Rounding and Adjusting

Add the round number, then give back the change.

Add the round number, then put it right

29 is awkward to add, but 30 is easy, and 29 is only 1 less than 30. So to work out 45 + 29, add 30 instead: 45 + 30 = 75. That added 1 too many, so take the 1 away: 75 − 1 = 74.

The answer is exact, not a guess. Adding 30 and then taking 1 away adds exactly 29, so 45 + 29 = 74. The move pays off on numbers ending in 8 or 9, which sit just below a round number.

Which round number?

Any round number gets to the answer. Add 40 and give back 11: 45 + 40 = 85, and 85 − 11 = 74. Add 20 and put on 9 more: 45 + 20 = 65, and 65 + 9 = 74. The nearest ten to 29 is 30, and it leaves only 1 to put right, so 30 is the one to use.

405060708090100110120+ 29+ 40− 114545 + 29 = 74

45 + 29 = 45 + 40 − 11: adding 40 overshoots by 11, so 11 is given back and the total stays 74

Move the round jump to leave the least to adjust

Whichever round jump is made, putting right the difference lands on 74. The jump of 30 leaves the least to put right.

Hundreds work the same way

98 is 2 less than 100, so 47 + 98 = 47 + 100 − 2 = 145. The number taken off is always the gap between the round number and the number you meant to add. For 98 that gap is 2. For 77 it would be 23, and taking off 23 is no easier than adding 77.

406080100120140160+ 100− 234747 + 77 = 124

adding 100 and then subtracting 100 − b is the same as adding b, so the total is exact; here the correction is 23

Make the correction 2

The jump is always 100. The step back is 100 take away the number being added, so the closer that number is to 100, the shorter the step back.

Taking away

Subtraction works the same way, but the correction goes the other way. For 62 − 19, take away 20: 62 − 20 = 42. That took away 1 more than 19, so give the 1 back: 42 + 1 = 43.

Keep the two directions apart. Adding a round number that is too big adds too much, so the extra is taken off. Taking away a round number that is too big takes away too much, so the extra is added back.

3570−20+162

For 62 − 19, a hop back of 20 lands on 42, and a hop forward of 1 lands on 43.

Worked example: Prices Just Below a Hundred

Question Mrs Tan buys a fan for $56 and a kettle for $99. (a) How much do the fan and the kettle cost together? (b) She then buys a chair for $198. How much does she spend altogether?

  1. 1.99 is 1 less than 100, so add 100 first: 56 + 100 = 156.

    56156+100
    56156+100
    99 is 1 less than 100, so add 100 first: 56 + 100 = 156.

  2. 2.(a) That is 1 too many, so take 1 away: 156 − 1 = 155. The fan and the kettle cost $155 together.

    56156155+100back 1(a) 56 + 100 − 1 = $155
    56156155+100back 1(a) 56 + 100 − 1 = $155
    (a) That is 1 too many. 156 − 1 = 155, so the two cost $155.

  3. 3.198 is 2 less than 200, so add 200 first: 155 + 200 = 355.

    56156155+100back 1155355+200(a) 56 + 100 − 1 = $155
    56156155+100back 1155355+200(a) 56 + 100 − 1 = $155
    198 is 2 less than 200, so add 200 first: 155 + 200 = 355.

  4. 4.(b) That is 2 too many, so take 2 away: 355 − 2 = 353. She spends $353 altogether.

    56156155+100back 1155355353+200back 2(a) 56 + 100 − 1 = $155(b) 155 + 200 − 2 = $353
    56156155+100back 1155355353+200back 2(a) 56 + 100 − 1 = $155(b) 155 + 200 − 2 = $353
    (b) That is 2 too many. 355 − 2 = 353, so she spends $353.

Answer: (a) $155; (b) $353

Common mistakes

  • Adding 100 and then adding 1 more to get 157. Adding 100 was already 1 more than the price, so the 1 is taken away.
  • Taking away 1 for the chair as well. 198 is 2 less than 200, so the extra to take away is 2.

More adding and subtracting in your head problems, worked step by step →

Worked example: A Slip in a Pupil's Mental Subtraction

Question Ben has 245 stickers and gives away 98. He works out how many are left in his head. He says: 245 − 100 = 145, then 145 − 2 = 143. (a) How many stickers does Ben really have left? (b) How far is Ben's answer from the right answer?

  1. 1.Ben's first line is right. 98 is close to 100, and 245 − 100 = 145.

    245145143−100−2Ben: 245 − 100 = 145, then 145 − 2 = 143
    245145143−100−2Ben: 245 − 100 = 145, then 145 − 2 = 143
    The first line is right:245 − 100 = 145.

  2. 2.Ben took away 100, but he gives away only 98. He took away 2 stickers too many, so 145 is 2 too small.

    245145143−100−2He took away 100. He gives away only 98.
    245145143−100−2He took away 100. He gives away only 98.
    He took away 2 stickers too many, so 145 is 2 too small.

  3. 3.(a) Add the 2 back: 145 + 2 = 147. Ben really has 147 stickers left. Check: 147 + 100 − 2 = 245.

    245145143147−100−2+2(a) 145 + 2 = 147 stickers
    245145143147−100−2+2(a) 145 + 2 = 147 stickers
    (a) Add the 2 back: 145 + 2 = 147 stickers.

  4. 4.(b) Ben took away 2 more instead and got 143. 147 − 143 = 4, so his answer is 4 too small.

    245145143147−100−2+2(a) 145 + 2 = 147 stickers(b) 147 − 143 = 4 too small
    245145143147−100−2+2(a) 145 + 2 = 147 stickers(b) 147 − 143 = 4 too small
    (b) Ben took away 2 more and got 143. 147 − 143 = 4.

Answer: (a) 147 stickers; (b) 4

Common mistakes

  • Saying that Ben's answer is only 2 away. He moved 2 the wrong way from 145, and the right answer is 2 the other way, so the two answers are 4 apart.
  • Adjusting the same way as in an addition. After adding 100 in place of 98, the 2 is taken away. After taking away 100 in place of 98, the 2 is added back.

More adding and subtracting in your head problems, worked step by step →

Practice Rounding and Adjusting in the app