Adding by Splitting

Tens with tens, ones with ones, then together.

Split both numbers

To add 34 + 25 in your head, split each number into tens and ones. 34 is 3 tens and 4 ones, which is 30 + 4. 25 is 2 tens and 5 ones, which is 20 + 5.

3425

34 is 3 tens and 4 ones. 25 is 2 tens and 5 ones.

Tens with tens, ones with ones

Now add the tens together: 30 + 20 = 50. Then add the ones together: 4 + 5 = 9. Put the two parts back together: 50 + 9 = 59. So 34 + 25 = 59.

This works because addition is commutative: the parts can be added in any order. 30 + 4 + 20 + 5 has the same total as 30 + 20 + 4 + 5, and the second order puts the tens side by side and the ones side by side.

Keep tens with tens and ones with ones. Adding a ten to a one, such as 30 + 5, mixes the parts, and then one part is easily counted twice or left out.

30 + 20 = 504 + 5 = 934 + 25 = 59

The tens of both numbers go together, 30 + 20 = 50, and the ones go together, 4 + 5 = 9. Then 50 + 9 = 59.

When the ones make ten or more

For 47 + 36, the tens give 40 + 30 = 70 and the ones give 7 + 6 = 13. 13 is 1 ten and 3 ones, so it is added to the 70: 70 + 13 = 83.

Do not write the two answers side by side. 7 tens and 13 ones written next to each other read 713, which is far too big: two numbers below 50 add up to less than 100.

40 + 30 = 707 + 6 = 1347 + 36 = 83

The tens make 70 and the ones make 13. The 13 ones are 1 ten and 3 more, so 70 + 13 = 83.

4736tensonesnext stepstart again

47 + 36

Add 47 + 36 by splitting

Step through 47 + 36: the tens go together, then the ones. The 13 ones hold a full ten, which bundles into one more rod: 70 + 13 = 83.

Hundreds too

Three-digit numbers split into hundreds, tens and ones, and each part is added to the same part. For 231 + 426: 200 + 400 = 600, 30 + 20 = 50 and 1 + 6 = 7, so 231 + 426 = 657.

Worked example: Stickers in Two Albums

Question Ali has 46 stickers in his red album and 38 stickers in his blue album. His sister has 253 stickers in one album and 145 stickers in another album. (a) How many stickers does Ali have? (b) How many stickers does his sister have?

  1. 1.Split each of Ali's numbers into tens and ones. 46 is 40 and 6. 38 is 30 and 8.

    TensOnes4640638308
    TensOnes4640638308
    46 is 40 and 6. 38 is 30 and 8.
  2. 2.Add the tens: 40 + 30 = 70. Add the ones: 6 + 8 = 14.

    TensOnes4640638308Add7014
    TensOnes4640638308Add7014
    The tens make 40 + 30 = 70. The ones make 6 + 8 = 14.
  3. 3.(a) 70 + 14 = 84, so Ali has 84 stickers.

    TensOnes4640638308Add7014(a) 70 + 14 = 84 stickers
    TensOnes4640638308Add7014(a) 70 + 14 = 84 stickers
    (a) 70 + 14 = 84 stickers.
  4. 4.Split his sister's numbers into hundreds, tens and ones, and add each part: 200 + 100 = 300, 50 + 40 = 90 and 3 + 5 = 8.

    HundredsTensOnes253200503145100405Add300908(a) 70 + 14 = 84 stickers
    HundredsTensOnes253200503145100405Add300908(a) 70 + 14 = 84 stickers
    The hundreds make 300, the tens make 90 and the ones make 8.
  5. 5.(b) 300 + 90 + 8 = 398, so his sister has 398 stickers.

    HundredsTensOnes253200503145100405Add300908(a) 70 + 14 = 84 stickers(b) 300 + 90 + 8 = 398 stickers
    HundredsTensOnes253200503145100405Add300908(a) 70 + 14 = 84 stickers(b) 300 + 90 + 8 = 398 stickers
    (b) 300 + 90 + 8 = 398 stickers.

Answer: (a) 84 stickers; (b) 398 stickers

Common mistakes

  • Writing the two sums side by side as 714. The 14 ones are 1 ten and 4 ones, so they are added to the 70: 70 + 14 = 84.
  • Adding a tens part to a ones part, such as 40 + 8. Tens are added to tens and ones are added to ones, so that no part is used twice or left out.

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

Practice Adding by Splitting in the app