2 digits, 13. 12 does not go into the first digit, so we take digits from the left until we have a number that 12 can go into.13 ÷ 12 = 1 remainder 1 (since 12 × 1 = 12)
- Bring down the next digit, 2, to make 12. The remainder 1 goes in front of the 2. This is the same as carrying the remainder to the next column.12 ÷ 12 = 1 (since 12 × 1 = 12)
- Write the answer. Read the digits along the top.11 11 12) 132
132 ÷ 12 = 11
Check. Multiply back: 11 × 12 = 132. ✓
Watch out. If 12 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 96 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.8 ) 96
- Start with the first digit, 9. Work from the left. We ask how many times 8 goes into 9.9 ÷ 8 = 1 remainder 1 (since 8 × 1 = 8)
- Bring down the next digit, 6, to make 16. The remainder 1 goes in front of the 6. This is the same as carrying the remainder to the next column.16 ÷ 8 = 2 (since 8 × 2 = 16)
- Write the answer. Read the digits along the top.12 1 8) 96
96 ÷ 8 = 12
Check. Multiply back: 12 × 8 = 96. ✓
Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 936 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.4 ) 936
- Start with the first digit, 9. Work from the left. We ask how many times 4 goes into 9.9 ÷ 4 = 2 remainder 1 (since 4 × 2 = 8)
- Bring down the next digit, 3, to make 13. The remainder 1 goes in front of the 3. This is the same as carrying the remainder to the next column.13 ÷ 4 = 3 remainder 1 (since 4 × 3 = 12)
- Bring down the next digit, 6, to make 16. The remainder 1 goes in front of the 6. This is the same as carrying the remainder to the next column.16 ÷ 4 = 4 (since 4 × 4 = 16)
- Write the answer. Read the digits along the top.234 11 4) 936
936 ÷ 4 = 234
Check. Multiply back: 234 × 4 = 936. ✓
Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 6 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 1548 under the "bus stop" and 6 outside it. The answer will be written on top, one digit above each digit we divide.6 ) 1548
- Start with the first 2 digits, 15. 6 does not go into the first digit, so we take digits from the left until we have a number that 6 can go into.15 ÷ 6 = 2 remainder 3 (since 6 × 2 = 12)
- Bring down the next digit, 4, to make 34. The remainder 3 goes in front of the 4. This is the same as carrying the remainder to the next column.34 ÷ 6 = 5 remainder 4 (since 6 × 5 = 30)
- Bring down the next digit, 8, to make 48. The remainder 4 goes in front of the 8. This is the same as carrying the remainder to the next column.48 ÷ 6 = 8 (since 6 × 8 = 48)
- Write the answer. Read the digits along the top.258 134 6) 1548
1548 ÷ 6 = 258
Check. Multiply back: 258 × 6 = 1548. ✓
Watch out. If 6 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 4032 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.8 ) 4032
- Start with the first 2 digits, 40. 8 does not go into the first digit, so we take digits from the left until we have a number that 8 can go into.40 ÷ 8 = 5 (since 8 × 5 = 40)
- Bring down the next digit, 3. The remainder was 0, so the new number to divide is just that digit.8 does not go into 3, so write 0 and carry on.
