GCSE Maths: Dividing decimals (Higher)

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   2 ) 0.8
2. Divide 0.8 by 2 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   0 ÷ 2 = 0 exactly
   Put the decimal point in the answer straight above the decimal point in the question.
   8 ÷ 2 = 4 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   0.8 ÷ 2 = 0.4

Check. Multiply back: 0.4 × 2 = 0.8. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   3 ) 6.9
2. Divide 6.9 by 3 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   6 ÷ 3 = 2 exactly
   Put the decimal point in the answer straight above the decimal point in the question.
   9 ÷ 3 = 3 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   6.9 ÷ 3 = 2.3

Check. Multiply back: 2.3 × 3 = 6.9. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   5 ) 0.45
2. Divide 0.45 by 5 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   0 ÷ 5 = 0 exactly
   Put the decimal point in the answer straight above the decimal point in the question.
   4 ÷ 5 = 0 remainder 4
   45 ÷ 5 = 9 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   0.45 ÷ 5 = 0.09

Check. Multiply back: 0.09 × 5 = 0.45. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   6 ) 12.6
2. Divide 12.6 by 6 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   1 ÷ 6 = 0 remainder 1
   12 ÷ 6 = 2 exactly
   Put the decimal point in the answer straight above the decimal point in the question.
   6 ÷ 6 = 1 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   12.6 ÷ 6 = 2.1

Check. Multiply back: 2.1 × 6 = 12.6. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   8 ) 4.8
2. Divide 4.8 by 8 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   4 ÷ 8 = 0 remainder 4
   Put the decimal point in the answer straight above the decimal point in the question.
   48 ÷ 8 = 6 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   4.8 ÷ 8 = 0.6

Check. Multiply back: 0.6 × 8 = 4.8. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   7 ) 9.1
2. Divide 9.1 by 7 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   9 ÷ 7 = 1 remainder 2
   Put the decimal point in the answer straight above the decimal point in the question.
   21 ÷ 7 = 3 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   9.1 ÷ 7 = 1.3

Check. Multiply back: 1.3 × 7 = 9.1. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   4 ) 5.6
2. Divide 5.6 by 4 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   5 ÷ 4 = 1 remainder 1
   Put the decimal point in the answer straight above the decimal point in the question.
   16 ÷ 4 = 4 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   5.6 ÷ 4 = 1.4

Check. Multiply back: 1.4 × 4 = 5.6. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   3 ) 9.45
2. Divide 9.45 by 3 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   9 ÷ 3 = 3 exactly
   Put the decimal point in the answer straight above the decimal point in the question.
   4 ÷ 3 = 1 remainder 1
   15 ÷ 3 = 5 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   9.45 ÷ 3 = 3.15

Check. Multiply back: 3.15 × 3 = 9.45. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   9 ) 0.72
2. Divide 0.72 by 9 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   0 ÷ 9 = 0 exactly
   Put the decimal point in the answer straight above the decimal point in the question.
   7 ÷ 9 = 0 remainder 7
   72 ÷ 9 = 8 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   0.72 ÷ 9 = 0.08

Check. Multiply back: 0.08 × 9 = 0.72. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   5 ) 13.5
2. Divide 13.5 by 5 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   1 ÷ 5 = 0 remainder 1
   13 ÷ 5 = 2 remainder 3
   Put the decimal point in the answer straight above the decimal point in the question.
   35 ÷ 5 = 7 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   13.5 ÷ 5 = 2.7

Check. Multiply back: 2.7 × 5 = 13.5. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   8 ) 1.2
2. Divide 1.2 by 8 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   1 ÷ 8 = 0 remainder 1
   Put the decimal point in the answer straight above the decimal point in the question.
   12 ÷ 8 = 1 remainder 4
   40 ÷ 8 = 5 exactly (an extra zero added after the decimal point)
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   1.2 ÷ 8 = 0.15

Check. Multiply back: 0.15 × 8 = 1.2. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide a decimal by a whole number, use short division and keep the decimal point in line.

1. Set up the short division. Write the number being divided under the bus stop and the divisor outside it. The decimal point in the answer will sit directly above the decimal point in the question.
   9 ) 2.07
2. Divide 2.07 by 9 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   2 ÷ 9 = 0 remainder 2
   Put the decimal point in the answer straight above the decimal point in the question.
   20 ÷ 9 = 2 remainder 2
   27 ÷ 9 = 3 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   2.07 ÷ 9 = 0.23

Check. Multiply back: 0.23 × 9 = 2.07. ✓

Watch out. Keep the decimal point in the answer directly above the decimal point in the question, and do not forget to add zeros if a remainder is left.

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide by a decimal, first multiply both numbers by 10, 100... so that the divisor is a whole number. Then use short division, keeping the decimal point in line.

