Identifying Denominations

Identifying Denominations
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Emily's mom wanted to buy some groceries for the week. She drove her car to the supermarket and bought the items.

The shopkeeper gave her a shopping bill for $185. She handed her two $100 bills. The shopkeeper then handed over three $5 bills back to her.

Emily wanted to know why some money was given back to her mom. She asked, "Mom, it is we who bought the groceries, so why is the shopkeeper paying us?"

Her mom replied that the items they bought were for $185 and that the money that was returned was the amount remaining after the purchase.

queue in supermarket 

In this lesson, you will learn what is money, its monetary value, denominations meaning, adding and subtracting money, US currency notes and coins.

Lesson Plan

What Is Identifying Denominations?

Money is a common term used for currency.

It is exchanged between various people, used in trade, and deposited in banks.

Money, be it a printed currency note or a coin, as such does not have any value.

Its value is decided by the government or economists of a country who give it a particular value.

We buy goods or avail a service based on the numerical value denoted by money.

Evolution of Money

Now let us learn about the history of money and what existed before money.

The usage of money has changed and evolved over the years.

The earliest system to buy and exchange goods was known as "Bartering," which involved the direct trade of goods and services.

Following the usage of bartering, the Chinese introduced a circular-shaped bronze object known as a "Coin." However, "Lydia" was the first region to manufacture coins.

The next transition by the Chinese was around 700 B.C when they introduced paper money. This is the modern-day currency that is in existence now.

Mode of Payment of Money

Currency notes are printed on paper and are mostly issued by the governments. These are still in use today.

In the earlier days, they were issued by banks and some private institutions.

Apart from that, we also have plastic cards (Credit and debit cards), electronic money transfer and crypto currency. A classic example for crypto currency is the "Bitcoin."

What Do You Mean By Denomination of Money?

Splitting up a given number into various smaller numbers is called denomination.

Denomination meaning in the context of  money can be well understood by thinking of place values.

The place values are ones, tens, hundreds, thousands, and so on.

$1, $10, $100 are similar to place values of units, tens, and hundreds.

There can be any number of one dollar, ten dollars, hundred dollars in a given amount.

For example, we can say a hundred dollars comprises hundred $1 or ten $10 or one $100.

\(\begin{align} 100 \:= \:(1 \times 100) \:or\: (10 \times 10)\: or \:(100 \times 1)\:\end{align}\)

These are the currency notes used in the United States.

US dollars

The paper notes come in the following denominations:

  • One dollar ($1)
  • Two dollars ($2)
  • Five dollars ($5)
  • Ten dollars ($10)
  • Twenty dollars ($20)
  • Fifty dollars ($50)
  • Hundred dollars ($100)

Apart from currency notes, we have circular-shaped objects called coins.

Each coin denotes a specified number of cents. 

The coin denominations available are:

  • 1 cent (Penny)
  • 5 cents (Nickel), 
  • 10 cents (One dime) 
  • 25 cents (Quarter dollar) 
  • 50 cents (Half dollar)
  • Dollar coins

A cent looks like this.

American cents

100 cents make one dollar.

100 cents = 1 dollar

Every bill and coin has a monetary value. 

55.16 dollars

This is read as 55 dollars and 16 cents. 

The symbol for US dollars and cents are shown below.

Dollars and cents symbol

Addition and Subtraction With Denominations

In this section we will glance through some arithmetic operations on money.

When you buy goods, you will have to pay some amount to the party from whom you bought the goods.

It is not possible to give the exact amount every time.

Let us say you go to a shopping mall and buy things worth $465.

You have five $100 bills which add up to $500. 

You have to pay $465, so what happens to the remaining amount?

The shop keeper subtracts the amount to be paid by you from the total amount you've given. The extra amount is returned to you.

$35 will be returned to you probably as three $10 and one $5. 

Subtracting Denomination - $465 worth of groceries in the cart for which you pay $500 and get back $35.

In this case, you pay $500 and you are given back $500 - $465, which is equal to $35

In some instances, you may need to add the denominations of money.