- Bring down the next digit, 2, to make 32. The remainder 3 goes in front of the 2. This is the same as carrying the remainder to the next column.32 ÷ 8 = 4 (since 8 × 4 = 32)
- Write the answer. Read the digits along the top.504 4 3 8) 4032
4032 ÷ 8 = 504
Check. Multiply back: 504 × 8 = 4032. ✓
Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 5 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 6175 under the "bus stop" and 5 outside it. The answer will be written on top, one digit above each digit we divide.5 ) 6175
- Start with the first digit, 6. Work from the left. We ask how many times 5 goes into 6.6 ÷ 5 = 1 remainder 1 (since 5 × 1 = 5)
- Bring down the next digit, 1, to make 11. The remainder 1 goes in front of the 1. This is the same as carrying the remainder to the next column.11 ÷ 5 = 2 remainder 1 (since 5 × 2 = 10)
- Bring down the next digit, 7, to make 17. The remainder 1 goes in front of the 7. This is the same as carrying the remainder to the next column.17 ÷ 5 = 3 remainder 2 (since 5 × 3 = 15)
- Bring down the next digit, 5, to make 25. The remainder 2 goes in front of the 5. This is the same as carrying the remainder to the next column.25 ÷ 5 = 5 (since 5 × 5 = 25)
- Write the answer. Read the digits along the top.1235 112 5) 6175
6175 ÷ 5 = 1235
Check. Multiply back: 1235 × 5 = 6175. ✓
Watch out. If 5 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 6 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 487 under the "bus stop" and 6 outside it. The answer will be written on top, one digit above each digit we divide.6 ) 487
- Start with the first 2 digits, 48. 6 does not go into the first digit, so we take digits from the left until we have a number that 6 can go into.48 ÷ 6 = 8 (since 6 × 8 = 48)
- Bring down the next digit, 7. The remainder was 0, so the new number to divide is just that digit.7 ÷ 6 = 1 remainder 1 (since 6 × 1 = 6)
- Write the answer. Read the digits along the top.81 4 6) 487
487 ÷ 6 = 81 remainder 1
Check. Multiply back: 81 × 6 = 486, then add the remainder 1: 486 + 1 = 487. ✓
Watch out. If 6 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 1000 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.7 ) 1000
- Start with the first 2 digits, 10. 7 does not go into the first digit, so we take digits from the left until we have a number that 7 can go into.10 ÷ 7 = 1 remainder 3 (since 7 × 1 = 7)
- Bring down the next digit, 0, to make 30. The remainder 3 goes in front of the 0. This is the same as carrying the remainder to the next column.30 ÷ 7 = 4 remainder 2 (since 7 × 4 = 28)
- Bring down the next digit, 0, to make 20. The remainder 2 goes in front of the 0. This is the same as carrying the remainder to the next column.20 ÷ 7 = 2 remainder 6 (since 7 × 2 = 14)
- Write the answer. Read the digits along the top.142 132 7) 1000
1000 ÷ 7 = 142 remainder 6
Check. Multiply back: 142 × 7 = 994, then add the remainder 6: 994 + 6 = 1000. ✓
Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 9 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 2345 under the "bus stop" and 9 outside it. The answer will be written on top, one digit above each digit we divide.9 ) 2345
- Start with the first 2 digits, 23. 9 does not go into the first digit, so we take digits from the left until we have a number that 9 can go into.23 ÷ 9 = 2 remainder 5 (since 9 × 2 = 18)
- Bring down the next digit, 4, to make 54. The remainder 5 goes in front of the 4. This is the same as carrying the remainder to the next column.54 ÷ 9 = 6 (since 9 × 6 = 54)
- Bring down the next digit, 5. The remainder was 0, so the new number to divide is just that digit.9 does not go into 5, so write 0 and carry on.
- Write the answer. Read the digits along the top.260 25 9) 2345
2345 ÷ 9 = 260 remainder 5
Check. Multiply back: 260 × 9 = 2340, then add the remainder 5: 2340 + 5 = 2345. ✓
Watch out. If 9 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 24 into each number in turn, carrying the remainder to the next digit.