1. Make the number you divide by (the divisor) a whole number: multiply both numbers by 10. Multiplying both numbers by the same thing does not change the answer (it works like equivalent fractions), and dividing by a whole number is much easier.
   6 × 10 = 60
   0.3 × 10 = 3
   So 6 ÷ 0.3 = 60 ÷ 3
2. Divide 60 by 3 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   6 ÷ 3 = 2 exactly
   0 ÷ 3 = 0 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   60 ÷ 3 = 20

Check. Multiply back: 20 × 0.3 = 6. ✓

Watch out. You must multiply both numbers by the same power of 10. 6 ÷ 0.3 becomes 60 ÷ 3 (not 6 ÷ 3).

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide by a decimal, first multiply both numbers by 10, 100... so that the divisor is a whole number. Then use short division, keeping the decimal point in line.

1. Make the number you divide by (the divisor) a whole number: multiply both numbers by 10. Multiplying both numbers by the same thing does not change the answer (it works like equivalent fractions), and dividing by a whole number is much easier.
   2.4 × 10 = 24
   0.6 × 10 = 6
   So 2.4 ÷ 0.6 = 24 ÷ 6
2. Divide 24 by 6 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   2 ÷ 6 = 0 remainder 2
   24 ÷ 6 = 4 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   24 ÷ 6 = 4

Check. Multiply back: 4 × 0.6 = 2.4. ✓

Watch out. You must multiply both numbers by the same power of 10. 6 ÷ 0.3 becomes 60 ÷ 3 (not 6 ÷ 3).

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide by a decimal, first multiply both numbers by 10, 100... so that the divisor is a whole number. Then use short division, keeping the decimal point in line.

1. Make the number you divide by (the divisor) a whole number: multiply both numbers by 100. Multiplying both numbers by the same thing does not change the answer (it works like equivalent fractions), and dividing by a whole number is much easier.
   0.84 × 100 = 84
   0.07 × 100 = 7
   So 0.84 ÷ 0.07 = 84 ÷ 7
2. Divide 84 by 7 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   8 ÷ 7 = 1 remainder 1
   14 ÷ 7 = 2 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   84 ÷ 7 = 12

Check. Multiply back: 12 × 0.07 = 0.84. ✓

Watch out. You must multiply both numbers by the same power of 10. 6 ÷ 0.3 becomes 60 ÷ 3 (not 6 ÷ 3).

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide by a decimal, first multiply both numbers by 10, 100... so that the divisor is a whole number. Then use short division, keeping the decimal point in line.

1. Make the number you divide by (the divisor) a whole number: multiply both numbers by 100. Multiplying both numbers by the same thing does not change the answer (it works like equivalent fractions), and dividing by a whole number is much easier.
   1.5 × 100 = 150
   0.05 × 100 = 5
   So 1.5 ÷ 0.05 = 150 ÷ 5
2. Divide 150 by 5 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   1 ÷ 5 = 0 remainder 1
   15 ÷ 5 = 3 exactly
   0 ÷ 5 = 0 exactly
3. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   150 ÷ 5 = 30

Check. Multiply back: 30 × 0.05 = 1.5. ✓

Watch out. You must multiply both numbers by the same power of 10. 6 ÷ 0.3 becomes 60 ÷ 3 (not 6 ÷ 3).

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide by a decimal, first multiply both numbers by 10, 100... so that the divisor is a whole number. Then use short division, keeping the decimal point in line.

1. Make the number you divide by (the divisor) a whole number: multiply both numbers by 100. Multiplying both numbers by the same thing does not change the answer (it works like equivalent fractions), and dividing by a whole number is much easier.
   9 × 100 = 900
   0.15 × 100 = 15
   So 9 ÷ 0.15 = 900 ÷ 15
2. Write the multiples of 15 to help. You will need to know how many times the divisor goes into each number, so list the first nine multiples.
   1: 15, 2: 30, 3: 45, 4: 60, 5: 75, 6: 90, 7: 105, 8: 120, 9: 135
3. Divide 900 by 15 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   9 ÷ 15 = 0 remainder 9
   90 ÷ 15 = 6 exactly
   0 ÷ 15 = 0 exactly
4. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   900 ÷ 15 = 60

Check. Multiply back: 60 × 0.15 = 9. ✓

Watch out. You must multiply both numbers by the same power of 10. 6 ÷ 0.3 becomes 60 ÷ 3 (not 6 ÷ 3).

Key words. The divisor is the number you divide by. The quotient is the answer to a division. The remainder is what is left over.

Method. To divide by a decimal, first multiply both numbers by 10, 100... so that the divisor is a whole number. Then use short division, keeping the decimal point in line.

