Step-by-step Maths Level 5: Estimating with the tables, and checking
Part of the Step-by-step Maths Level 5 short division with remainders chapter. Chapter overview · whole chapter on one page
Estimating with the tables, and checking
To estimate, find the multiples of the number you divide by that are either side of the number. 47 ÷ 5: 5 × 9 = 45 and 5 × 10 = 50, so the answer is 9 with a remainder.
To check, multiply the whole number of groups by the divisor and add the remainder. You should get the number you started with.
Key ideas
- Use the table of the divisor to estimate.
- Check: groups × divisor + remainder = the number.
- The remainder must be smaller than the divisor.
Method. Find the multiple of the divisor that is just below the number. It tells you the whole number of groups.
- Count in 5s. Keep counting until you go past 47.5, 10, ... up to 47
- Find the largest multiple. It is the last multiple that is not more than the number.45 is not more than 47
- Write the multiple. This is the number that helps you find the division.45
Check. Check: 9 × 5 = 45, and 45 is not more than 47.
Watch out. Do not pick the multiple just above the number; it is more than the number.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 5 are in 47. Use the times table of the divisor.9 groups of 5 = 45
- Find what is left over. The remainder is the number left after the groups.47 - 45 = 2
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.9 × 5 + 2 = 45 + 2 = 47
- Write the answer. This is the answer with its remainder.9 remainder 2
Check. Check: 9 × 5 + 2 = 47.
Watch out. If the check does not give the number you started with, divide again.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.9 × 5 + 2 = 47
- Compare with 47. The result must be 47, and the remainder must be smaller than 5.47 is the same as 47; 2 is smaller than 5
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 9 remainder 2.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Watch out
Watch out. 9 remainder 7 is not correct for 47 ÷ 5. The remainder must be less than 5.
Exam tip
Grown-up tip. Ask the child to check every answer by multiplying back, using the same times table.
Exercise 5D Practice: estimating and checking divisions
Non-calculatorMethod. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.4 × 7 + 6 = 34
- Compare with 41. The result must be 41, and the remainder must be smaller than 7.34 is not the same as 41; 6 is smaller than 7
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 5 remainder 6.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Find the multiple of the divisor that is just below the number. It tells you the whole number of groups.
- Count in 5s. Keep counting until you go past 53.5, 10, ... up to 53
- Find the largest multiple. It is the last multiple that is not more than the number.50 is not more than 53
- Write the multiple. This is the number that helps you find the division.50
Check. Check: 10 × 5 = 50, and 50 is not more than 53.
Watch out. Do not pick the multiple just above the number; it is more than the number.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 7 are in 29. Use the times table of the divisor.4 groups of 7 = 28
- Find what is left over. The remainder is the number left after the groups.29 - 28 = 1
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.4 × 7 + 1 = 28 + 1 = 29
- Write the answer. This is the answer with its remainder.4 remainder 1
Check. Check: 4 × 7 + 1 = 29.
Watch out. If the check does not give the number you started with, divide again.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.16 × 3 + 0 = 48
- Compare with 48. The result must be 48, and the remainder must be smaller than 3.48 is the same as 48; 0 is smaller than 3
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 16.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.21 × 4 + 0 = 84
- Compare with 88. The result must be 88, and the remainder must be smaller than 4.84 is not the same as 88; 0 is smaller than 4
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 22.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 8 are in 22. Use the times table of the divisor.2 groups of 8 = 16
- Find what is left over. The remainder is the number left after the groups.22 - 16 = 6
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.2 × 8 + 6 = 16 + 6 = 22
- Write the answer. This is the answer with its remainder.2 remainder 6
Check. Check: 2 × 8 + 6 = 22.
Watch out. If the check does not give the number you started with, divide again.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 7 are in 38. Use the times table of the divisor.5 groups of 7 = 35
- Find what is left over. The remainder is the number left after the groups.38 - 35 = 3
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.5 × 7 + 3 = 35 + 3 = 38
- Write the answer. This is the answer with its remainder.5 remainder 3
Check. Check: 5 × 7 + 3 = 38.
Watch out. If the check does not give the number you started with, divide again.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.1 × 4 + 3 = 7
- Compare with 10. The result must be 10, and the remainder must be smaller than 4.7 is not the same as 10; 3 is smaller than 4
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 2 remainder 2.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Find the multiple of the divisor that is just below the number. It tells you the whole number of groups.
- Count in 3s. Keep counting until you go past 87.3, 6, ... up to 87
- Find the largest multiple. It is the last multiple that is not more than the number.87 is not more than 87
- Write the multiple. This is the number that helps you find the division.87
Check. Check: 29 × 3 = 87, and 87 is not more than 87.
Watch out. Do not pick the multiple just above the number; it is more than the number.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 2 are in 74. Use the times table of the divisor.37 groups of 2 = 74
- Find what is left over. The remainder is the number left after the groups.74 - 74 = 0
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.37 × 2 + 0 = 74 + 0 = 74
- Write the answer. This is the answer with its remainder.37
Check. Check: 37 × 2 + 0 = 74.
Watch out. If the check does not give the number you started with, divide again.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.12 × 8 + 2 = 98
- Compare with 98. The result must be 98, and the remainder must be smaller than 8.98 is the same as 98; 2 is smaller than 8
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 12 remainder 2.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.11 × 6 + 4 = 70
- Compare with 70. The result must be 70, and the remainder must be smaller than 6.70 is the same as 70; 4 is smaller than 6
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 11 remainder 4.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.11 × 9 + 7 = 106
- Compare with 97. The result must be 97, and the remainder must be smaller than 9.106 is not the same as 97; 7 is smaller than 9
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 10 remainder 7.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Divide, then check: answer × divisor + remainder = the number we started with.
- Find how many groups of 2 are in 56. Use the times table of the divisor.28 groups of 2 = 56
- Find what is left over. The remainder is the number left after the groups.56 - 56 = 0
- Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.28 × 2 + 0 = 56 + 0 = 56
- Write the answer. This is the answer with its remainder.28
Check. Check: 28 × 2 + 0 = 56.
Watch out. If the check does not give the number you started with, divide again.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.17 × 5 + 2 = 87
- Compare with 82. The result must be 82, and the remainder must be smaller than 5.87 is not the same as 82; 2 is smaller than 5
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 16 remainder 2.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.
Method. Check with multiplication and addition: groups × divisor + remainder must equal the number, and the remainder must be smaller than the divisor.
- Multiply the whole number of groups by the divisor, then add the remainder. Check with multiplication and addition.14 × 3 + 2 = 44
- Compare with 47. The result must be 47, and the remainder must be smaller than 3.44 is not the same as 47; 2 is smaller than 3
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 15 remainder 2.
Watch out. A remainder that is as big as the divisor means the answer is wrong. Find the mistake if the check does not work.