If you have to buy some books worth $10 and a pack of pens worth $5, you can add both the denominations of money and pay $15

Adding denominations - Pens for $5, books for $10, and $15 in currency notes

The table below shows the amount of money and their denominations.

Amount of Money Denominations
\(\begin{align}$2000\end{align}\) \(\begin{align}20 \times $100\end{align}\) or \(\begin{align}200 \times $10\end{align}\) or \(\begin{align}2000 \times $1\end{align}\)
\(\begin{align}$500\end{align}\) \(\begin{align}5 \times $100\end{align}\) or \(\begin{align}50 \times $10\end{align}\) or \(\begin{align}500 \times $1\end{align}\)
\(\begin{align}$100\end{align}\) \(\begin{align}1 \times $100\end{align}\) or \(\begin{align}10 \times $10\end{align}\) or \(\begin{align}20 \times $5\end{align}\) or \(\begin{align}100 \times $1\end{align}\)
\(\begin{align}$10\end{align}\) \(\begin{align}1 \times $10\end{align}\) or \(\begin{align}10 \times $1\end{align}\) or \(\begin{align}2 \times $5\end{align}\)
important notes to remember
Important Notes
  1. There are 100 cents in 1 dollar.
  2. Any amount can be expressed as dollars and cents.
  3. Money can be paid as paper notes or through an electronic transfer.

Solved Examples

Example 1



Add and subtract the following amounts.

a) \(\begin{align}$25.50 + $50.16\end{align}\)

b) \(\begin{align}$300 + $85\end{align}\)

c) \(\begin{align}$45.23 - $20.86\end{align}\)

d) \(\begin{align}$285 - $120\end{align}\)


\(\begin{align}$25.50 + $50.16 \:=\: $75.66\end{align}\)

\(\begin{align}$300 + $85 \:=\:$385\end{align}\)

\(\begin{align}$45.23 - $20.86 \:=\:$24.37\end{align}\)

\(\begin{align}$285 - $120\:=\:$165\end{align}\)

Example 2



James has decided to purchase some winter wear and some decoration for Christmas.

Help James calculate the amount he should pay for these items.

Winter wear and Christmas decoration items with prices


Cost of Christmas tree = \(\begin{align}$10\end{align}\)

Cost of toy gift box = \(\begin{align}$1\end{align}\)

Cost of toy candy = \(\begin{align}$1\end{align}\)

Cost of toy bell = \(\begin{align}$2\end{align}\)

Cost of holly = \(\begin{align}$1\end{align}\)

Cost of sock = \(\begin{align}$2\end{align}\)

Cost of glove = \(\begin{align}$4\end{align}\)

Cost of woolen cap = \(\begin{align}$1\end{align}\)

Cost of snowman = \(\begin{align}$5\end{align}\)

Therefore, the total amount James has to pay is

\(\begin{align}$10+$1+$1+$2+$1+$2+$4+$1+$5 = $27\end{align}\)

Total amount to be paid is  \(\begin{align}$27\end{align}\)
Example 3



Olivia wants to deposit \(\begin{align}$500\end{align}\) in her savings bank account.

She has twenty \(\begin{align}$50\end{align}\) bills, ten \(\begin{align}$100\end{align}\) dollar bills, fifty \(\begin{align}$10\end{align}\) bills.

What are the possible denominations that she can choose to make the deposit?


Olivia has twenty \(\begin{align}$50\end{align}\) bills, ten \(\begin{align}$100\end{align}\) dollar bills, fifty \(\begin{align}$10\end{align}\) bills.

To make \(\begin{align}$500\end{align}\) using \(\begin{align}$50\end{align}\) bills, she needs \(\begin{align}10 \times $50 = $500\end{align}\) 

To make \(\begin{align}$500\end{align}\) using \(\begin{align}$100\end{align}\) bills, she needs \(\begin{align}5 \times $100 = $500\end{align}\) 

To make \(\begin{align}$500\end{align}\) using \(\begin{align}$10\end{align}\) bills, she needs \(\begin{align}50 \times $10 = $500\end{align}\) 

Olivia can use ten 

\(\begin{align}$50\end{align}\) bills or 

five \(\begin{align}$100\end{align}\) bills or 

ten \(\begin{align}$50\end{align}\) bills.