1. Make the number you divide by (the divisor) a whole number: multiply both numbers by 100. Multiplying both numbers by the same thing does not change the answer (it works like equivalent fractions), and dividing by a whole number is much easier.
   4.2 × 100 = 420
   0.35 × 100 = 35
   So 4.2 ÷ 0.35 = 420 ÷ 35
2. Write the multiples of 35 to help. You will need to know how many times the divisor goes into each number, so list the first nine multiples.
   1: 35, 2: 70, 3: 105, 4: 140, 5: 175, 6: 210, 7: 245, 8: 280, 9: 315
3. Divide 420 by 35 using short division (the bus stop method), working left to right. At each digit: put any remainder in front of the next digit, divide, and write the answer on top. If a remainder is left at the end of the number, add zeros after the decimal point and keep going. Adding zeros after the decimal point does not change the value.
   4 ÷ 35 = 0 remainder 4
   42 ÷ 35 = 1 remainder 7
   70 ÷ 35 = 2 exactly
4. Read the quotient (the answer on top). Write the digits you found, with the decimal point in the position shown.
   420 ÷ 35 = 12

Check. Multiply back: 12 × 0.35 = 4.2. ✓

Watch out. You must multiply both numbers by the same power of 10. 6 ÷ 0.3 becomes 60 ÷ 3 (not 6 ÷ 3).

Method. Use the fact you know. Work out how each number has been multiplied or divided by a power of 10 and what that does to the answer.

1. Compare the first numbers (the ones being divided). See what has happened to the number being divided, compared with the fact you know.
   9.6 = 96 ÷ 10
2. Compare the second numbers (the divisors). Do the same for the number you divide by.
   8 is the same as 8, so nothing changes.
3. Work out what each change does to the answer. Making the number being divided 10 times bigger makes the answer 10 times bigger. Making the divisor 10 times bigger makes the answer 10 times smaller, because it fits in fewer times.
   First number: the answer is divided by 10.
   Divisor: no change.
4. Combine the changes and update the known answer. Start from the known answer 96 ÷ 8 = 12.
   12 ÷ 10 = 1.2

Check. Multiply back: 1.2 × 8 = 9.6. ✓

Watch out. Making the divisor smaller makes the answer bigger, so changes to the divisor work the opposite way round to changes to the number being divided.

Method. Use the fact you know. Work out how each number has been multiplied or divided by a power of 10 and what that does to the answer.

1. Compare the first numbers (the ones being divided). See what has happened to the number being divided, compared with the fact you know.
   0.96 = 96 ÷ 100
2. Compare the second numbers (the divisors). Do the same for the number you divide by.
   8 is the same as 8, so nothing changes.
3. Work out what each change does to the answer. Making the number being divided 10 times bigger makes the answer 10 times bigger. Making the divisor 10 times bigger makes the answer 10 times smaller, because it fits in fewer times.
   First number: the answer is divided by 100.
   Divisor: no change.
4. Combine the changes and update the known answer. Start from the known answer 96 ÷ 8 = 12.
   12 ÷ 100 = 0.12

Check. Multiply back: 0.12 × 8 = 0.96. ✓

Watch out. Making the divisor smaller makes the answer bigger, so changes to the divisor work the opposite way round to changes to the number being divided.

Method. Use the fact you know. Work out how each number has been multiplied or divided by a power of 10 and what that does to the answer.

1. Compare the first numbers (the ones being divided). See what has happened to the number being divided, compared with the fact you know.
   960 = 96 × 10
2. Compare the second numbers (the divisors). Do the same for the number you divide by.
   0.8 = 8 ÷ 10
3. Work out what each change does to the answer. Making the number being divided 10 times bigger makes the answer 10 times bigger. Making the divisor 10 times bigger makes the answer 10 times smaller, because it fits in fewer times.
   First number: the answer is multiplied by 10.
   Divisor: the answer is multiplied by 10.
4. Combine the changes and update the known answer. Start from the known answer 96 ÷ 8 = 12.
   12 × 100 = 1200

Check. Multiply back: 1200 × 0.8 = 960. ✓

Watch out. Making the divisor smaller makes the answer bigger, so changes to the divisor work the opposite way round to changes to the number being divided.

Method. Use the fact you know. Work out how each number has been multiplied or divided by a power of 10 and what that does to the answer.

1. Compare the first numbers (the ones being divided). See what has happened to the number being divided, compared with the fact you know.
   0.96 = 96 ÷ 100
2. Compare the second numbers (the divisors). Do the same for the number you divide by.
   0.08 = 8 ÷ 100
3. Work out what each change does to the answer. Making the number being divided 10 times bigger makes the answer 10 times bigger. Making the divisor 10 times bigger makes the answer 10 times smaller, because it fits in fewer times.
   First number: the answer is divided by 100.
   Divisor: the answer is multiplied by 100.
4. Combine the changes. The two changes cancel out, so the answer is the same as the one you know.
   12

Check. Multiply back: 12 × 0.08 = 0.96. ✓

Watch out. Making the divisor smaller makes the answer bigger, so changes to the divisor work the opposite way round to changes to the number being divided.