Which Coins are Missing?
Basics on the topic Which Coins are Missing?
Finding Missing US 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 US coins. The table below shows the names and values of US coins:
Name  Value 

Quarter  25 cents 
Dime  10 cents 
Nickel  5 cents 
Penny  1 cent 
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 cents, it is best to use the following combination of a quarter, two dimes, and a penny.
How to Find Missing Coins
Sometimes we may need to know what coins are missing to make a certain amount. 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 cents but have the coins shown below in your hand. How can you find out what other coins you should take to make 46 cents?
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 dime and a quarter, you add 10 cents and 25 cents to get 35 cents. Therefore, you have 35 cents in your hand.
 Step 2: Subtract the amount that you have from the total amount that you want. Since you want to make 46 cents, you now subtract 35 cents from 46 cents to get 11 cents. 46 – 35 = 11
 Step 3: Finally, make 11 cents using the least number of coins. To make 11 cents with the fewest coins, we can use 1 dime and 1 penny.
Therefore, 46 cents can be made by using 1 quarter, 2 dimes and 1 penny.
Find the Missing Coins – Summary
Let’s repeat what we learned about finding the missing coins 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 quarters, dimes, nickels and/ or pennies to make the amount that is missing. Remember that the coin names and their values are as follows:
Name  Value 

Quarter  25 cents 
Dime  10 cents 
Nickel  5 cents 
Penny  1 cent 
Be sure to test and expand your knowledge on counting coins with the other videos in this topic as well as our interactive exercises!
Transcript Which Coins are Missing?
Freddie is feeling nervous about starting his new job tomorrow as a cashier at the local market. “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 store right here, so we can practice.” Zuri made a purchase from Freddie’s van market and the register tells him he needs to give her fortysix cents in change. We can help Freddie get ready for his new job by determining... “Which Coins are Missing?” Let’s review the US coins and their values. We have rarely used coins like the one dollar and a half dollar... Quarters have the value of twentyfive cents… dimes are worth ten cents… nickels are worth five cents… and pennies have the value of one cent. 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 cents for Zuri. Zuri shows the following coins and asks him which coins are missing to complete the change. Zuri has shown Freddie a dime and a quarter. 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 start by putting the coins in order from greatest to least value. Twentyfive and ten more make thirtyfive. Which coins are missing to make the change? Adding a dime and penny is the way to make eleven with fewest coins. Zuri’s next purchase would give the change of sixtysix cents. She shows Freddie the following coins… Two quarters and a penny. We need to add the given coin values first before we can find the missing coins. Twentyfive and twentyfive make fifty, and one more make fiftyone cents. Now, subtract fiftyone from the total. Sixtysix minus fiftyone is fifteen cents. Which two coins are missing? A dime and a nickel would make fifteen cents. Freddie would give two quarters, a dime, a nickel, and a penny for change. For final practice, Freddie needs to make eightynine cents... 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 quarter and a dime are the fewest coins needed to make eightynine. How did we solve? We counted twentyfive, fifty, fiftyone. Fiftytwo, fiftythree, fiftyfour… and subtracted fiftyfour from eightynine to get thirtyfive cents. Freddie would give three quarters, one dime, and four pennies change. Now that Freddie is ready for his first day at work, let’s summarize. All coins in the US have a value assigned to them. We can determine missing coins from change given by… organizing the coins from greatest to least and 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 ring up my first purchase!” “That’ll be thirteen dollars and sixtythree cents.”
Which Coins are Missing? exercise

Match each coin with its correct value.
HintsRemember, the penny has the lowest value and is a different color than most of the others.
Remember, the dollar coin has the highest value, and is not silver or grey.
Solution A dollar coin is worth $1.00
 A half dollar coin is worth 50 cents
 A quarter is worth 25 cents
 A dime is worth 10 cents
 A nickel is worth 5 cents
 A penny is worth 1 cent

Find the missing coin.
HintsFirst, add up the values of the coins Freddie has.
Second, subtract the value of the coins Freddie has from 42 cents.
How many cents does Freddie still need to make 42 cents? What coin can he use?
Solution First add the value of the coins Freddie has, which is a quarter (25 cents), a dime (10 cents), and two pennies (2 cents). That is 37 cents.
 Next, subtract 42  37 = 5 cents.
 The missing coin Freddie needs is a nickel to make 42 cents change.

Help Freddie make change.
HintsThis is the value of each coin.
 What is the value of 1 quarter and 1 dime?
 What other coins will you need?
After Freddie takes 1 quarter and 1 dime, subtract their value from 50 cents. This is how much more he needs.
Solution First, add the values of the coins given. The quarter is worth 25 cents and the dime is worth 10 cents.
 Then, subtract that value from 50 cents. (5035=?)
 You get 15 cents. Which coins make 15 cents? One dime and one nickel.

What coin is missing?
HintsThese are the values of each coin.
 How much is two quarters worth?
 What other coins will you need?
Once you find the value of two quarters, subtract that from 87 cents to figure out what else you will need.
It helps to start counting coins with the highest value.
SolutionFreddie starts with two quarters, so this is 25 + 25 = 50 cents.
Subtract 50 cents from 87 cents to figure out how much more Freddie needs: 87  50 = 37 cents.
You need one quarter, one dime, and two pennies to add together to make 37 cents: 25 + 10 + 1 + 1 = 37.

What coin is missing?
HintsFirst, add the value of the quarter and two pennies.
Subtract that value from 52 cents to find number of cents left.
What coin is the same as the value you found?
SolutionFirst, add the values of the coins given. The quarter is worth 25 cents and the two pennies is worth 2 cents.
Then, subtract that value from 52 cents: 52  27 = 25
You get 25 cents, so the missing coin is a quarter.

Find pairs of coins that add up to 75 cents.
HintsCount each set of coins.
Figure out how much is left to make 75 cents. Find the number of coins that shows that value.
SolutionThese sets of coins make 75 cents:
 1 quarter, 1 dime, and 1 nickel + 3 dimes and 1 nickel
 2 quarters, 1 dime, and 1 nickel + 1 quarter and 1 dime
 1 dime and 1 nickel + 2 quarters and 1 nickel
 1 quarter + 2 quarters