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Which Coins are Missing?

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Basics on the topic Which 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?

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

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

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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.

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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.

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 forty-six 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 forty-six 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, forty-six. Forty-six 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 forty-six 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 sixty-eight 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 fifty-six from the total. Sixty-eight minus fifty-six 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 eighty-nine 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 eighty-nine. How did we solve? We counted fifty, sixty. Sixty two, sixty three, and subtracted sixty-three from eighty-nine to get twenty-six 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 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