Too big for one column
Set out 47 + 28 in columns, ones under ones and tens under tens, and start with the ones: 7 + 8 = 15.
Each place in the answer holds only one digit, and 15 has two digits. So 15 cannot all be written in the ones column.
The ones column holds 7 and 8, which make 15.
Ten ones make a ten
15 ones are 1 ten and 5 ones. The 5 ones stay in the ones column, so write 5 under the line. The 1 ten belongs with the other tens, so write a small 1 above the tens column.
Moving the ten into the tens column is called carrying. The carried 1 is a real ten: 10 of the ones have been swapped for 1 ten.
fewer than ten ones: the ones digit counts them, the tens digit is 0, and 10 = 1 ten is not yet reached
Drop ten ones, then drag the bundle into the tens column
Add ones to the ones column until there are 10 or more. Ten of them make one bundle of ten, and the bundle moves across into the tens column. The ones left over stay where they are.
The 5 is written in the ones column, and the carried 1 sits above the tens column.
Add the carried ten
Now add the tens column, and include the carried 1: 1 + 4 + 2 = 7. Write the 7 in the tens place. The answer is 75.
A quick estimate checks it: 47 is about 50 and 28 is about 30, so the answer should be about 80. 75 is close to 80.
The tens: the carried 1, then 4 and 2, make 7. The answer is 75.
4 tens, 2 tens and the carried ten make 7 tens, with 5 ones left over: 75.
Two slips
Leaving out the carried 1 gives 65. The ten made by the 15 ones has been lost.
Writing all of 15 under the ones gives 615. The 1 is a ten, so it belongs in the tens column.
A carry works the same way in any column. When the tens make 10 or more, 10 tens are 1 hundred, so a 1 is carried into the hundreds column.
Worked example: One Amount Is More, Then the Total of Both
Question Ben has 368 stamps. Ali has 257 more stamps than Ben. (a) How many stamps does Ali have? (b) How many stamps do the two boys have altogether?
1.Draw Ben's bar, 368. Ali's bar is as long as Ben's bar with 257 more on the end. The total needs Ali's number, so find it first.
Ali has as many stamps as Ben and 257 more. Find Ali's number before the total. 2.(a) 368 + 257. Ones: 8 + 7 = 15, so write 5 and carry 1. Tens: 6 + 5 + 1 = 12, so write 2 and carry 1. Hundreds: 3 + 2 + 1 = 6. Ali has 625 stamps.
(a) 8 + 7 = 15, 6 + 5 + 1 = 12 and 3 + 2 + 1 = 6. Ali has 625 stamps. 3.Now add the two boys' stamps: 368 + 625. Ones: 8 + 5 = 13, so write 3 and carry 1.
Add the two boys' stamps. Ones: 8 + 5 = 13, write 3 and carry 1. 4.(b) Tens: 6 + 2 + 1 = 9. Hundreds: 3 + 6 = 9. The two boys have 993 stamps altogether. Check: 368 + 368 + 257 = 993.
(b) Tens: 6 + 2 + 1 = 9. Hundreds: 3 + 6 = 9. They have 993 stamps altogether.
Answer: (a) 625 stamps; (b) 993 stamps
Common mistakes
- Adding 368 and 257 and giving 625 as the total. 257 is not Ali's number of stamps. It is how many more stamps he has than Ben.
- Carrying to the hundreds when nothing was carried. In 368 + 625 the tens are 6 + 2 + 1 = 9, which is less than 10, so nothing goes to the hundreds.
More written addition and subtraction problems, worked step by step →