Example 4



Merwin visited a toy shop which had the toys displayed in the picture below.

a) How many toys can he pick if he had $45?

b) What amount of money will be returned to Merwin if he pays a \(\begin{align}$50\end{align}\) for buying a car, a teddy bear, and a ship?

c) What will be the total amount to be paid if he wants to buy all the toys?

Various toys and their prices


a) Cost of building blocks = \(\begin{align}$20\end{align}\)

    Cost of toy car = \(\begin{align}$15\end{align}\)

    Cost of letter puzzles = \(\begin{align}$3\end{align}\)

    Cost of ship = \(\begin{align}$5\end{align}\)

    Total cost of all the toys = \(\begin{align}$20 + $15 + $3 + $5  = $43\end{align}\)   

    There is one more combination of toys that can be bought.

    Cost of building blocks = \(\begin{align}$20\end{align}\)

    Cost of teddy = \(\begin{align}$12\end{align}\)

    Cost of letter puzzles = \(\begin{align}$3\end{align}\)

    Cost of ship = \(\begin{align}$5\end{align}\)

    Total cost of all the toys = \(\begin{align}$20 + $12 + $3 + $5  = $40\end{align}\)   

b)  Cost of car  = \(\begin{align}$15\end{align}\)

    Cost of teddy bear  = \(\begin{align}$12\end{align}\)

    Cost of ship  = \(\begin{align}$5\end{align}\) 

    Total cost of all the toys = \(\begin{align}$15+ $12 + $5\ = $32\end{align}\)

    Amount paid by Merwin = \(\begin{align}$50\end{align}\)

    Therefore, the amount that will be returned to Merwin is \(\begin{align}$50 - $32 = $18\end{align}\)

c)  Cost of building blocks = \(\begin{align}$20\end{align}\)

    Cost of toy car = \(\begin{align}$15\end{align}\)

    Cost of letter puzzles = \(\begin{align}$3\end{align}\)

    Cost of teddy bear = \(\begin{align}$12\end{align}\)

    Cost of ship = \(\begin{align}$5\end{align}\)

    Therefore, total cost of all the toys  = \(\begin{align}$20+$15+$12+$3+$5 = $55\end{align}\)

a) Merwin can pick at least 4 types of toys for example, he can pick building blocks, toy car, letter puzzles, and a ship for \(\begin{align}$45\end{align}\) or he can pick building blocks, teddy, letter puzzles, and a ship for \(\begin{align}$40\end{align}\)

b) Amount returned to Merwin is \(\begin{align}$18\end{align}\)

c) Total cost of all the toys is \(\begin{align}$55\end{align}\).

Challenge your math skills
Challenging Questions
  1. Bridget bought some books for $45.36.
    She was left with 36.30 after the purchase.
    How much money did she have initially?
  2. How many cents are there in one hundred dollars?

Interactive Questions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.



Let's Summarize

The lesson targeted the fascinating concept of identifying denominations. By now you will be able to count money and identify denominations in a given amount of money. Solving the interactive questions and going through the solved examples would enrich your knowledge further on the subject. Here lies the magic with Cuemath.

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Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

FAQs on Identifying Denominations

1. Why is money important?

We require money to buy goods or avail services. Money can also be saved for future usage.

2. What does denomination mean?

The amount of money expressed using currency notes and coins is called denomination.

3. How is the extra amount of money returned to you after your purchase of goods or services?

The extra amount of money is returned in the form of currency notes and coins. 

4. What are the modes of payment of money?

Money can be paid using currency notes and coins, payments can be made via an electronic transfer from one account to another, or by using credit and debit cards.

5. What is the highest denomination of currency note in the US?

One hundred dollars is the highest currency note denomination in the US.

6. How do you add and subtract money?

We use the same process of arithmetic operation of addition and subtraction but we add a $ symbol to the answer.

7. What are the US currency denominations?

One dollar, two dollars, five dollars, ten dollars, twenty dollars, fifty dollars, and hundred dollars are the paper currency notes and one cent, two cents, five cents, ten cents, twenty five cents, and fifty cents are the coin denominations.

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