Year 4: Estimating and checking your answers
Part of the Year 4 column addition and subtraction chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Estimating and checking your answers
Before you do a calculation, it helps to estimate the answer. An estimate is a good guess that is close to the real answer. To estimate, round the numbers to the nearest 10, 100 or 1000, then do the easy calculation. For 3,874 + 2,129, round to the nearest 1000: 4,000 + 2,000 = 6,000. We write 3,874 + 2,129 ≈ 6,000. The sign ≈ means “is about equal to”.
An estimate tells you if your answer is sensible. If your exact answer is not close to your estimate, you have made a mistake somewhere. Rounding to the nearest 100 gives a closer estimate than rounding to the nearest 1000, but it is a bit harder.
Checking with the inverse. Addition and subtraction are inverse (opposite) operations. They undo each other. If 4,644 + 2,486 = 7,130, then 7,130 − 2,486 should take us back to 4,644. The four numbers make a fact family.
The fact family: 4,644 + 2,486 = 7,130 2,486 + 4,644 = 7,130 7,130 − 2,486 = 4,644 7,130 − 4,644 = 2,486.
Missing numbers. To find a missing number in a sum like ? + 2,486 = 7,130, think of a bar model. The whole is 7,130. One part is 2,486. The other part is the missing number, so take the part away from the whole: 7,130 − 2,486.
Key words. An estimate is a close answer. Inverse operations are opposites. Sensible means that the answer is the right sort of size.
Key ideas
- To estimate, round each number (to the nearest 10, 100 or 1000), then do the easy calculation.
- ≈ means “is about equal to”.
- An exact answer should be close to the estimate. If not, check your working.
- Addition and subtraction are inverses: if a + b = c, then c − b = a.
- Use a bar model to find a missing number: find a part by subtracting, find a whole by adding.
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 3,874 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.3,874 ≈ 4,000 (the hundreds digit is 8, so round up)
- Round 2,129 to the nearest 1,000. Do the same for the second number.2,129 ≈ 2,000 (the hundreds digit is 1, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.4,000 + 2,000 = 6,000
Check. The exact answer is 6,003. It is close to the estimate of 6,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 100, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 6,548 to the nearest 100. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.6,548 ≈ 6,500 (the tens digit is 4, so round down)
- Round 2,891 to the nearest 100. Do the same for the second number.2,891 ≈ 2,900 (the tens digit is 9, so round up)
- Do the easy calculation. Rounded numbers are easy to add or subtract.6,500 − 2,900 = 3,600
Check. The exact answer is 3,657. It is close to the estimate of 3,600. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Method. Estimate the answer by rounding. If Jack’s answer is nowhere near the estimate, it cannot be right.
- Round both numbers. Round to the nearest 100 so the sum is easy.5,423 ≈ 5,400 (the tens digit is 2, so round down)
2,687 ≈ 2,700 (the tens digit is 8, so round up) - Work out the estimate. 5,400 − 2,700 = 2,700
- Compare with Jack’s answer. Jack got 3,264. The estimate says the answer should be close to 2,700.3,264 is a long way from 2,700, so it is not sensible.
- Find the correct answer. Use the column method carefully.
Th H T O 4 513 411 213 3− 2 6 8 7 2 7 3 6
5,423 − 2,687 = 2,736
Check. The correct answer 2,736 is close to the estimate 2,700. ✓
Watch out. Always ask: is my answer about the right size? An estimate takes a few seconds and can catch big mistakes.
Key words. Inverse operations are opposites. Addition is the inverse of subtraction, and subtraction is the inverse of addition.
Method. Use the inverse (opposite) operation to check. Addition and subtraction undo each other. If you go back, you should reach the number you started with.
- Write Sam’s answer as an inverse calculation. The opposite operation should take us back to the first number.4,518 + 2,787 = 7,205 so 7,205 − 2,787 should be 4,518
- Work it out. Use the column method.7,205 − 2,787 = 4,418
Th H T O 6 711 29 015 5− 2 7 8 7 4 4 1 8 - Compare. We should get 4,518.We got 4,418. 4,418 is not 4,518, so Sam is wrong.