- Write out the 24 times table up to 24 × 9. Having the multiples ready makes it quick to see how many times 24 goes into each number.24 × 1 = 24
24 × 2 = 48
24 × 3 = 72
24 × 4 = 96
24 × 5 = 120
24 × 6 = 144
24 × 7 = 168
24 × 8 = 192
24 × 9 = 216 - Set out the division. Write 936 under the "bus stop" and 24 outside it. The answer will be written on top, one digit above each digit we divide.24 ) 936
- Start with the first 2 digits, 93. 24 does not go into the first digit, so we take digits from the left until we have a number that 24 can go into.24 goes into 93 3 times: 24 × 3 = 72
Subtract: 93 − 72 = 21 - Bring down the next digit, 6, to make 216. The remainder 21 goes in front of the 6. This is the same as carrying the remainder to the next column.24 goes into 216 9 times: 24 × 9 = 216
Subtract: 216 − 216 = 0 - Write the answer. Read the digits along the top.39 24) 936 72 -- 216 216 --- 0
936 ÷ 24 = 39
Check. Multiply back: 39 × 24 = 936. ✓
Watch out. If 24 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 34 into each number in turn, carrying the remainder to the next digit.
- Write out the 34 times table up to 34 × 9. Having the multiples ready makes it quick to see how many times 34 goes into each number.34 × 1 = 34
34 × 2 = 68
34 × 3 = 102
34 × 4 = 136
34 × 5 = 170
34 × 6 = 204
34 × 7 = 238
34 × 8 = 272
34 × 9 = 306 - Set out the division. Write 7523 under the "bus stop" and 34 outside it. The answer will be written on top, one digit above each digit we divide.34 ) 7523
- Start with the first 2 digits, 75. 34 does not go into the first digit, so we take digits from the left until we have a number that 34 can go into.34 goes into 75 2 times: 34 × 2 = 68
Subtract: 75 − 68 = 7 - Bring down the next digit, 2, to make 72. The remainder 7 goes in front of the 2. This is the same as carrying the remainder to the next column.34 goes into 72 2 times: 34 × 2 = 68
Subtract: 72 − 68 = 4 - Bring down the next digit, 3, to make 43. The remainder 4 goes in front of the 3. This is the same as carrying the remainder to the next column.34 goes into 43 1 time: 34 × 1 = 34
Subtract: 43 − 34 = 9 - Write the answer. Read the digits along the top.221 34) 7523 68 -- 72 68 -- 43 34 -- 9
7523 ÷ 34 = 221 remainder 9
Check. Multiply back: 221 × 34 = 7514, then add the remainder 9: 7514 + 9 = 7523. ✓
Watch out. If 34 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 28 into each number in turn, carrying the remainder to the next digit.
- Write out the 28 times table up to 28 × 9. Having the multiples ready makes it quick to see how many times 28 goes into each number.28 × 1 = 28
28 × 2 = 56
28 × 3 = 84
28 × 4 = 112
28 × 5 = 140
28 × 6 = 168
28 × 7 = 196
28 × 8 = 224
28 × 9 = 252 - Set out the division. Write 4704 under the "bus stop" and 28 outside it. The answer will be written on top, one digit above each digit we divide.28 ) 4704
- Start with the first 2 digits, 47. 28 does not go into the first digit, so we take digits from the left until we have a number that 28 can go into.28 goes into 47 1 time: 28 × 1 = 28
Subtract: 47 − 28 = 19 - Bring down the next digit, 0, to make 190. The remainder 19 goes in front of the 0. This is the same as carrying the remainder to the next column.28 goes into 190 6 times: 28 × 6 = 168
Subtract: 190 − 168 = 22 - Bring down the next digit, 4, to make 224. The remainder 22 goes in front of the 4. This is the same as carrying the remainder to the next column.28 goes into 224 8 times: 28 × 8 = 224
Subtract: 224 − 224 = 0 - Write the answer. Read the digits along the top.168 28) 4704 28 -- 190 168 --- 224 224 --- 0
4704 ÷ 28 = 168
Check. Multiply back: 168 × 28 = 4704. ✓
Watch out. If 28 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 16 into each number in turn, carrying the remainder to the next digit.
