Year 2: Inverse checks and missing numbers
Part of the Year 2 adding and subtracting chapter. Chapter overview · whole chapter on one page
Inverse checks and missing numbers
Adding and taking away undo each other. We call this the inverse.
If 46 + 27 = 73, then 73 − 27 must give 46. Use this to check your answer.
A missing number is shown with a box. Do the opposite to find it.
Key ideas
- Check an addition by taking away one part from the total.
- Check a take-away by adding back.
- To find a missing number, do the opposite.
- Put the number in the box to check the sum.
Method. Check an addition by taking away one of the parts from the total.
- Write the check. Take 27 away from 73, the total.73 − 27
- Work it out. The answer should be the first number, 46.73 − 27 = 46
- Compare. It matches the first number, so the addition is correct.46 = 46
Check. 46 + 27 = 73, and 73 − 27 = 46. ✓
Watch out. The inverse of adding is taking away. Use it to check.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.? + 15 = 40
- Do the opposite to find it. To undo adding 15, take 15 away from 40.40 − 15 = 25
- Check it in the sum. Put the number in the box and see if it works.25 + 15 = 40
Check. 25 + 15 = 40. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.50 − ? = 28
- Do the opposite to find it. The box is the part to take away. Take 28 from 50.50 − 28 = 22
- Check it in the sum. Put the number in the box and see if it works.50 − 22 = 28
Check. 50 − 22 = 28. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Watch out
Watch out: for 50 − ? = 28, the box is 22. Do not add 50 and 28.
Exam tip
Grown-up tip. Write 46 + 27 = 73 on paper. Ask: “What is 73 take away 27?” Then check it together.
Exercise 2F Inverse checks and missing numbers
Non-calculatorMethod. Check an addition by taking away one of the parts from the total.
- Write the check. Take 27 away from 73, the total.73 − 27
- Work it out. The answer should be the first number, 46.73 − 27 = 46
- Compare. It matches the first number, so the addition is correct.46 = 46
Check. 46 + 27 = 73, and 73 − 27 = 46. ✓
Watch out. The inverse of adding is taking away. Use it to check.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.? + 15 = 40
- Do the opposite to find it. To undo adding 15, take 15 away from 40.40 − 15 = 25
- Check it in the sum. Put the number in the box and see if it works.25 + 15 = 40
Check. 25 + 15 = 40. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.50 − ? = 28
- Do the opposite to find it. The box is the part to take away. Take 28 from 50.50 − 28 = 22
- Check it in the sum. Put the number in the box and see if it works.50 − 22 = 28
Check. 50 − 22 = 28. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.? − 18 = 36
- Do the opposite to find it. To undo taking 18 away, add 18 to 36.36 + 18 = 54
- Check it in the sum. Put the number in the box and see if it works.54 − 18 = 36
Check. 54 − 18 = 36. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.38 + ? = 70
- Do the opposite to find it. To undo adding 38, take 38 away from 70.70 − 38 = 32
- Check it in the sum. Put the number in the box and see if it works.38 + 32 = 70
Check. 38 + 32 = 70. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.64 − ? = 40
- Do the opposite to find it. The box is the part to take away. Take 40 from 64.64 − 40 = 24
- Check it in the sum. Put the number in the box and see if it works.64 − 24 = 40
Check. 64 − 24 = 40. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. Work out the sum or difference, then compare it with what was said.
- Work out 75 − 39. Use a method that you know.75 − 39 = 36
- Compare with the claim. The claim says 36, and that matches.Yes. 75 − 39 = 36
Check. Add 39 to 36. You get 75. ✓
Watch out. Check the tens first, then the ones. A carry or an exchange is easy to forget.
Method. Work out the sum or difference, then compare it with what was said.
- Work out 40 + 27. Use a method that you know.40 + 27 = 67
- Compare with the claim. The claim says 58, but the answer is 67.No. 40 + 27 = 67
Check. Take 27 away from 67. You get 40. ✓
Watch out. Check the tens first, then the ones. A carry or an exchange is easy to forget.
Method. Work out the sum or difference, then compare it with what was said.
- Work out 58 − 23. Use a method that you know.58 − 23 = 35
- Compare with the claim. The claim says 35, and that matches.Yes. 58 − 23 = 35
Check. Add 23 to 35. You get 58. ✓
Watch out. Check the tens first, then the ones. A carry or an exchange is easy to forget.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.? + 25 = 60
- Do the opposite to find it. To undo adding 25, take 25 away from 60.60 − 25 = 35
- Check it in the sum. Put the number in the box and see if it works.35 + 25 = 60
Check. 35 + 25 = 60. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. The box is a number we do not know. Do the opposite to find it.
- Read the sum with the box. The box stands for the missing number.80 − ? = 45
- Do the opposite to find it. The box is the part to take away. Take 45 from 80.80 − 45 = 35
- Check it in the sum. Put the number in the box and see if it works.80 − 35 = 45
Check. 80 − 35 = 45. ✓
Watch out. Adding undoes taking away. Taking away undoes adding.
Method. Find the missing number. Then put it back in the sum to check.
- Do the opposite. To find the box, take 24 away from 50.50 − 24 = 26
- Check Leo’s answer. If the box is 74, then 74 + 24 would be much more than 50.74 + 24 = 98
- Write the answer. Leo is wrong. The missing number is 26.No. The missing number is 26.
Check. 26 + 24 = 50. ✓
Watch out. Do not add the two numbers you can see. Take one away from the total.
Method. The same box must work in both sums.
- Find the box in the first sum. Take 10 away from 35.35 − 10 = 25
- Check the second sum. The second box must also be 25.35 − 25 = 10
- Write the answer. Both sums work with 25.25
Check. 25 + 10 = 35, and 35 − 25 = 10. ✓
Watch out. Check both sums with the same number.