- Find the correct answer. Do the original calculation again.4,518 + 2,787 = 7,305
Th H T O 4 5 1 8 + 2 7 8 7 7 3 0 5 1 1 1
Check. The correct answer is 7,305. 7,305 − 2,787 = 4,518. ✓
Watch out. The inverse of + is −. The inverse of − is +. If the check does not work, one of the calculations has a mistake.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.? + 2,486 = 7,130
- Draw a bar model. The whole is the total, and we know one part. The other part is the missing number.
- Choose the operation. To find a missing part, take the part we know away from the whole.7,130 − 2,486
- Work it out. Use the column method if the numbers are big.7,130 − 2,486 = 4,644
Th H T O 6 710 112 310 0− 2 4 8 6 4 6 4 4 - Check in the number sentence. Put the answer back in the box.4,644 + 2,486 = 7,130 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.5,000 − ? = 3,276
- Draw a bar model. The whole is the first number. The missing number is one of the parts.
- Choose the operation. To find a missing part, take the part we know away from the whole.5,000 − 3,276
- Work it out. Use the column method if the numbers are big.5,000 − 3,276 = 1,724
Th H T O 4 59 09 010 0− 3 2 7 6 1 7 2 4 - Check in the number sentence. Put the answer back in the box.5,000 − 1,724 = 3,276 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Watch out
An estimate is not the exact answer, so do not expect it to match exactly. It should only be close. And when you check with the inverse, use the opposite sign: check an addition by subtracting, and check a subtraction by adding.Exercise 2D Estimating, inverse operations and missing numbers
Non-calculatorKey words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 100, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 3,482 to the nearest 100. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.3,482 ≈ 3,500 (the tens digit is 8, so round up)
- Round 4,617 to the nearest 100. Do the same for the second number.4,617 ≈ 4,600 (the tens digit is 1, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.3,500 + 4,600 = 8,100
Check. The exact answer is 8,099. It is close to the estimate of 8,100. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 100, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 7,940 to the nearest 100. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.7,940 ≈ 7,900 (the tens digit is 4, so round down)
- Round 2,318 to the nearest 100. Do the same for the second number.2,318 ≈ 2,300 (the tens digit is 1, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.7,900 − 2,300 = 5,600
Check. The exact answer is 5,622. It is close to the estimate of 5,600. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 100, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 5,286 to the nearest 100. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.5,286 ≈ 5,300 (the tens digit is 8, so round up)
- Round 3,714 to the nearest 100. Do the same for the second number.3,714 ≈ 3,700 (the tens digit is 1, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.5,300 + 3,700 = 9,000
Check. The exact answer is 9,000. It is close to the estimate of 9,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 100, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 8,503 to the nearest 100. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.8,503 ≈ 8,500 (the tens digit is 0, so round down)
- Round 4,279 to the nearest 100. Do the same for the second number.4,279 ≈ 4,300 (the tens digit is 7, so round up)
- Do the easy calculation. Rounded numbers are easy to add or subtract.8,500 − 4,300 = 4,200
Check. The exact answer is 4,224. It is close to the estimate of 4,200. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 3,482 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.3,482 ≈ 3,000 (the hundreds digit is 4, so round down)
- Round 4,617 to the nearest 1,000. Do the same for the second number.4,617 ≈ 5,000 (the hundreds digit is 6, so round up)
- Do the easy calculation. Rounded numbers are easy to add or subtract.3,000 + 5,000 = 8,000
Check. The exact answer is 8,099. It is close to the estimate of 8,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 7,940 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.7,940 ≈ 8,000 (the hundreds digit is 9, so round up)
- Round 2,318 to the nearest 1,000. Do the same for the second number.2,318 ≈ 2,000 (the hundreds digit is 3, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.8,000 − 2,000 = 6,000
Check. The exact answer is 5,622. It is close to the estimate of 6,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 5,286 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.5,286 ≈ 5,000 (the hundreds digit is 2, so round down)
- Round 3,714 to the nearest 1,000. Do the same for the second number.3,714 ≈ 4,000 (the hundreds digit is 7, so round up)
- Do the easy calculation. Rounded numbers are easy to add or subtract.5,000 + 4,000 = 9,000
Check. The exact answer is 9,000. It is close to the estimate of 9,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 8,503 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.8,503 ≈ 9,000 (the hundreds digit is 5, so round up)
- Round 4,279 to the nearest 1,000. Do the same for the second number.4,279 ≈ 4,000 (the hundreds digit is 2, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.9,000 − 4,000 = 5,000
Check. The exact answer is 4,224. It is close to the estimate of 5,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Method. Round both numbers, work out an easy estimate, then find the choice that is closest.