- Write out the 16 times table up to 16 × 9. Having the multiples ready makes it quick to see how many times 16 goes into each number.16 × 1 = 16
16 × 2 = 32
16 × 3 = 48
16 × 4 = 64
16 × 5 = 80
16 × 6 = 96
16 × 7 = 112
16 × 8 = 128
16 × 9 = 144 - Set out the division. Write 10000 under the "bus stop" and 16 outside it. The answer will be written on top, one digit above each digit we divide.16 ) 10000
- Start with the first 3 digits, 100. 16 does not go into the first digit, so we take digits from the left until we have a number that 16 can go into.16 goes into 100 6 times: 16 × 6 = 96
Subtract: 100 − 96 = 4 - Bring down the next digit, 0, to make 40. The remainder 4 goes in front of the 0. This is the same as carrying the remainder to the next column.16 goes into 40 2 times: 16 × 2 = 32
Subtract: 40 − 32 = 8 - Bring down the next digit, 0, to make 80. The remainder 8 goes in front of the 0. This is the same as carrying the remainder to the next column.16 goes into 80 5 times: 16 × 5 = 80
Subtract: 80 − 80 = 0 - Write the answer. Read the digits along the top.625 16) 10000 96 -- 40 32 -- 80 80 -- 0
10 000 ÷ 16 = 625
Check. Multiply back: 625 × 16 = 10 000. ✓
Watch out. If 16 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 9 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.4 ) 9
- Start with the first digit, 9. Work from the left. We ask how many times 4 goes into 9.9 ÷ 4 = 2 remainder 1 (since 4 × 2 = 8)
- There is a remainder of 1, so add a 0 on the end and bring it down to make 10. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.10 ÷ 4 = 2 remainder 2 (since 4 × 2 = 8)
- There is a remainder of 2, so add a 0 on the end and bring it down to make 20. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.20 ÷ 4 = 5 (since 4 × 5 = 20)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.2.25 12 4) 9.00
9 ÷ 4 = 2.25
Check. Multiply back: 2.25 × 4 = 9. ✓
Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 3 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.8 ) 3
- Start with the first digit, 3. Work from the left. We ask how many times 8 goes into 3.8 does not go into 3, so write 0 and carry on.
- There is a remainder of 3, so add a 0 on the end and bring it down to make 30. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.30 ÷ 8 = 3 remainder 6 (since 8 × 3 = 24)
- There is a remainder of 6, so add a 0 on the end and bring it down to make 60. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.60 ÷ 8 = 7 remainder 4 (since 8 × 7 = 56)
- There is a remainder of 4, so add a 0 on the end and bring it down to make 40. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.40 ÷ 8 = 5 (since 8 × 5 = 40)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.0.375 364 8) 3.000
3 ÷ 8 = 0.375
Check. Multiply back: 0.375 × 8 = 3. ✓
Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 20 into each number in turn, carrying the remainder to the next digit.
- Write out the 20 times table up to 20 × 9. Having the multiples ready makes it quick to see how many times 20 goes into each number.20 × 1 = 20
20 × 2 = 40
20 × 3 = 60
20 × 4 = 80
20 × 5 = 100
20 × 6 = 120
20 × 7 = 140
20 × 8 = 160
20 × 9 = 180 - Set out the division. Write 17 under the "bus stop" and 20 outside it. The answer will be written on top, one digit above each digit we divide.20 ) 17
- Start with the first 2 digits, 17. 20 does not go into the first digit, so we take digits from the left until we have a number that 20 can go into.20 does not go into 17, so write 0 in the answer.
- There is a remainder of 17, so add a 0 on the end and bring it down to make 170. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.20 goes into 170 8 times: 20 × 8 = 160
Subtract: 170 − 160 = 10 - There is a remainder of 10, so add a 0 on the end and bring it down to make 100. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.20 goes into 100 5 times: 20 × 5 = 100
Subtract: 100 − 100 = 0 - Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.0.85 20) 17.00 160 --- 100 100 --- 0
17 ÷ 20 = 0.85
Check. Multiply back: 0.85 × 20 = 17. ✓
Watch out. If 20 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 16 into each number in turn, carrying the remainder to the next digit.
