How can fractions help us understand money?
Get ready to discover how fractions and money work together!
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Did you know that every coin is a fraction of a dollar?
A dollar is made up of 100 cents. So when we think about coins as fractions, we're asking: "What part of 100 cents is this coin?"
If a whole pizza has 100 slices, and you eat 25 slices, you ate 25/100 of the pizza, which equals 1/4 of the pizza!
Money works the same way! A quarter is 25 cents out of 100 cents, so it's 25/100 of a dollar, or 1/4 of a dollar!
Let's explore each coin and its fraction value! 🪙
A penny is worth 1 cent, and there are 100 cents in a dollar.
So 1 penny = 1/100 of a dollar
Imagine you have 100 pennies in a jar. If you take out 1 penny, you've taken 1/100 of all the pennies.
Since 100 pennies = $1.00, that means 1 penny = 1/100 of a dollar!
Penny: 1¢ = 1/100 of a dollar
Remember: The denominator (bottom number) tells us there are 100 cents in a dollar!
| Coin | Value in Cents | Fraction of a Dollar | Simplified Fraction |
|---|---|---|---|
| 🪙 Penny | 1¢ | 1/100 | 1/100 |
| 🪙 Nickel | 5¢ | 5/100 | 1/20 |
| 🪙 Dime | 10¢ | 10/100 | 1/10 |
| 🪙 Quarter | 25¢ | 25/100 | 1/4 |
| 🪙 Half Dollar | 50¢ | 50/100 | 1/2 |
Notice that we can simplify most of these fractions! A dime is 10/100, but we can divide both the numerator and denominator by 10 to get 1/10.
Why /100? Because there are 100 cents in one dollar!
🪙 Penny (1¢): 1/100 of a dollar
🪙 Nickel (5¢): 5/100 = 1/20 of a dollar
🪙 Dime (10¢): 10/100 = 1/10 of a dollar
🪙 Quarter (25¢): 25/100 = 1/4 of a dollar
🪙 Half Dollar (50¢): 50/100 = 1/2 of a dollar
Quick Check: Which coin is worth exactly 1/4 of a dollar? The quarter!
Just like with equivalent fractions, we can make the same amount of money using different coins!
Different combinations of coins can equal the same fraction of a dollar!
There are MANY ways to make 50¢, which is 1/2 of a dollar:
All of these combinations are equivalent — they all equal 1/2 of a dollar!
Using Fractions:
1/4 + 1/4 = 2/4
2/4 simplifies to 1/2
When we add fractions with the same denominator, we add the numerators:
So 2 quarters = 1/2 dollar = 50¢!
Using Fractions:
1/4 + 1/4 + 1/4 = 3/4
3 quarters = 3/4 of a dollar = 75¢
If a whole dollar is divided into 4 equal parts (quarters), and you have 3 of those parts, you have 3/4 of a dollar!
This is 75¢ because 25¢ + 25¢ + 25¢ = 75¢
Using Fractions:
1/10 + 1/10 + 1/10 + 1/10 + 1/10 = 5/10
5/10 simplifies to 1/2
5 dimes
= 5/10 dollar
= 1/2 dollar
= 50¢
2 quarters
= 2/4 dollar
= 1/2 dollar
= 50¢
Both equal 1/2 dollar!
Now let's use our fraction knowledge to solve division problems with money — WITHOUT using decimals!
When we divide money, we're really asking: "What fraction of the total does each person get?"
Problem: You have $1 and want to share it equally with a friend. How much does each person get?
Think with fractions:
$1 ÷ 2 people = Each person gets 1/2 of a dollar
1/2 of a dollar = 50¢
Answer: Each person gets $0.50 (or 50¢)
We can use what we know about coin fractions to solve these problems! 🪙
Step 1: Think about it as a fraction
$1 ÷ 2 means "1 dollar divided into 2 equal parts"
This is the same as asking: "What is 1/2 of a dollar?"
Step 2: Remember our coin knowledge!
We know that 2 quarters = 1/2 of a dollar
1/2 of a dollar = 50¢
Step 3: Write the answer
$1 ÷ 2 = $0.50
Think: What is 1/4 of a dollar?
We know a quarter is 1/4 of a dollar!
