Subtracting with Borrowing – Addition and Subtraction to 1000 (Primary 3 Mathematics) | Ganzaa

Addition and Subtraction to 1000

Lessons

Primary 3 · Mathematics

Addition and Subtraction to 1000

3 lessons

Lesson 2 of 3

Subtracting with Borrowing

14 min

Keza goes to the shop

Keza has 352 Frw in her hand. She buys a pen for 128 Frw.

She starts to subtract, but she gets stuck straight away: the ones column says 2 − 8, and 2 is smaller than 8!

Do not worry, Keza. There is a clever trick called borrowing, and by the end of this lesson it will be easy for you.

An easy one first: 486 − 152

H	T	O
4	8	6
− 1	5	2
3	3	4

Ones: 6 − 2 = 4.

Tens: 8 − 5 = 3.

Hundreds: 4 − 1 = 3.

So 486 − 152 = 334. Every top digit was big enough, so there was nothing to borrow.

Keza's sum: 352 − 128

Ones: 2 − 8. You cannot take 8 away from 2. So go next door and borrow.

Picture the tens as bundles of ten sticks. Keza has 5 bundles and 2 loose sticks. She unties one bundle. Now she has 4 bundles and 10 + 2 = 12 loose sticks.

So the 5 tens becomes 4 tens, and the 2 ones becomes 12 ones. Cross out the 5, write 4 above it. Write a small 1 in front of the 2 to make 12.

H	T	O
3	4 (was 5)	12 (was 2)
− 1	2	8
2	2	4

Ones: 12 − 8 = 4.

Tens: 4 − 2 = 2 (remember, the 5 became 4).

Hundreds: 3 − 1 = 2.

So 352 − 128 = 224. Keza has 224 Frw left.

Borrowing in the tens: 425 − 163

Ones: 5 − 3 = 2. Easy, no borrowing.

Tens: 2 − 6. Too small! Borrow 1 hundred from the hundreds column.

One hundred is ten tens. So the 4 hundreds becomes 3 hundreds, and the 2 tens becomes 10 + 2 = 12 tens.

Tens: 12 − 6 = 6.

Hundreds: 3 − 1 = 2 (the 4 became 3).

So 425 − 163 = 262.

A zero gets in the way: 405 − 168

This one looks scary. Take it slowly.

Ones: 5 − 8. Too small, so borrow from the tens... but the tens digit is 0. There is nothing there to borrow!

So first go one more house along. Borrow 1 hundred and turn it into 10 tens:

4 hundreds becomes 3 hundreds, and 0 tens becomes 10 tens.

Now the tens column has plenty. Borrow 1 ten from it for the ones:

10 tens becomes 9 tens, and 5 ones becomes 15 ones.

Ones: 15 − 8 = 7.

Tens: 9 − 6 = 3.

Hundreds: 3 − 1 = 2.

So 405 − 168 = 237.

Always check by adding back

Subtraction has a built-in checker. Add your answer to the number you took away. If you get the number you started with, you are right.

237 + 168: ones 7 + 8 = 15, write 5 carry 1. Tens 3 + 6 + 1 = 10, write 0 carry 1. Hundreds 2 + 1 + 1 = 4.

That gives 405 — exactly the number we started with. Your answer is correct!

Warning

The trap that catches everyone. In 352 − 128, the ones column is 2 − 8. Many children flip it around and write 8 − 2 = 6, because that feels easier.

That is always wrong. The top number is what you HAVE. You cannot take away from what you have by turning the sum upside down. If the top digit is too small, you must borrow.

Tip

Borrowing is just untying a bundle. One ten becomes ten ones. One hundred becomes ten tens.

Whenever you borrow, TWO digits change: the one you borrowed from gets 1 smaller, and the one you borrowed for gets 10 bigger. Change both, or the answer will be wrong.

✦

Try it yourself

Set each one out in columns. Start with the ones. Then tap Show answer to check.

675 − 243
384 − 157
512 − 261
800 − 345
Gatete had 620 Frw. He bought a school notebook for 385 Frw. How much money does he have left?

Answers

432. No borrowing needed: 5 − 3 = 2, 7 − 4 = 3, 6 − 2 = 4.
227. Ones: 4 − 7 is too small, so borrow. The 8 tens becomes 7, the 4 ones becomes 14. Then 14 − 7 = 7, 7 − 5 = 2, 3 − 1 = 2.
251. Ones: 2 − 1 = 1. Tens: 1 − 6 is too small, so borrow a hundred. The 5 hundreds becomes 4, the 1 ten becomes 11. Then 11 − 6 = 5, 4 − 2 = 2.
455. Both zeros need help. Borrow a hundred: 8 becomes 7 and the tens become 10. Borrow a ten: the tens become 9 and the ones become 10. Then 10 − 5 = 5, 9 − 4 = 5, 7 − 3 = 4.
235 Frw. 620 − 385. Ones: borrow, so 2 tens becomes 1 and 0 ones becomes 10; 10 − 5 = 5. Tens: 1 − 8 is too small, so borrow again; 6 hundreds becomes 5 and the 1 ten becomes 11; 11 − 8 = 3. Hundreds: 5 − 3 = 2. Check: 235 + 385 = 620.

Quick check

In 352 − 128 the ones are 2 − 8, so you can do 8 − 2 = 6 instead.

What you learned today

Subtract from the right, one column at a time, starting with the ones.
If the top digit is too small, borrow: the neighbour on the left gives up 1, and your digit grows by 10.
If the neighbour is a 0, borrow from the next house along first, then come back.
Check your answer by adding it to the number you took away.

1Keza goes to the shop

2An easy one first: 486 − 152

3Keza's sum: 352 − 128

4Borrowing in the tens: 425 − 163

5A zero gets in the way: 405 − 168

6Always check by adding back