Step-by-step Maths Level 5 Long multiplication of two-digit by one-digit numbers: Estimating and checking
Part of the Step-by-step Maths Level 5 long multiplication of two-digit by one-digit numbers chapter. Chapter overview · whole chapter on one page
Estimating and checking
An estimate uses numbers that are easy to multiply, such as a multiple of 10. 38 × 6 is about 40 × 6 = 240.
Check a product by dividing the answer by one of the numbers. You should get the other number back.
Key ideas
- Round to a number that is easy to multiply.
- The exact answer should be close to the estimate.
- Check a product by division.
Method. Round to a number that is easy to multiply, then calculate.
- Round 38 to the nearest 10. Look at the ones digit: 5 or more rounds up.38 is about 40
- Multiply the rounded number. Use a fact we know from the tables.40 × 6 = 240
- Write the estimate. The exact answer should be close to this.240
Check. The exact answer is 228, which is close to 240.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 7. If the multiplication is right, dividing by the same number gives back the first number.168 ÷ 7 = 24
- Compare with 24. Is the answer 24?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 168.
Watch out. Find the mistake in the columns if the check does not work.
Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.
- Multiply the ones digit by 4. Write 8 in the ones column and carry 2 to the tens column.7 × 4 = 28
- Multiply the tens digit by 4. Write 2 in the tens column and carry 2 to the hundreds column.5 × 4 = 20, plus 2 carried = 22
- Write the carried number in front. The carried number is the next digit on the left.2 in the hundreds column
- Write the answer. Read the digits from the bottom of each column, from the left.228
Check. Check: 228 ÷ 4 = 57.
Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.
Watch out
Watch out. An estimate tells you whether the answer is about right, not whether it is exact.
Exam tip
Grown-up tip. Ask: “Is the answer close to the estimate?” before the child checks the exact answer.
Exercise 4D Practice: estimating and checking
Non-calculatorMethod. Round to a number that is easy to multiply, then calculate.
- Round 91 to the nearest 10. Look at the ones digit: 5 or more rounds up.91 is about 90
- Multiply the rounded number. Use a fact we know from the tables.90 × 2 = 180
- Write the estimate. The exact answer should be close to this.180
Check. The exact answer is 182, which is close to 180.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Round to a number that is easy to multiply, then calculate.
- Round 66 to the nearest 10. Look at the ones digit: 5 or more rounds up.66 is about 70
- Multiply the rounded number. Use a fact we know from the tables.70 × 8 = 560
- Write the estimate. The exact answer should be close to this.560
Check. The exact answer is 528, which is close to 560.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Round to a number that is easy to multiply, then calculate.
- Round 56 to the nearest 10. Look at the ones digit: 5 or more rounds up.56 is about 60
- Multiply the rounded number. Use a fact we know from the tables.60 × 6 = 360
- Write the estimate. The exact answer should be close to this.360
Check. The exact answer is 336, which is close to 360.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 5. If the multiplication is right, dividing by the same number gives back the first number.520 ÷ 5 = 104
- Compare with 64. Is the answer 64?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 320.
Watch out. Find the mistake in the columns if the check does not work.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 6. If the multiplication is right, dividing by the same number gives back the first number.582 ÷ 6 = 97
- Compare with 97. Is the answer 97?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 582.
Watch out. Find the mistake in the columns if the check does not work.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 4. If the multiplication is right, dividing by the same number gives back the first number.69 ÷ 4 = 17 remainder 1
- Compare with 17. Is the answer 17?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 68.
Watch out. Find the mistake in the columns if the check does not work.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 5. If the multiplication is right, dividing by the same number gives back the first number.447 ÷ 5 = 89 remainder 2
- Compare with 89. Is the answer 89?Not the same
- Write Yes or No. Yes if the check works; No if it does not.No
Check. The correct answer is 445.
Watch out. Find the mistake in the columns if the check does not work.
Method. Round to a number that is easy to multiply, then calculate.
- Round 52 to the nearest 10. Look at the ones digit: 5 or more rounds up.52 is about 50
- Multiply the rounded number. Use a fact we know from the tables.50 × 7 = 350
- Write the estimate. The exact answer should be close to this.350
Check. The exact answer is 364, which is close to 350.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Round to a number that is easy to multiply, then calculate.
- Round 71 to the nearest 10. Look at the ones digit: 5 or more rounds up.71 is about 70
- Multiply the rounded number. Use a fact we know from the tables.70 × 9 = 630
- Write the estimate. The exact answer should be close to this.630
Check. The exact answer is 639, which is close to 630.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Round to a number that is easy to multiply, then calculate.
- Round 55 to the nearest 10. Look at the ones digit: 5 or more rounds up.55 is about 60
- Multiply the rounded number. Use a fact we know from the tables.60 × 6 = 360
- Write the estimate. The exact answer should be close to this.360
Check. The exact answer is 330, which is close to 360.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 7. If the multiplication is right, dividing by the same number gives back the first number.273 ÷ 7 = 39
- Compare with 39. Is the answer 39?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 273.
Watch out. Find the mistake in the columns if the check does not work.
Method. Round to a number that is easy to multiply, then calculate.
- Round 13 to the nearest 10. Look at the ones digit: 5 or more rounds up.13 is about 10
- Multiply the rounded number. Use a fact we know from the tables.10 × 9 = 90
- Write the estimate. The exact answer should be close to this.90
Check. The exact answer is 117, which is close to 90.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Round to a number that is easy to multiply, then calculate.
- Round 44 to the nearest 10. Look at the ones digit: 5 or more rounds up.44 is about 40
- Multiply the rounded number. Use a fact we know from the tables.40 × 9 = 360
- Write the estimate. The exact answer should be close to this.360
Check. The exact answer is 396, which is close to 360.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 8. If the multiplication is right, dividing by the same number gives back the first number.480 ÷ 8 = 60
- Compare with 60. Is the answer 60?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 480.
Watch out. Find the mistake in the columns if the check does not work.
Method. Round to a number that is easy to multiply, then calculate.
- Round 90 to the nearest 10. Look at the ones digit: 5 or more rounds up.90 is about 90
- Multiply the rounded number. Use a fact we know from the tables.90 × 8 = 720
- Write the estimate. The exact answer should be close to this.720
Check. The exact answer is 720, which is close to 720.
Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.
Method. Check a multiplication by division: the answer divided by one factor gives the other factor.
- Divide the answer by 3. If the multiplication is right, dividing by the same number gives back the first number.48 ÷ 3 = 16
- Compare with 16. Is the answer 16?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 48.
Watch out. Find the mistake in the columns if the check does not work.