- Round the numbers to the nearest 1,000. Rounded numbers are quick to add or subtract.6,184 ≈ 6,000 (the hundreds digit is 1, so round down)
2,897 ≈ 3,000 (the hundreds digit is 8, so round up) - Work out the estimate. 6,000 − 3,000 = 3,000
- Choose the closest answer. The choices are very different sizes, so only one can be close.A: 300
B: 3,000 (close to the estimate)
C: 9,000
D: 30,000
Check. The exact answer is 3,287, which is close to 3,000. ✓
Watch out. You do not need the exact answer. Round, work out the easy sum, and look for the closest choice.
Method. Round both numbers, work out an easy estimate, then find the choice that is closest.
- Round the numbers to the nearest 1,000. Rounded numbers are quick to add or subtract.3,806 ≈ 4,000 (the hundreds digit is 8, so round up)
4,189 ≈ 4,000 (the hundreds digit is 1, so round down) - Work out the estimate. 4,000 + 4,000 = 8,000
- Choose the closest answer. The choices are very different sizes, so only one can be close.A: 800
B: 8,000 (close to the estimate)
C: 80,000
D: 4,000
Check. The exact answer is 7,995, which is close to 8,000. ✓
Watch out. You do not need the exact answer. Round, work out the easy sum, and look for the closest choice.
Method. The inverse of addition is subtraction. Start with the answer and take away one of the numbers you added.
- Write the calculation and its answer. The answer is the whole.4,208 + 1,563 = 5,771
- Take one part away from the whole. This undoes the addition and takes us back to the other part.5,771 − 1,563 = 4,208
Th H T O 5 7 6 711 1− 1 5 6 3 4 2 0 8 - Write the inverse calculation. 5,771 − 1,563 = 4,208 (or 5,771 − 4,208 = 1,563)
Check. It works because 4,208 is what is left when you take 1,563 from 5,771. ✓
Watch out. The inverse of + is −. Start with the biggest number, the answer.
Method. The inverse of subtraction is addition. Add the number you took away back on to the answer.
- Write the calculation and its answer. The number we started with is the whole.9,020 − 3,475 = 5,545
- Add the part back on. This undoes the subtraction and takes us back to the start.5,545 + 3,475 = 9,020
- Write the inverse calculation. 5,545 + 3,475 = 9,020
Check. Check: 9,020 − 5,545 = 3,475, the number we took away. ✓
Watch out. The inverse of − is +. The answer to the subtraction plus the number taken away makes the number you started with.
Method. The inverse of addition is subtraction. Start with the answer and take away one of the numbers you added.
- Write the calculation and its answer. The answer is the whole.2,750 + 3,860 = 6,610
- Take one part away from the whole. This undoes the addition and takes us back to the other part.6,610 − 3,860 = 2,750
Th H T O 5 615 611 10 − 3 8 6 0 2 7 5 0 - Write the inverse calculation. 6,610 − 3,860 = 2,750 (or 6,610 − 2,750 = 3,860)
Check. It works because 2,750 is what is left when you take 3,860 from 6,610. ✓
Watch out. The inverse of + is −. Start with the biggest number, the answer.
Method. The inverse of subtraction is addition. Add the number you took away back on to the answer.
- Write the calculation and its answer. The number we started with is the whole.6,000 − 1,245 = 4,755
- Add the part back on. This undoes the subtraction and takes us back to the start.4,755 + 1,245 = 6,000
- Write the inverse calculation. 4,755 + 1,245 = 6,000
Check. Check: 6,000 − 4,755 = 1,245, the number we took away. ✓
Watch out. The inverse of − is +. The answer to the subtraction plus the number taken away makes the number you started with.
Key words. Inverse operations are opposites. Addition is the inverse of subtraction, and subtraction is the inverse of addition.
Method. Use the inverse (opposite) operation to check. Addition and subtraction undo each other. If you go back, you should reach the number you started with.