- Write out the 16 times table up to 16 × 9. Having the multiples ready makes it quick to see how many times 16 goes into each number.16 × 1 = 16
16 × 2 = 32
16 × 3 = 48
16 × 4 = 64
16 × 5 = 80
16 × 6 = 96
16 × 7 = 112
16 × 8 = 128
16 × 9 = 144 - Set out the division. Write 45 under the "bus stop" and 16 outside it. The answer will be written on top, one digit above each digit we divide.16 ) 45
- Start with the first 2 digits, 45. 16 does not go into the first digit, so we take digits from the left until we have a number that 16 can go into.16 goes into 45 2 times: 16 × 2 = 32
Subtract: 45 − 32 = 13 - There is a remainder of 13, so add a 0 on the end and bring it down to make 130. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.16 goes into 130 8 times: 16 × 8 = 128
Subtract: 130 − 128 = 2 - There is a remainder of 2, so add a 0 on the end and bring it down to make 20. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.16 goes into 20 1 time: 16 × 1 = 16
Subtract: 20 − 16 = 4 - There is a remainder of 4, so add a 0 on the end and bring it down to make 40. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.16 goes into 40 2 times: 16 × 2 = 32
Subtract: 40 − 32 = 8 - There is a remainder of 8, so add a 0 on the end and bring it down to make 80. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.16 goes into 80 5 times: 16 × 5 = 80
Subtract: 80 − 80 = 0 - Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.2.8125 16) 45.0000 32 -- 13 0 128 --- 20 16 -- 40 32 -- 80 80 -- 0
45 ÷ 16 = 2.8125
Check. Multiply back: 2.8125 × 16 = 45. ✓
Watch out. If 16 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 5 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 7.5 under the "bus stop" and 5 outside it. The answer will be written on top, one digit above each digit we divide.5 ) 7.5
- Start with the first digit, 7. Work from the left. We ask how many times 5 goes into 7.7 ÷ 5 = 1 remainder 2 (since 5 × 1 = 5)
- The next digit is after the decimal point. Put a decimal point in the answer, then bring down 5 to make 25. The decimal point in the answer goes directly above the decimal point in the question.25 ÷ 5 = 5 (since 5 × 5 = 25)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.1.5 2 5) 7.5
7.5 ÷ 5 = 1.5
Check. Multiply back: 1.5 × 5 = 7.5. ✓
Watch out. If 5 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 0.84 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.7 ) 0.84
- The number is less than 1, so the answer starts "0." Put the decimal point in the answer, then look at the first digit after the point, 8. We still ask how many times 7 goes into 8.8 ÷ 7 = 1 remainder 1 (since 7 × 1 = 7)
- Bring down the next digit, 4, to make 14. The remainder 1 goes in front of the 4. This is the same as carrying the remainder to the next column.14 ÷ 7 = 2 (since 7 × 2 = 14)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.0.12 1 7) 0.84
0.84 ÷ 7 = 0.12
Check. Multiply back: 0.12 × 7 = 0.84. ✓
Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 9 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 12.6 under the "bus stop" and 9 outside it. The answer will be written on top, one digit above each digit we divide.9 ) 12.6
- Start with the first 2 digits, 12. 9 does not go into the first digit, so we take digits from the left until we have a number that 9 can go into.12 ÷ 9 = 1 remainder 3 (since 9 × 1 = 9)
- The next digit is after the decimal point. Put a decimal point in the answer, then bring down 6 to make 36. The decimal point in the answer goes directly above the decimal point in the question.36 ÷ 9 = 4 (since 9 × 4 = 36)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.1.4 1 3 9) 12.6
12.6 ÷ 9 = 1.4
Check. Multiply back: 1.4 × 9 = 12.6. ✓
Watch out. If 9 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 12 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 20.4 under the "bus stop" and 12 outside it. The answer will be written on top, one digit above each digit we divide.12 ) 20.4
- Start with the first 2 digits, 20. 12 does not go into the first digit, so we take digits from the left until we have a number that 12 can go into.20 ÷ 12 = 1 remainder 8 (since 12 × 1 = 12)
- The next digit is after the decimal point. Put a decimal point in the answer, then bring down 4 to make 84. The decimal point in the answer goes directly above the decimal point in the question.84 ÷ 12 = 7 (since 12 × 7 = 84)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.1.7 2 8 12) 20.4
20.4 ÷ 12 = 1.7
Check. Multiply back: 1.7 × 12 = 20.4. ✓
Watch out. If 12 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.
