Why borrowing works

Quick answer

Borrowing works because we can exchange one big unit for ten smaller units. When we need to subtract but can't take away, we break up one group of ten into ten individual units to make the subtraction possible.

Learning outcome

By the end of this page, you will understand why borrowing works in subtraction and be able to use it confidently when subtracting numbers.

• You can explain that borrowing means exchanging one group for ten smaller groups
• You can use borrowing to subtract larger numbers correctly
• You can check your subtraction by adding your answer back to the number you subtracted
• You can spot when borrowing is needed in subtraction problems

Why this matters

Subtraction with borrowing helps you solve bigger problems, like calculating how much money you have left after buying something expensive or working out how many more points you need to win a game. It's like having a magic trick that lets you take away what you need to, even when you don't have enough in the ones place.

When you understand borrowing, you can do more complex maths, like working out how many pages are left in a book or how much time is left before your birthday. It's also helpful for games, cooking, and measuring things.

How it works

Let's imagine you're sharing cookies with friends:

1. You have 24 cookies
2. You want to give 17 cookies to your friends
3. When you try to take away 7 cookies from the ones place, you only have 4 cookies there
4. You can't take 7 away from 4, so you need to borrow
5. You take one group of ten (from the tens place) and break it into ten individual cookies
6. Now you have 1 group of ten and 14 individual cookies
7. You can now take 7 away from 14, which leaves 7
8. You continue with the tens place and take 1 from 1, leaving 0
9. Your answer is 7

Examples you can see

Let's look at a few examples using visual steps:

Try it as a mini adventure

The Great Cookie Quest

You are a cookie baker and have 32 cookies in your oven. You need to give 18 cookies to your friends. But you're in a tricky situation!

First time: You have 3 tens and 2 ones. You need to give away 8 ones, but only have 2. What do you do?

Second time: You borrow 1 ten and break it into 10 ones. Now you have 2 tens and 12 ones.

Third time: You give away 8 ones from 12 = 4 ones left.

Fourth time: You give away 1 ten from 2 tens = 1 ten left.

Fifth time: You check your answer by adding 14 + 18 = 32. It matches!

You've saved your cookie adventure by using borrowing!

Common mistakes

• Mistake: Forgetting to subtract 1 from the tens place when borrowing
• Why it happens: Kids get confused about which numbers change when borrowing
• Fix: Always remember to take 1 from the next column when you borrow

• Mistake: Borrowing from the wrong column
• Why it happens: Not knowing which column needs to be broken down
• Fix: Always borrow from the column that has a number bigger than 0

• Mistake: Not checking the answer
• Why it happens: Rushing through problems without double-checking
• Fix: Add your answer back to the number you subtracted to see if it matches the original

Parent and carer guide

Help your child understand borrowing by:

1. Using physical objects like counters or blocks to show the exchange
2. Practicing with simple numbers first, like 24 - 17
3. Encouraging them to explain each step in their own words
4. Checking their work by adding the answer back to the number they subtracted
5. Reinforcing that borrowing is just a way to make subtraction easier

Don't worry if they make mistakes – borrowing is tricky and takes practice. Be patient and celebrate small wins!

Practice questions

1. 52 - 27 = ?
2. 73 - 48 = ?
3. 91 - 56 = ?
4. 100 - 34 = ?
5. 65 - 29 = ?

Answers:

1. 52 - 27 = 25
2. 73 - 48 = 25
3. 91 - 56 = 35
4. 100 - 34 = 66
5. 65 - 29 = 36

FAQ

Why do we borrow when we subtract?

We borrow when we need to take away more than we have in one column. It's like exchanging a £10 note for 10 £1 coins – you still have the same amount, but now you have more individual units to work with.

What happens if I borrow from zero?

If you need to borrow but the next column has zero, you keep borrowing from the next non-zero column until you can borrow. For example, in 100 - 27, you borrow from the hundreds place to make tens, then from tens to make ones.

Is borrowing the same as carrying in addition?

Yes, they're related! Borrowing and carrying are both about exchanging between place values. In addition, you carry when you have too many in one column. In subtraction, you borrow when you don't have enough.

How can I help my child practice borrowing?

Use everyday situations like sharing snacks or counting money. Let them explain the steps out loud. Practice with visual aids like blocks or drawings. Make it fun with games or challenges!

Why is borrowing important in maths?

Borrowing helps us solve larger subtraction problems that we couldn't do otherwise. It's a crucial skill for future maths like long division, money calculations, and problem-solving with bigger numbers.