- Write Aisha’s answer as an inverse calculation. The opposite operation should take us back to the first number.3,604 + 2,718 = 6,322 so 6,322 − 2,718 should be 3,604
- Work it out. Use the column method.6,322 − 2,718 = 3,604
Th H T O 5 613 31 212 2− 2 7 1 8 3 6 0 4 - Compare. We should get 3,604.We got 3,604. 3,604 = 3,604, so Aisha is correct.
Check. The correct answer is 6,322. Aisha was right. ✓
Watch out. The inverse of + is −. The inverse of − is +. If the check does not work, one of the calculations has a mistake.
Key words. Inverse operations are opposites. Addition is the inverse of subtraction, and subtraction is the inverse of addition.
Method. Use the inverse (opposite) operation to check. Addition and subtraction undo each other. If you go back, you should reach the number you started with.
- Write Aisha’s answer as an inverse calculation. The opposite operation should take us back to the first number.7,005 − 2,864 = 4,241 so 4,241 + 2,864 should be 7,005
- Work it out. Use the column method.4,241 + 2,864 = 7,105
Th H T O 4 2 4 1 + 2 8 6 4 7 1 0 5 1 1 - Compare. We should get 7,005.We got 7,105. 7,105 is not 7,005, so Aisha is wrong.
- Find the correct answer. Do the original calculation again.7,005 − 2,864 = 4,141
Th H T O 6 79 010 05 − 2 8 6 4 4 1 4 1
Check. The correct answer is 4,141. 4,141 + 2,864 = 7,005. ✓
Watch out. The inverse of + is −. The inverse of − is +. If the check does not work, one of the calculations has a mistake.
Key words. Inverse operations are opposites. Addition is the inverse of subtraction, and subtraction is the inverse of addition.
Method. Use the inverse (opposite) operation to check. Addition and subtraction undo each other. If you go back, you should reach the number you started with.
- Write Aisha’s answer as an inverse calculation. The opposite operation should take us back to the first number.5,190 + 3,844 = 9,034 so 9,034 − 3,844 should be 5,190
- Work it out. Use the column method.9,034 − 3,844 = 5,190
Th H T O 8 99 013 34 − 3 8 4 4 5 1 9 0 - Compare. We should get 5,190.We got 5,190. 5,190 = 5,190, so Aisha is correct.
Check. The correct answer is 9,034. Aisha was right. ✓
Watch out. The inverse of + is −. The inverse of − is +. If the check does not work, one of the calculations has a mistake.
Key words. Inverse operations are opposites. Addition is the inverse of subtraction, and subtraction is the inverse of addition.
Method. Use the inverse (opposite) operation to check. Addition and subtraction undo each other. If you go back, you should reach the number you started with.
- Write Aisha’s answer as an inverse calculation. The opposite operation should take us back to the first number.8,300 − 4,568 = 3,832 so 3,832 + 4,568 should be 8,300
- Work it out. Use the column method.3,832 + 4,568 = 8,400
Th H T O 3 8 3 2 + 4 5 6 8 8 4 0 0 1 1 1 - Compare. We should get 8,300.We got 8,400. 8,400 is not 8,300, so Aisha is wrong.
- Find the correct answer. Do the original calculation again.8,300 − 4,568 = 3,732
Th H T O 7 812 39 010 0− 4 5 6 8 3 7 3 2
Check. The correct answer is 3,732. 3,732 + 4,568 = 8,300. ✓
Watch out. The inverse of + is −. The inverse of − is +. If the check does not work, one of the calculations has a mistake.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.? + 2,500 = 6,000
- Draw a bar model. The whole is the total, and we know one part. The other part is the missing number.
- Choose the operation. To find a missing part, take the part we know away from the whole.6,000 − 2,500
- Work it out. Use the column method if the numbers are big.6,000 − 2,500 = 3,500
Th H T O 5 610 00 0 − 2 5 0 0 3 5 0 0 - Check in the number sentence. Put the answer back in the box.3,500 + 2,500 = 6,000 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.1,850 + ? = 4,000
- Draw a bar model. The whole is the total, and we know one part. The other part is the missing number.
- Choose the operation. To find a missing part, take the part we know away from the whole.4,000 − 1,850
- Work it out. Use the column method if the numbers are big.4,000 − 1,850 = 2,150
Th H T O 3 49 010 00 − 1 8 5 0 2 1 5 0 - Check in the number sentence. Put the answer back in the box.1,850 + 2,150 = 4,000 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.? − 1,275 = 2,140
- Draw a bar model. The missing number is the whole. It is made of the two parts we know.