- Make the number you are dividing by a whole number. Multiplying both numbers by 10 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.7.2 ÷ 0.4 = 72 ÷ 4
(7.2 × 10 = 72 and 0.4 × 10 = 4) - Set out the division. Write 72 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.4 ) 72
- Start with the first digit, 7. Work from the left. We ask how many times 4 goes into 7.7 ÷ 4 = 1 remainder 3 (since 4 × 1 = 4)
- Bring down the next digit, 2, to make 32. The remainder 3 goes in front of the 2. This is the same as carrying the remainder to the next column.32 ÷ 4 = 8 (since 4 × 8 = 32)
- Write the answer. Read the digits along the top.18 3 4) 72
72 ÷ 4 = 18
Check. Multiply back: 18 × 4 = 72. ✓
Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.
- Make the number you are dividing by a whole number. Multiplying both numbers by 100 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.5.6 ÷ 0.07 = 560 ÷ 7
(5.6 × 100 = 560 and 0.07 × 100 = 7) - Set out the division. Write 560 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.7 ) 560
- Start with the first 2 digits, 56. 7 does not go into the first digit, so we take digits from the left until we have a number that 7 can go into.56 ÷ 7 = 8 (since 7 × 8 = 56)
- Bring down the next digit, 0. The remainder was 0, so the new number to divide is just that digit.7 does not go into 0, so write 0 and carry on.
- Write the answer. Read the digits along the top.80 5 7) 560
560 ÷ 7 = 80
Check. Multiply back: 80 × 7 = 560. ✓
Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 3 into each number in turn, carrying the remainder to the next digit.
- Make the number you are dividing by a whole number. Multiplying both numbers by 100 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.0.9 ÷ 0.03 = 90 ÷ 3
(0.9 × 100 = 90 and 0.03 × 100 = 3) - Set out the division. Write 90 under the "bus stop" and 3 outside it. The answer will be written on top, one digit above each digit we divide.3 ) 90
- Start with the first digit, 9. Work from the left. We ask how many times 3 goes into 9.9 ÷ 3 = 3 (since 3 × 3 = 9)
- Bring down the next digit, 0. The remainder was 0, so the new number to divide is just that digit.3 does not go into 0, so write 0 and carry on.
- Write the answer. Read the digits along the top.30 3) 90
90 ÷ 3 = 30
Check. Multiply back: 30 × 3 = 90. ✓
Watch out. If 3 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Long division: work from the left, dividing 15 into each number in turn, carrying the remainder to the next digit.
- Make the number you are dividing by a whole number. Multiplying both numbers by 10 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.4.5 ÷ 1.5 = 45 ÷ 15
(4.5 × 10 = 45 and 1.5 × 10 = 15) - Write out the 15 times table up to 15 × 9. Having the multiples ready makes it quick to see how many times 15 goes into each number.15 × 1 = 15
15 × 2 = 30
15 × 3 = 45
15 × 4 = 60
15 × 5 = 75
15 × 6 = 90
15 × 7 = 105
15 × 8 = 120
15 × 9 = 135 - Set out the division. Write 45 under the "bus stop" and 15 outside it. The answer will be written on top, one digit above each digit we divide.15 ) 45
- Start with the first 2 digits, 45. 15 does not go into the first digit, so we take digits from the left until we have a number that 15 can go into.15 goes into 45 3 times: 15 × 3 = 45
Subtract: 45 − 45 = 0 - Write the answer. Read the digits along the top.3 15) 45 45 -- 0
45 ÷ 15 = 3
Check. Multiply back: 3 × 15 = 45. ✓
Watch out. If 15 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Long division: work from the left, dividing 25 into each number in turn, carrying the remainder to the next digit.
