More addition & subtraction
Addition: regrouping tens and reordering
We add every day. The way you add often depends on the numbers. Here you add 2-digit and 3-digit numbers, regrouping the ones or the tens, and reorder numbers to make adding easier.
Regrouping the ones
When the ones add up to 10 or more, you regroup 10 ones as 1 ten. Example: 67 + 29. The ones are 7 + 9 = 16 ones. That is 1 ten and 6 ones. Carry the new ten across to the tens column.
Regrouping the tens
When the tens add up to 10 tens or more, you regroup 10 tens as 1 hundred. Example: 84 + 62. The tens are 8 tens + 6 tens = 14 tens. That is 1 hundred and 4 tens. This is the new idea in this unit.
Estimate first
Before you add, round each number to the nearest 10 and add those. The estimate tells you roughly what the answer should be. Example: for 645 + 272, round to 650 + 270 = 920. Your real answer should be close to 920.
Reorder to add
Addition is commutative and associative, so you can add numbers in any order. Look for pairs that make a ten, add them first, then add on the rest. Example: 8 + 5 + 2 → add 8 + 2 = 10 first, then 10 + 5 = 15.
Worked examples
Regrouping the ones
- Add 67 + 29.
- Ones: 7 + 9 = 16 ones = 1 ten and 6 ones.
- Tens: 60 + 20 + the new 10 = 90.
- Put the parts together: 90 + 6.
Answer: 67 + 29 = 96
Regrouping the tens
- Add 84 + 62.
- Ones: 4 + 2 = 6.
- Tens: 8 tens + 6 tens = 14 tens = 1 hundred and 4 tens.
- Put the parts together: 100 + 40 + 6.
Answer: 84 + 62 = 146
Estimate then add a 3-digit sum
- Add 645 + 272.
- Estimate: 650 + 270 = 920.
- Decompose: 645 = 600 + 40 + 5 and 272 = 200 + 70 + 2.
- Add: 800 + 110 + 7 = 917 (close to the estimate of 920).
Answer: 645 + 272 = 917
Reorder to add
- Add 3 + 7 + 2 + 9.
- Find a pair that makes a ten: 3 + 7 = 10.
- Add on the rest: 10 + 9 = 19, then 19 + 2 = 21.
Answer: 3 + 7 + 2 + 9 = 21
Where you see this in real life
- Adding the fiction and non-fiction books in a library.
- Adding the scores of dancers in a competition.
- Adding the prices of things you buy in a shop.
Key words
- Regroup
- To swap 10 ones for 1 ten, or 10 tens for 1 hundred, when a column has too many.
- Exchange
- Another word for regroup — trading 10 of one place value for 1 of the next.
- Column addition
- Adding numbers by lining up the ones, tens and hundreds and adding each column.
- Commutative
- You can add numbers in any order and get the same total.
- Associative
- You can group numbers in any way when adding and get the same total.
- Estimate
- A close guess of the answer, often found by rounding to the nearest 10.