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Chapter Notes: Money

Money is something we use every single day. You might use it to buy lunch, save up for a toy, or help your family at the grocery store. Understanding money means knowing how to count it, compare it, make change, and solve problems with it. When you know how money works, you can make smart choices and keep track of what you have. In this chapter, you will learn all about coins, bills, counting money, making change, and solving real-world problems that involve money.

Understanding Coins and Bills

In the United States, we use coins and bills as our money. Coins are small, round pieces of metal. Bills are paper rectangles. Each coin and bill has a different value.

Coins

There are four coins you use most often:

  • Penny = 1 cent = 1¢
  • Nickel = 5 cents = 5¢
  • Dime = 10 cents = 10¢
  • Quarter = 25 cents = 25¢

A cent is the smallest unit of money in the United States. The symbol for cents is ¢. When we write money amounts less than one dollar, we can write them with the cent symbol or with a dollar sign. For example, 50 cents can be written as 50¢ or $0.50.

Think of coins like building blocks. A nickel is worth the same as 5 pennies stacked together. A dime is worth the same as 10 pennies. A quarter is worth the same as 25 pennies.

Bills

Bills are also called paper money or dollar bills. Here are the bills you will see most often:

  • One-dollar bill = $1.00 = 100 cents
  • Five-dollar bill = $5.00 = 500 cents
  • Ten-dollar bill = $10.00 = 1,000 cents
  • Twenty-dollar bill = $20.00 = 2,000 cents

When we write amounts of money that are one dollar or more, we use the dollar sign ($) and a decimal point. The decimal point separates dollars from cents. For example, $3.45 means 3 dollars and 45 cents.

Counting Money

Counting money means finding the total value of a group of coins and bills. The best strategy is to start with the coins or bills that have the highest value and count forward.

Counting Coins

Follow these steps to count coins:

  1. Sort the coins into groups: quarters, dimes, nickels, and pennies.
  2. Start with the quarters and count by 25s.
  3. Next, count the dimes by 10s.
  4. Then count the nickels by 5s.
  5. Finally, count the pennies by 1s.

Example:  You have 2 quarters, 1 dime, 2 nickels, and 3 pennies.

What is the total value?

Solution:

Start with the quarters: 25¢, 50¢

Add the dime: 50¢ + 10¢ = 60¢

Add the nickels: 60¢ + 5¢ = 65¢, then 65¢ + 5¢ = 70¢

Add the pennies: 70¢ + 1¢ = 71¢, then 71¢ + 1¢ = 72¢, then 72¢ + 1¢ = 73¢

The total value is 73¢ or $0.73.

Counting Bills and Coins Together

When you have both bills and coins, always count the bills first because they have higher values. Then count the coins from highest to lowest value.

Example:  You have 1 ten-dollar bill, 2 one-dollar bills, 3 quarters, and 1 nickel.

How much money do you have in total?

Solution:

Start with the ten-dollar bill: $10.00

Add the one-dollar bills: $10.00 + $1.00 = $11.00, then $11.00 + $1.00 = $12.00

Add the quarters: $12.00 + $0.25 = $12.25, then $12.25 + $0.25 = $12.50, then $12.50 + $0.25 = $12.75

Add the nickel: $12.75 + $0.05 = $12.80

The total amount is $12.80.

Writing Money Amounts

There are two ways to write money amounts: using the cent symbol (¢) or using the dollar sign ($) with a decimal point.

Amounts Less Than One Dollar

If the amount is less than one dollar, you can write it two ways:

  • With the cent symbol: 45¢
  • With the dollar sign and decimal: $0.45

Both mean exactly the same thing: 45 cents. Notice that when you use the dollar sign, you must write a zero before the decimal point.

Amounts One Dollar or More

If the amount is one dollar or more, always use the dollar sign and decimal point. The numbers to the left of the decimal are dollars. The numbers to the right are cents.

  • $7.00 means 7 dollars and 0 cents
  • $7.25 means 7 dollars and 25 cents
  • $7.05 means 7 dollars and 5 cents (notice the zero holds the tens place)

The decimal point is like a fence that separates dollars from cents. Everything on the left side is dollars. Everything on the right side is cents.

Comparing Money Amounts

Sometimes you need to know which amount is more or which is less. To compare money amounts, follow these steps:

  1. Make sure both amounts are written the same way (both with $).
  2. Compare the dollars first.
  3. If the dollars are the same, compare the cents.

Example:  Which is more: $3.85 or $3.58?

Solution:

Both amounts have 3 dollars, so we compare the cents.

85 cents is greater than 58 cents.

Therefore, $3.85 is more than $3.58.

Making Change

Making change means finding out how much money you should get back when you pay for something with more money than it costs.

The Subtraction Method

One way to find change is to subtract the cost from the amount you paid.

Example:  A book costs $6.75.
You pay with a $10 bill.

How much change do you get back?

Solution:

Amount paid = $10.00

Cost of book = $6.75

Change = $10.00 - $6.75

First, subtract the cents: 0 cents - 75 cents. We need to borrow from the dollars. Change 1 dollar into 100 cents: 100¢ - 75¢ = 25¢

Next, subtract the dollars: $9 - $6 = $3

Change = $3.25

You will get back $3.25 in change.

The Counting Up Method

Another way to find change is to count up from the cost to the amount paid. Start at the cost and add money until you reach the amount you paid.

Example:  A toy costs $4.35.
You pay with a $5 bill.

How much change should you get?