- Make the number you are dividing by a whole number. Multiplying both numbers by 100 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.18 ÷ 0.25 = 1800 ÷ 25
(18 × 100 = 1800 and 0.25 × 100 = 25) - Write out the 25 times table up to 25 × 9. Having the multiples ready makes it quick to see how many times 25 goes into each number.25 × 1 = 25
25 × 2 = 50
25 × 3 = 75
25 × 4 = 100
25 × 5 = 125
25 × 6 = 150
25 × 7 = 175
25 × 8 = 200
25 × 9 = 225 - Set out the division. Write 1800 under the "bus stop" and 25 outside it. The answer will be written on top, one digit above each digit we divide.25 ) 1800
- Start with the first 3 digits, 180. 25 does not go into the first digit, so we take digits from the left until we have a number that 25 can go into.25 goes into 180 7 times: 25 × 7 = 175
Subtract: 180 − 175 = 5 - Bring down the next digit, 0, to make 50. The remainder 5 goes in front of the 0. This is the same as carrying the remainder to the next column.25 goes into 50 2 times: 25 × 2 = 50
Subtract: 50 − 50 = 0 - Write the answer. Read the digits along the top.72 25) 1800 175 --- 50 50 -- 0
1800 ÷ 25 = 72
Check. Multiply back: 72 × 25 = 1800. ✓
Watch out. If 25 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 12 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 156 under the "bus stop" and 12 outside it. The answer will be written on top, one digit above each digit we divide.12 ) 156
- Start with the first 2 digits, 15. 12 does not go into the first digit, so we take digits from the left until we have a number that 12 can go into.15 ÷ 12 = 1 remainder 3 (since 12 × 1 = 12)
- Bring down the next digit, 6, to make 36. The remainder 3 goes in front of the 6. This is the same as carrying the remainder to the next column.36 ÷ 12 = 3 (since 12 × 3 = 36)
- Write the answer. Read the digits along the top.13 13 12) 156
156 ÷ 12 = 13
Check. Multiply back: 13 × 12 = 156. ✓
Watch out. If 12 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Method. Divide, then think about the remainder. If everything must be fitted in, round the answer up. If only full groups count, round down.
- Decide the calculation. We are finding how many groups of 6 there are in 50. That is a division.50 ÷ 6
- Divide. Use short or long division. The remainder is what is left over.50 ÷ 6 = 8 remainder 2
(check: 6 × 8 = 48, and 50 − 48 = 2) - Decide what to do with the remainder. We only want full albums, so the 2 stickers left over are not counted. We round down.8 full albums
- Write the answer in words. 8 full albums
Check. Multiply back: 8 × 6 = 48, plus 2 left over = 50. ✓
Watch out. The remainder is not the answer. Ask yourself what the remainder means in the question: round up to fit everyone in, or down to count full groups only.
Method. Divide, then think about the remainder. If everything must be fitted in, round the answer up. If only full groups count, round down.
- Decide the calculation. We are finding how many groups of 53 there are in 420. That is a division.420 ÷ 53
- Divide. Use short or long division. The remainder is what is left over.420 ÷ 53 = 7 remainder 49
(check: 53 × 7 = 371, and 420 − 371 = 49) - Decide what to do with the remainder. There are 49 students left over. They still need somewhere to go, so one more coach is needed. We round up even though 49 is a small number.7 + 1 = 8
- Write the answer in words. 8 coaches
Check. 8 coaches holds up to 424 students (enough for 420), but 7 coaches holds only 371, which is not enough. ✓
Watch out. The remainder is not the answer. Ask yourself what the remainder means in the question: round up to fit everyone in, or down to count full groups only.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Short division: work from the left, dividing 5 into each number in turn, carrying the remainder to the next digit.
