IMOClass 2 › Addition (2-digit)

Addition (2-digit)

Adding Without Carrying

To add 2-digit numbers, add the ones first, then the tens. When the ones add up to less than 10, there is no carrying. For example, 23 + 14: ones 3 + 4 = 7, tens 2 + 1 = 3, so the answer is 37.

Addition can be done in any order: 23 + 14 is the same as 14 + 23.

Example 1: Add: 42 + 35.
Ones 2 + 5 = 7, tens 4 + 3 = 7, so 42 + 35 = 77.
Example 2: Add: 51 + 6.
Ones 1 + 6 = 7, tens stays 5, so 51 + 6 = 57.
Quick recap
  • Add ones first, then tens.
  • Order does not change the sum: a + b = b + a.
✓ Quick check
Add: 34 + 25 = ?
Ones 4 + 5 = 9, tens 3 + 2 = 5, so 59.
Add: 60 + 7 = ?
60 + 7 = 67.

Adding With Carrying

When the ones add up to 10 or more, we carry the ten over to the tens place. For 28 + 16: ones 8 + 6 = 14, write 4 and carry 1 ten. Tens: 2 + 1 + 1 (carried) = 4, so the answer is 44.

Example 1: Add: 47 + 38.
Ones 7 + 8 = 15, write 5 carry 1; tens 4 + 3 + 1 = 8, so 85.
Example 2: Add: 56 + 9.
Ones 6 + 9 = 15, write 5 carry 1; tens 5 + 1 = 6, so 65.
Quick recap
  • If ones make 10 or more, carry 1 to the tens.
  • Add the carried ten with the other tens.
✓ Quick check
Add: 29 + 14 = ?
Ones 9 + 4 = 13, write 3 carry 1; tens 2 + 1 + 1 = 4, so 43.
Add: 38 + 27 = ?
Ones 8 + 7 = 15, write 5 carry 1; tens 3 + 2 + 1 = 6, so 65.

Adding Three Numbers & Word Problems

We can add three numbers by adding two of them first, then adding the third. In word problems, words like in all, altogether and total tell us to add.

Example 1: Add: 12 + 13 + 5.
12 + 13 = 25, then 25 + 5 = 30.
Example 2: Riya has 24 stickers and gets 18 more. How many in all?
24 + 18 = 42 stickers.
Quick recap
  • Add three numbers two at a time.
  • 'In all / altogether / total' means add.
✓ Quick check
Add: 10 + 20 + 30 = ?
10 + 20 = 30, then 30 + 30 = 60.
A box has 15 red and 17 blue balls. How many balls in all?
15 + 17 = 32 balls.
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