# Which Coins are Missing?

Content Which Coins are Missing?
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## Basics on the topicWhich Coins are Missing?

Let’s learn all about coin problems and finding missing coins.

## Coins problems

In the UK, we use eight main coins. When we receive change after paying for something, we often receive a combination of these coins. There are many combinations of coins that can be made, but we want to try and make the combination that uses the fewest amount of coins possible. We may be presented with coin word problems where we have to work out the correct combination of coins to give or which coins are missing from a group to make a given amount.

## How to solve coin problems

In this problem, the customer needs 46 p change. We already have two twenty pence coins to give them but which other coins do they need?

First of all, we can add these two coins together. 20 + 20 = 40.

Now we can subtract 40 from the total needed; 46.

We are left with 6. We now need to think, how can we make 6 p with the fewest number of coins? We can use a 5 p and a 1 p.

## Solving coin problems - Summary

When solving problems with missing coins we can follow these steps:

• Putting the coins we have in order and adding them together.
• Subtract this from the total amount needed.
• Find the coin combination that equals this amount. Remember, use the fewest number of coins possible.

## Coin problems worksheet and more

For further practice, have a look at our coin word problems worksheet where you can find coin problems with solutions and answers. We also have interactive exercises and activities to further develop your understanding of money.

### TranscriptWhich Coins are Missing?

“I am so excited to serve my first customer!” “That’ll be thirteen pounds and sixty-three pence please.”

## Which Coins are Missing? exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Which Coins are Missing?.
• ### Match each coin with its correct value.

Hints

The 1 p and 2 p coins are copper in colour.

The two coins that are worth an amount in pounds are gold and silver in colour.

5 p and 10 p coins are round.

Solution

Here we can see the coins and their values.

• ### How can we make 42 p?

Hints

First, add up the values of the coins Freddie has.

Next, subtract the value of the coins Freddie has from 42 pence.

How many pence does Freddie still need to make 42 pence? What coin can he use?

Solution

The correct answer is E, a 2 p coin.

• First add the values of the coins Freddie has, which is a 20 p, a 10 p and two 5 p coins. That is 40 pence.
• Next, subtract 42 - 40 = 2 pence.
• The missing coin Freddie needs is a 2 p to make 42 pence change.
• ### Help Freddie make change.

Hints

What is 56 - 10? This is how much more Freddie needs to make.

Divide 40 by 2 to find the two coins Freddie uses to make 40 p.

Freddie uses two coins to make 6 p; which two coins add together to make this value?

Solution

Freddie needs to make 56 pence, but he only has 10 p. He needs 46 p more.

He makes 40 p first which he does with two 20 p coins.

He then makes 6 p with two coins: a 5 p and a 1 p.

Freddie has made 56 p with two 20 p coins, a 10 p, a 5 p and a 1 p.

• ### Which coins are missing?

Hints

First, subtract 50 from 87.

87 - 50 = 37. Which group of coins equals 37 p?

It helps to start counting coins with the highest value.

Solution

Freddie needed to make 87 p. He started with 50 p so firstly subtract 50 from 87.

87 - 50 = 37.

We need to find a group of coins that equal 37 p.

We can see above that 20 p + 10 p + 5 p + 2 p = 37 p.

• ### Which coin is missing?

Hints

First, add the values of the coins Freddie has.

20 p + 2 p = 22 p

Subtract 22 p from 27 p to find the value of the missing coin.

Which coin is the same as the value you found?

Solution

The missing coin was a 5 p.

First, add the values of the coins given. 20 p + 2 p = 22 p.

Then, subtract that value from 27 pence: 27 - 22 = 5

You get 5 so the missing coin in a 5 p.

• ### Find pairs of coins that add up to £1.00.

Hints

Count each set of coins to find the total. How much needs adding to the total to make £1.00?

For example, 20 p + 5 p = 25 p.

£1 = 100 p so 100 p - 25 p = 75 p.

We need to find a group of coins that equals 75 p.

Solution

Above we can see one matching pair.

On the left 20 p + 5 p = 25 p and on the right 50 p + 20 p + 5 p = 75 p.

25 p + 75 p = £1.00

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The other pairs are:

• 10 p + 2 p + 2 p = 14 p; 50 p + 20 p + 10 p + 5 p + 1 p = 86 p; 14 p + 86 p = £1.00
• 50 p + 5 p = 55 p; 20 p + 20 p + 5 p = 45 p; 55 p + 45 p = £1.00
• 50 p + 20 p + 2 p = 72 p; 10 p + 10 p + 5 p + 2 p + 1 p = 28 p; 72 p + 28 p = £1.00