- Choose the operation. To find the whole, add the two parts together.2,140 + 1,275
- Work it out. Use the column method if the numbers are big.2,140 + 1,275 = 3,415
Th H T O 2 1 4 0 + 1 2 7 5 3 4 1 5 1 - Check in the number sentence. Put the answer back in the box.3,415 − 1,275 = 2,140 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.9,000 − ? = 6,785
- Draw a bar model. The whole is the first number. The missing number is one of the parts.
- Choose the operation. To find a missing part, take the part we know away from the whole.9,000 − 6,785
- Work it out. Use the column method if the numbers are big.9,000 − 6,785 = 2,215
Th H T O 8 99 09 010 0− 6 7 8 5 2 2 1 5 - Check in the number sentence. Put the answer back in the box.9,000 − 2,215 = 6,785 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Method. Draw a bar model, then use the inverse (opposite) operation to find the missing number.
- Look at the number sentence. The box stands for the number we want to find.3,450 + ? = 8,000
- Draw a bar model. The whole is the total, and we know one part. The other part is the missing number.
- Choose the operation. To find a missing part, take the part we know away from the whole.8,000 − 3,450
- Work it out. Use the column method if the numbers are big.8,000 − 3,450 = 4,550
Th H T O 7 89 010 00 − 3 4 5 0 4 5 5 0 - Check in the number sentence. Put the answer back in the box.3,450 + 4,550 = 8,000 ✓
Check. Read the whole number sentence with your answer in the box. It must be true. ✓
Watch out. The missing number is not always the last number. Think about which number is the whole, then decide whether to add or subtract.
Key words. To estimate is to find an answer that is close, usually by rounding the numbers first. ≈ means “is about equal to”.
Method. Round both numbers to the nearest 1,000, then work out the easy calculation. The answer is only an estimate (a good guess), so it will not be exact.
- Round 3,892 to the nearest 1,000. Look at the digit just to the right. 5 or more: round up. 4 or less: round down.3,892 ≈ 4,000 (the hundreds digit is 8, so round up)
- Round 4,127 to the nearest 1,000. Do the same for the second number.4,127 ≈ 4,000 (the hundreds digit is 1, so round down)
- Do the easy calculation. Rounded numbers are easy to add or subtract.4,000 + 4,000 = 8,000
Check. The exact answer is 8,019. It is close to the estimate of 8,000. ✓
Watch out. An estimate is not the exact answer. Use the sign ≈ (about equal to).
Key words. Column addition is a written method. You write the numbers one under the other, with ones under ones, tens under tens and so on, and add one column at a time. When a column adds up to 10 or more, you carry the tens into the next column.
Method. Write the numbers in columns with the same place values lined up. Add the ones first, then the tens, the hundreds and the thousands. If a column makes 10 or more, carry to the next column.
- Line up the digits in columns. Ones go under ones, tens under tens, hundreds under hundreds and thousands under thousands. Then every digit is added to a digit with the same value.
Th H T O 3 8 9 2 + 4 1 2 7 - Add the ones. Always start with the ones, on the right.2 + 7 = 9
9 is less than 10, so write 9 in the ones column. There is nothing to carry. - Add the tens. Now the next column to the left.9 + 2 = 11
11 is 1 hundred and 1 ten. Write 1 in the tens column and carry 1 to the hundreds column. - Add the hundreds. Now the next column to the left. Add the 1 we carried as well.8 + 1 + 1 = 10
10 is 1 thousand and 0 hundreds. Write 0 in the hundreds column and carry 1 to the thousands column. - Add the thousands. Now the next column to the left. Add the 1 we carried as well.3 + 4 + 1 = 8
8 is less than 10, so write 8 in the thousands column. There is nothing to carry. - Read the answer. Check the answer has the right number of digits, then write it.
Th H T O 3 8 9 2 + 4 1 2 7 8 0 1 9 1 1
3,892 + 4,127 = 8,019
Check. Use the opposite (inverse) operation: 8,019 − 4,127 = 3,892. ✓
Estimate: 4,000 + 4,000 = 8,000 (rounding to the nearest 1,000). It is close to the exact answer. ✓
Watch out. Do not forget the carried digits. Write each one small under the answer line, and add it in the next column.
