Which Coins are Missing?
Basics on the topic Which Coins are Missing?
Finding Missing Coins by Counting Coins
It is important for us to be able to count coins. Counting coins allows us to know the amount of money that we have or the amount of change that we need to get or make. To do this, we need to know the value of coins. The table below shows the values of UK coins:
Coin  Value 

1 p  One pence 
2 p  Two pence 
5 p  Five pence 
10 p  Ten pence 
20 p  Twenty pence 
50 p  Fifty pence 
£1  One pound 
£2  Two pounds 
To make a certain amount of money, we can combine these coins in different ways. However, the best way to combine coins to make a certain amount is to use the least number of coins. For example, to make 46 pence, it is best to use the following combination of two 20 p coins, a 5 p coin and a 1 p coin.
How to Solve Coin Problems
Sometimes we may need to know which coins are missing to make a certain amount to solve coins problems. This is helpful if we are making change or we are going to purchase something.
To find the missing coins, follow these steps:
 Step 1: Add up the coins to find the amount that you have.
 Step 2: Subtract the amount that you have from the total.
 Step 3: Make the amount with the fewest coins.
For example, let us assume that you want to make 46 pence but only have a 20 p and a 5 p in your hand. How can you find out what other coins you should take to make 46 pence?
We could follow these steps to find out.
 Step 1: Add up the coins in your hand to find the amount that you have. Since you have a 20 p coin and a 5 p coin, you add 20 and 5 to get 25. Therefore, you have 25 pence in your hand.
 Step 2: Subtract the amount that you have from the total amount that you want. Since you want to make 46 pence, you now subtract 25 pence from 46 pence to get 21 pence. 46 – 25 = 21
 Step 3: Finally, make 21 pence using the least number of coins. To make 21 pence with the fewest coins, we can use one 20 p coin and one 1 p coin.
Therefore, 46 pence can be made by using two 20 p coins, a 5 p coin and a 1 p coin.
Find the Missing Coins – Summary
Let’s repeat what we learnt about finding the missing coins and solving coin problems today.
When making a certain amount of money using coins, we try to use the least number of coins. If we want to find the missing coins to make a certain amount, we subtract the amount that we have from the total and use a combination of coins to make the amount that is missing. Remember that the coin values are as follows:
Coin  Value 

1 p  One pence 
2 p  Two pence 
5 p  Five pence 
10 p  Ten pence 
20 p  Twenty pence 
50 p  Fifty pence 
£1  One pound 
£2  Two pounds 
Be sure to test and expand your knowledge on counting coins with the other videos in this topic as well as our interactive exercises and coin word problems worksheet! These include coin problems with solution and answer.
Transcript Which Coins are Missing?
Freddie is feeling nervous about starting his new job tomorrow as an assistant at the local shop. “What if I mess up tomorrow and go too slow or give people the wrong change!” “You’ll be fine!” “I’ve set up a shop right here, so we can practice.” Zuri made a purchase from Freddie’s van market and the till tells him he needs to give her fortysix pence in change. We can help Freddie get ready for his new job by determining “Which Coins are Missing?” Let’s review the UK coins and their values. We have eight commonly used coins in the UK. These ones have the largest values and are worth one pound and two pounds. "We also have these six coins which are worth smaller amounts." This is a fifty pence coin. This is a twenty pence coin. This is ten pence coin. This is a five pence coin. This is a two pence coin, and this is a one pence coin. When making change, we can use a combination of these coins to make the different amounts. 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. Freddie is thinking of coins that can make fortysix pence for Zuri. Zuri shows the following coins and asks him which coins are missing to complete the change. Zuri has shown Freddie two twenty pence coins. She asks him which two coins are missing. In order to find the missing coins, we need to add up the given coin values and subtract them from the total. We would usually start by putting the coins in order from greatest to least value. These two coins are worth the same amount so we put them next to each other like this. Now, let’s add them together. Twenty plus twenty equals forty. Next subtract forty from the total, fortysix. Fortysix minus forty is six. Which coins are missing to make the change? Adding a five pence coin and a one pence coin makes six pence. To make fortysix pence, Freddie would give back two twenty pence coins, a five pence coin, and a one pence coin. Zuri’s next purchase would give the change of sixtyeight pence. She shows Freddie the following coins: a fifty pence, a five pence and a one pence. We need to add the given coin values first before we can find the missing coins. Fifty plus five equals fifty five plus one more equals fifty six. Now, subtract fiftysix from the total. Sixtyeight minus fiftysix is twelve pence. Which two coins are missing? A ten pence coin and a two pence coin would make twelve pence. Freddie would give a fifty pence, a ten pence, a five pence, a two pence and a one pence for change. For the final practice, Freddie needs to make eightynine pence, and Zuri shows the following coins. Which coins are missing? Pause the video if you need additional time and resume when you're ready. Adding a twenty pence, a five pence and a one pence would make eightynine. How did we solve? We counted fifty, sixty. Sixty two, sixty three, and subtracted sixtythree from eightynine to get twentysix pence. Freddie would give a fifty pence, a twenty pence, a ten pence, a five pence, a two pence and two one pence coins to make eighty nine pence change. Now that Freddie is ready for his first day at work, let’s summarise. All coins in the UK have a value assigned to them. We can determine missing coins from change given by organising the coins from greatest to least, adding up the known coin values, and subtracting that amount from the total. Then, we find the coin combination needed to make them using the fewest coins possible.
“I am so excited to serve my first customer!” “That’ll be thirteen pounds and sixtythree pence please.”
Which Coins are Missing? exercise

Match each coin with its correct value.
HintsThe 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.
SolutionHere we can see the coins and their values.

How can we make 42 p?
HintsFirst, 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?
SolutionThe 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.
HintsWhat 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?
SolutionFreddie 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?
HintsFirst, subtract 50 from 87.
87  50 = 37. Which group of coins equals 37 p?
It helps to start counting coins with the highest value.
SolutionFreddie 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?
HintsFirst, 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?
SolutionThe 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 is a 5 p.

Find pairs of coins that add up to £1.00.
HintsCount 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.
SolutionAbove 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