Solution:

Start at the cost: $4.35

Count up to the next easy amount. Add 5 cents to get to $4.40.

Add 10 cents to get to $4.50.

Add 50 cents to get to $5.00.

Total change = 5¢ + 10¢ + 50¢ = 65¢ or $0.65

You should get 65 cents back in change.

Adding and Subtracting Money

When you add or subtract money, treat it just like regular numbers, but remember to line up the decimal points.

Adding Money

To add money amounts:

  1. Write the amounts in a column.
  2. Line up the decimal points.
  3. Add the cents first, then the dollars.
  4. If the cents add up to 100 or more, regroup into dollars.

Example:  You buy a sandwich for $5.75 and a drink for $2.50.

How much do you spend in total?

Solution:

Write the amounts in a column:
$5.75
+ $2.50

Add the cents: 75 + 50 = 125 cents. That is 1 dollar and 25 cents. Write 25 in the cents place and carry 1 to the dollars.

Add the dollars: 5 + 2 + 1 (carried) = 8 dollars

Total = $8.25

You spend $8.25 in total.

Subtracting Money

To subtract money amounts:

  1. Write the amounts in a column.
  2. Line up the decimal points.
  3. Subtract the cents first, then the dollars.
  4. If you need to, borrow from the dollars.

Example:  You have $20.00.
You spend $12.75.

How much money do you have left?

Solution:

Write the amounts in a column:
$20.00
- $12.75

Subtract the cents: 0 - 75 is not possible, so borrow 1 dollar = 100 cents. Now we have 100 - 75 = 25 cents.

Subtract the dollars: 19 - 12 = 7 dollars (we borrowed 1, so 20 became 19)

Amount left = $7.25

You have $7.25 left.

Solving Word Problems with Money

Word problems with money ask you to use what you know about adding, subtracting, and comparing money to solve real-life situations.

Steps to Solve Money Word Problems

  1. Read the problem carefully.
  2. Identify what you know and what you need to find.
  3. Decide whether to add, subtract, multiply, or divide.
  4. Do the calculation.
  5. Check if your answer makes sense.

Example:  Maria wants to buy a book that costs $8.50.
She has saved $5.25 so far.

How much more money does she need?

Solution:

What we know: Book costs $8.50, Maria has $5.25

What we need to find: How much more money she needs

Operation: Subtract what she has from the cost of the book

Calculation: $8.50 - $5.25 = $3.25

Maria needs $3.25 more.

Example:  Tom buys 3 pencils.
Each pencil costs $0.45.

How much does he spend in total?

Solution:

What we know: 3 pencils, each costs $0.45

What we need to find: Total cost

Operation: Multiply the number of pencils by the cost of one pencil

Calculation: 3 × $0.45

First pencil = $0.45
Second pencil = $0.45 + $0.45 = $0.90
Third pencil = $0.90 + $0.45 = $1.35

Tom spends $1.35 in total.

Equivalent Amounts of Money

Equivalent means equal in value. Different combinations of coins and bills can have the same total value.

For example, 25 cents can be made in many ways:

  • 1 quarter
  • 2 dimes and 1 nickel
  • 5 nickels
  • 25 pennies
  • 1 dime, 3 nickels

All of these combinations are worth exactly 25 cents, so they are equivalent.

Example:  Show two different ways to make 50 cents using only dimes and nickels.

Solution:

Way 1: Use 5 dimes
5 × 10¢ = 50¢

Way 2: Use 3 dimes and 4 nickels
3 × 10¢ = 30¢
4 × 5¢ = 20¢
30¢ + 20¢ = 50¢

Both ways make 50 cents.

Rounding Money Amounts

Sometimes we round money amounts to make them easier to work with or to estimate totals. When rounding money to the nearest dollar, look at the cents:

  • If the cents are 50 or more, round up to the next dollar.
  • If the cents are less than 50, round down to the current dollar.
Original AmountRounded to Nearest Dollar
$3.25$3.00
$3.50$4.00
$3.75$4.00
$7.18$7.00
$7.89$8.00

Rounding is helpful when you want to quickly estimate whether you have enough money. If a toy costs $6.75 and you have $7, rounding $6.75 to $7 tells you that you have just about enough.

Using Money in Real Life

Understanding money helps you in many everyday situations:

  • Shopping: You can figure out if you have enough money to buy what you want.
  • Saving: You can keep track of how much you have saved and how much more you need.
  • Budgeting: You can plan how to spend your money wisely.
  • Making change: You can check that you get the correct change when you buy something.

Example:  Sarah gets $10 for her allowance each week.
She wants to buy a game that costs $45.

How many weeks does she need to save?

Solution:

What we know: Sarah saves $10 per week, the game costs $45

What we need to find: Number of weeks to save

Operation: Divide the total cost by the amount saved per week

Calculation: $45 ÷ $10 = 4.5 weeks

Since Sarah cannot save for half a week in this situation, she needs to save for at least 5 full weeks.

Sarah needs to save for 5 weeks to have enough money.

Tips for Working with Money

Here are some helpful tips to remember when working with money:

  • Always line up the decimal points when adding or subtracting.
  • Count coins starting with the highest value first.
  • Check your work by counting your answer a different way.
  • Remember that 100 cents = 1 dollar.
  • When writing money, always use two digits after the decimal for cents, even if it is zero (like $5.00, not $5).

Think of the decimal point as a boundary. The left side counts whole dollars. The right side counts parts of a dollar, which we call cents. Just like a ruler shows inches and parts of inches, money notation shows dollars and parts of dollars.

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