Start with the ones
Add 168 and 275 in columns. Write 275 under 168 with the ones under the ones, the tens under the tens and the hundreds under the hundreds. Then add one column at a time, starting with the ones on the right.
The ones give 8 + 5 = 13. A column can hold only one digit, and 13 ones are 1 ten and 3 ones. Write the 3 in the ones column. Carry the 1 ten: write a small 1 above the tens column, where tens belong.
8 + 5 = 13 ones. The 3 stays in the ones column, and the 1 ten is written above the tens.
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
The ones column starts with 8 ones. Drop in 5 more to make 13. Ten of them are one ten: drag that bundle across into the tens column, and 3 ones are left behind.
A second carry
Now add the tens, and count the carried ten too: 1 + 6 + 7 = 14. That is 14 tens, and the tens column can hold only one digit, so the same thing happens again. Ten tens make 1 hundred. Write the 4 in the tens column, and carry 1 hundred: a small 1 above the hundreds column.
Nothing about this carry is new. Ten ones make a ten, and ten tens make a hundred, so a carry from the tens column works exactly like a carry from the ones column.
1 + 6 + 7 = 14 tens. The 4 is written in the tens column, and 1 hundred is carried.
Finish with the hundreds
The hundreds give the carried 1, then 1 and 2: 1 + 1 + 2 = 4. That is fewer than ten, so there is nothing to carry. Write the 4 in the hundreds column and read the answer along the bottom row: 168 + 275 = 443.
Both carries sit above the columns they were added into. The answer is 443.
As many carries as there are columns
The rule goes on for as many columns as the numbers have. Add 3658 and 1476. The ones give 8 + 6 = 14: write 4 and carry 1. The tens give 1 + 5 + 7 = 13: write 3 and carry 1. The hundreds give 1 + 6 + 4 = 11: write 1 and carry 1. The thousands give 1 + 3 + 1 = 5.
So 3658 + 1476 = 5134. Three columns carried, and each carry was the same move: ten in one column is one in the next column to the left.
A carry above the tens, the hundreds and the thousands: 3658 + 1476 = 5134.
Add every carry in
The carried 1 is small, so it is easy to forget. In 168 + 275, leave out the carry from the ones and the tens give only 6 + 7 = 13, so the answer comes out as 433, ten too small. Leave out the carry from the tens and the hundreds give only 1 + 2 = 3, so the answer comes out as 343, a hundred too small.
Write each carry above its column as soon as you make it, and add it in with the other digits of that column.
Worked example: Two Parts Joined to Make a Whole
Question A library has 2467 story books and 2385 fact books. (a) How many books does the library have altogether? (b) The library then buys 579 new books. How many books does it have now?
1.Draw one bar with two parts, 2467 story books and 2385 fact books. The whole bar is the total, so add the two parts.
The two kinds of books are two parts. The whole bar is the total, so add. 2.Write 2385 under 2467 with the ones under the ones. Add the ones: 7 + 5 = 12. Write 2 and carry 1 to the tens. Add the tens: 6 + 8 + 1 = 15. Write 5 and carry 1 to the hundreds.
Ones: 7 + 5 = 12, write 2 and carry 1. Tens: 6 + 8 + 1 = 15, write 5 and carry 1. 3.(a) Add the hundreds: 4 + 3 + 1 = 8. Add the thousands: 2 + 2 = 4. The library has 4852 books altogether.
(a) Hundreds: 4 + 3 + 1 = 8. Thousands: 2 + 2 = 4. There are 4852 books altogether. 4.The 579 new books are one more part. Write 579 under 4852. Ones: 2 + 9 = 11, so write 1 and carry 1. Tens: 5 + 7 + 1 = 13, so write 3 and carry 1.
The 579 new books are one more part. Ones: 2 + 9 = 11. Tens: 5 + 7 + 1 = 13. 5.(b) Hundreds: 8 + 5 + 1 = 14, so write 4 and carry 1. Thousands: 4 + 1 = 5. The library has 5431 books now. Check: 5431 − 579 = 4852.
(b) Hundreds: 8 + 5 + 1 = 14. Thousands: 4 + 1 = 5. The library has 5431 books now.
Answer: (a) 4852 books; (b) 5431 books
Common mistakes
- Forgetting the 1 that was carried. In the tens, 6 + 8 is 14, but the carried 1 makes it 15. Write the small 1 above the next column so that it is not forgotten.
- Writing 579 with its 5 under the 4 of 4852. The 5 means 5 hundreds, so it goes under the 8 in the hundreds column.
More written addition and subtraction problems, worked step by step →