Method. Round both numbers to the nearest 100 and add. Then find the exact total to be sure.
- Round both numbers to the nearest 100. The tens digit tells us whether to round up or down.4,780 ≈ 4,800 (the tens digit is 8, so round up)
4,390 ≈ 4,400 (the tens digit is 9, so round up) - Add the rounded numbers. This is the estimate.4,800 + 4,400 = 9,200
- Work out the exact total. The estimate is only close, so we need the exact total to be sure.4,780 + 4,390 = 9,170
Th H T O 4 7 8 0 + 4 3 9 0 9 1 7 0 1 1 - Answer. 9,170 is more than 9,000.Anil is right: 9,170 tickets were sold, which is 170 more than the 9,000 seats.
Check. 9,170 − 4,390 = 4,780. ✓
Watch out. An estimate cannot always decide a question. If the estimate is very close to the limit, work out the exact answer too.
Method. Estimate the answer by rounding. If Mia’s answer is nowhere near the estimate, it cannot be right.
- Round both numbers. Round to the nearest 100 so the sum is easy.3,785 ≈ 3,800 (the tens digit is 8, so round up)
2,648 ≈ 2,600 (the tens digit is 4, so round down) - Work out the estimate. 3,800 + 2,600 = 6,400
- Compare with Mia’s answer. Mia got 5,323. The estimate says the answer should be close to 6,400.5,323 is a long way from 6,400, so it is not sensible.
- Find the correct answer. Use the column method carefully.
Th H T O 3 7 8 5 + 2 6 4 8 6 4 3 3 1 1 1
3,785 + 2,648 = 6,433
Check. The correct answer 6,433 is close to the estimate 6,400. ✓
Watch out. Always ask: is my answer about the right size? An estimate takes a few seconds and can catch big mistakes.
Method. Look at what happened to each number when it was rounded. Did it go up or down?
- Compare each number with its rounded number. If a number was rounded up, the rounded number is bigger than the real one.3,640 was rounded up to 4,000 (4,000 is 360 more)
2,580 was rounded up to 3,000 (3,000 is 420 more) - Decide what that means for the total. Both numbers were made bigger, so the estimate is bigger than the exact answer.The estimate (7,000) is more than the exact answer.
- Check with the exact total. 3,640 + 2,580 = 6,220
Th H T O 3 6 4 0 + 2 5 8 0 6 2 2 0 1 1
Check. 6,220 is less than 7,000. ✓
Watch out. If you round both numbers up, your estimate is too big. If you round both down, it is too small.
Method. Try some examples to see if you can find an estimate that is exact, and one that is not.
- Try numbers that are already round. Rounding does not change them.3,000 + 2,000: rounding to the nearest 1000 gives 3,000 + 2,000 = 5,000, and the exact answer is 5,000. They match.
- Try numbers that are not round. Rounding changes them.3,456 + 2,100: rounding to the nearest 1000 gives 3,000 + 2,000 = 5,000, but the exact answer is 5,556. They do not match.
- Decide. We found one example of each.Sometimes
Check. Another match: 3,449 + 2,451 ≈ 3,000 + 2,000 = 5,000 but the exact answer is 5,900, so that one does not match either. Matches only happen by luck or with round numbers. ✓
Watch out. “Sometimes” needs two examples: one that works and one that does not.
Method. 8,000 has 0 tens, so look at the tens digits first. This quickly cuts down the pairs to try. Then check the pairs that are left.
- Look at the tens digits. The tens digits of the two numbers must add up to 10 (or 0), to make 0 tens in the answer. All the ones digits are 0 already.Tens digits: 2,870 → 7, 3,640 → 4, 4,360 → 6, 5,250 → 5, 3,150 → 5
- Find the pairs whose tens digits add to 10. 4 + 6 = 10 and 5 + 5 = 10. No other pair works.3,640 and 4,360
5,250 and 3,150 - Add each pair that is left. Use the column method or partitioning.3,640 + 4,360 = 8,000 8,000!
5,250 + 3,150 = 8,400 - Write the answer. 3,640 and 4,360
Check. 3,640 + 4,360 = 8,000. ✓ The estimate agrees: 4,000 + 4,000 = 8,000.
Watch out. Do not stop at the first pair that looks right. Check that the total is exactly 8,000.