- Set out the division. Write 7.35 under the "bus stop" and 5 outside it. The answer will be written on top, one digit above each digit we divide.5 ) 7.35
- Start with the first digit, 7. Work from the left. We ask how many times 5 goes into 7.7 ÷ 5 = 1 remainder 2 (since 5 × 1 = 5)
- The next digit is after the decimal point. Put a decimal point in the answer, then bring down 3 to make 23. The decimal point in the answer goes directly above the decimal point in the question.23 ÷ 5 = 4 remainder 3 (since 5 × 4 = 20)
- Bring down the next digit, 5, to make 35. The remainder 3 goes in front of the 5. This is the same as carrying the remainder to the next column.35 ÷ 5 = 7 (since 5 × 7 = 35)
- Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.1.47 23 5) 7.35
7.35 ÷ 5 = 1.47
Check. Multiply back: 1.47 × 5 = 7.35. ✓
Watch out. If 5 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.
Method. Long division: work from the left, dividing 16 into each number in turn, carrying the remainder to the next digit.
- Write out the 16 times table up to 16 × 9. Having the multiples ready makes it quick to see how many times 16 goes into each number.16 × 1 = 16
16 × 2 = 32
16 × 3 = 48
16 × 4 = 64
16 × 5 = 80
16 × 6 = 96
16 × 7 = 112
16 × 8 = 128
16 × 9 = 144 - Set out the division. Write 2.4 under the "bus stop" and 16 outside it. The answer will be written on top, one digit above each digit we divide.16 ) 2.4
- Start with the first digit, 2. Work from the left. We ask how many times 16 goes into 2.16 does not go into 2, so write 0 in the answer.
- The next digit is after the decimal point. Put a decimal point in the answer, then bring down 4 to make 24. The decimal point in the answer goes directly above the decimal point in the question.16 goes into 24 1 time: 16 × 1 = 16
Subtract: 24 − 16 = 8 - There is a remainder of 8, so add a 0 on the end and bring it down to make 80. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.16 goes into 80 5 times: 16 × 5 = 80
Subtract: 80 − 80 = 0 - Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.0.15 16) 2.40 16 -- 80 80 -- 0
2.4 ÷ 16 = 0.15
Check. Multiply back: 0.15 × 16 = 2.4. ✓
Watch out. If 16 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.
Method. Dividing by 0.5 asks how many halves fit into 4. Halving is dividing by 2, not by 0.5.
- Say what Mia calculated. Half of 4 is 4 ÷ 2, not 4 ÷ 0.5.Mia worked out 4 ÷ 2 = 2.
- Say what the question asks. 4 ÷ 0.5 asks “how many halves are in 4?” There are 2 halves in every whole one.4 wholes × 2 halves in each = 8 halves
- Check with the written method. Multiply both numbers by 10 to make the divisor a whole number.4 ÷ 0.5 = 40 ÷ 5 = 8
Check. 8 × 0.5 = 4. ✓
Watch out. Dividing by a number smaller than 1 gives an answer bigger than the starting number.
Method. Write each division as a fraction. Multiplying the top and the bottom of a fraction by the same number gives an equivalent fraction.
- Write the division as a fraction. A division 7.2 ÷ 0.4 is the same as the fraction 7.2 over 0.4.7.20.4
- Multiply the top and the bottom by 10. Multiplying the top and bottom of a fraction by the same number gives an equivalent fraction, so its value does not change.7.20.4 = 7.2 × 100.4 × 10 = 724
- Work out the answer. 72 ÷ 4 = 18.7.2 ÷ 0.4 = 72 ÷ 4 = 18
Check. 18 × 0.4 = 7.2. ✓