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We encounter problems related to money almost every day. We might need to add or subtract money, or we might even have to convert it into a different denomination. Solving word problems related to money will help us get accustomed to these day-to-day problems. One of the most common money-related problems is calculating the change....Read MoreRead Less

Money is commonly used in everyday conversation to refer to income (‘he makes a lot of money’) or wealth (‘she has a lot of money’). In mathematics, money is defined as a medium of exchange, such as bills, coins, and demand deposits. These mediums are used to pay for goods and services. Money is used to pay for the value or price of an item or service. The official currency of the United States is the US dollar ($). A currency refers to a country’s monetary system.

For example, when you go to a bakery to buy a cake, you have to give money in cents or dollars to the shopkeeper to purchase that cake.

The coin is the oldest form of money still being used. Coins are tiny metal discs that were once made of precious metals such as bronze, aluminum, steel, silver, and gold.

Cash is a type of money that is made up of physical items that we can carry and trade, such as coins and bills.

The penny, nickel, dime, and quarter are the four most common coins. They are worth various amounts of money and also have distinct physical characteristics that can be used to separate them with your hands.

**Each coin has the following value:**

- A penny is equal to one cent. 1 penny = 1 cent
- The value of a nickel is 5 cents. 1 nickel = 5 cents
- A dime is equal to ten cents. 1 dime = 10 cents
- The value of a quarter is 25 cents. 1 quarter = 25 cents

The coins in ascending order are dime, penny, nickel, and quarter.

- The nickel is the heaviest of the four coins.

- The dime is the thinnest of the four coins.

- The edges of dimes and quarters are ridged.

- The edges of pennies and nickels are smooth.

**The various coins of cent are shown below. The symbol ‘****¢****’ stands for cent.**

**The various US dollar bills or notes are shown below. The symbol ‘$’ stands for dollars. One dollar represents 100 cents. 1 dollar = 100 cents.**

When you are at the store, it would be smart to calculate your change. You could even turn it into a game. Before you ask the cashier, try to figure out how much change you should get. Then count it out once you have got your change. Count the change you receive and add it to the price of the bill to double-check your change. All of this should equal the amount you paid.

**What you paid = change + bill** is the formula for checking the change.

Change is nothing but calculating the extra amount you get back from the shopkeeper when you pay more than the required amount to buy a thing.

For example, you go to a stationery store and buy a pen that costs 50 cents, but you have a one-dollar note. After you give that one-dollar note to the shopkeeper, the shopkeeper has to return 50 cents to you along with the pen. To find the change, we need to subtract.

100 cents – 50 cents = 50 cents change

When you add coins, you must also include the cents. One dollar equals 100 cents. If you have more than 100 cents, you have a dollar. If the coins amount to 145 cents, the denomination is 1 dollar and 45 cents. The total would be 521 cents if we add 5 dollars and 21 cents.

**Converting 1 dollar to a quarter,**

1 dollar = 100 cents

= 50 cents + 50 cents

= (25 + 25) cents + (25 + 25) cents

= 4 quarter coins.

**Converting 1 quarter to a dime and a nickel,**

1 quarter = 25 cents

= 10 cents + 10 cents + 5 cents

= (10 + 10) cents + 5 cents

= 2 dimes and 1 nickel.

**Converting 1 dime to a nickel,**

1 dime = 10 cents

= 5 cents + 5 cents

= (5 + 5) cents

= 2 nickel coins.

**Converting 1 nickel to a pennyn,**

1 nickel = 5 cents

= 1 cent + 1 cent + 1 cent + 1 cent + 1 cent

= (1 + 1 + 1 + 1 + 1) cents

= 5 pennies.

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**Example 1: In one pocket, you have two nickels and three pennies. In your other pocket, you have a dime and a quarter. What is the total amount of money you have? Will you be able to purchase a 60-cent toy car?**

**Solution: **We have

2 nickels + 3 pennies + 1 dime + 1 quarter

5 cents + 5 cents + 1 cent + 1 cent + 1cent + 10 cents + 25 cents = 48 cents.

The total amount we have is 48 cents, but we need 60 cents.

This shows that we do not have enough money to buy a toy car.

**Example 2: You have one nickel, two pennies, and one dime on you. How much cash do you have ?**

**Solution: **We have 1 nickel + 2 pennies + 1 dime

5 cent+1 cent + 1 cent+ 10 cents = 17 cents.

**Example 3: You purchase a pen. You give the shopkeeper two dollars. The shopkeeper returns 2 quarters and 1 penny. What is the price of the pen?**

**Solution: **

**What you paid = change + bill** is the formula for checking the change.

2$ = 2 quarters +1 penny + Bill

Bill = 2$ – 2 quarters –1 penny

Bill = 200 cents – 50 cents –1cent

(Since each dollar represents 100 cents and each quarter represents 25 cents, each penny represents 1 cent)

Bill = 149 cents (simplified)

Therefore, the cost of the pen is 149 cents, which means 1 dollar, 4 dimes, and 9 pennies.

**Example 4: A toy is purchased with fewer than six coins. To demonstrate how you pay for a 42-cent toy, draw and label the coins.**

**Solution: **

The toy costs 42 cents. 42 cents can be added up as 25 + 10 + 5 + 2.

So, we have to pay five coins, such as 1 quarter, 1 dime, 1 nickel, and 2 pennies.

**Example 5: A pet dog is purchased by John. He pays with a dollar and three nickels. How much did he have to pay?**

**Solution: **John has 3 nickels and a 1-dollar note.

Therefore, John pays 115 cents to buy the dog.

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Frequently Asked Questions

Money can provide security and safety to you and your family. Human beings require money to pay for all the necessities of life, such as housing, food, medical bills, and a good education. Money is required to obtain goods and services to survive, and a good knowledge of finance is essential. You must be responsible with your money and save enough for the future to ensure that you will have enough money left with you when you can no longer trade your labor for money.

When you pay for something with a little more money than it costs, you will get change. Change can also refer to any type of money in the form of a coin. Having exact change means knowing exactly how much something costs. In the United States, buses require passengers to have exact change. The bus does not refund money.