1 quarter = 25¢
$1 ÷ 4 = $0.25
Or we can say: Each person gets 1/4 dollar = 25¢
Do you see the pattern? When we divide $1, the fraction tells us what coin value we get!
Step 1: Write it as a fraction
$3 ÷ 6 = 3/6 dollars for each person
Step 2: Simplify the fraction
3/6 = 1/2 (divide both numbers by 3)
So each person gets 1/2 of a dollar
Step 3: Convert to cents
1/2 dollar = 50¢
$3 ÷ 6 = $0.50
1. Write the division as a fraction
2. Simplify the fraction if possible
3. Use your coin knowledge to convert to money!
$4 ÷ 8 = 4/8 dollars
4/8 simplifies to 1/2
1/2 dollar = 50¢ or $0.50
$6 ÷ 12 = 6/12 dollars
6/12 simplifies to 1/2
1/2 dollar = 50¢ or $0.50
$5 ÷ 10 = 5/10 dollars
5/10 simplifies to 1/2
1/2 dollar = 50¢ or $0.50
Notice: All of these simplify to 1/2 dollar = 50¢!
Remember unit rates? We can use fractions to help us find the price per item!
Unit Rate = Price ÷ Number of Items
This gives us the price for ONE item (the price per item)
Question: How much does each pencil cost?
Using Division:
$2 ÷ 4 pencils = ? per pencil
Using Fractions:
$2 ÷ 4 = 2/4 = 1/2
Each pencil costs 1/2 dollar = 50¢ or $0.50
What is the price per candy bar?
Step 1: Set up the division
Price per candy bar = $3 ÷ 6
Step 2: Write as a fraction
$3 ÷ 6 = 3/6 dollars
Step 3: Simplify
3/6 = 1/2 (divide both by 3)
Step 4: Convert to cents
1/2 dollar = 50¢
Each candy bar costs $0.50
Strategy:
Remember: Dividing money is just asking "what fraction does each person/item get?"
A dime is worth 10 cents.
Since there are 100 cents in a dollar:
10/100 = 1/10
A dime is 1/10 of a dollar! ✓
Step 1: What is 1/2 of a dollar in cents?
1/2 dollar = 50¢
Step 2: How much is each nickel worth?
1 nickel = 5¢
Step 3: Divide to find how many nickels
50¢ ÷ 5¢ = 10 nickels
Answer: 10 nickels = 1/2 dollar! ✓
Use fractions to help you!
Step 1: Think about it as a fraction
$1 ÷ 2 = "What is 1/2 of a dollar?"
Step 2: Use coin knowledge
1/2 dollar = 50¢
We can also think: 2 quarters = 50¢
$1 ÷ 2 = $0.50
Great job! Each person gets 50 cents! ✓
Step 1: Write as a fraction
$4 ÷ 8 = 4/8 dollars
Step 2: Simplify the fraction
4/8 = 1/2 (divide both numbers by 4)
Step 3: Convert to cents
1/2 dollar = 50¢
$4 ÷ 8 = $0.50
Excellent work! Each person gets $0.50! ✓
How much does each marker cost?
Step 1: Set up the problem
Price per marker = Total price ÷ Number of markers
Price per marker = $2 ÷ 4
Step 2: Write as a fraction and simplify
$2 ÷ 4 = 2/4 = 1/2
Step 3: Convert to cents
1/2 dollar = 50¢
Each marker costs $0.50
Perfect! You found the unit rate! 🎨 ✓
Step 1: Write as a fraction
$6 ÷ 12 = 6/12 dollars
Step 2: Simplify the fraction
6/12 = 1/2 (divide both numbers by 6)
Step 3: Convert to cents
1/2 dollar = 50¢
$6 ÷ 12 = $0.50
Awesome! Notice the pattern - these keep simplifying to 1/2! ✓
What is the price per book?
Step 1: Set up the division
Price per book = $4 ÷ 8
Step 2: Write as a fraction and simplify
$4 ÷ 8 = 4/8 = 1/2
Step 3: Convert to cents
1/2 dollar = 50¢
Each book costs $0.50
Great thinking! You used fractions to find the unit rate! 📚 ✓
Step 1: Write as a fraction
$5 ÷ 10 = 5/10 dollars
Step 2: Simplify the fraction
5/10 = 1/2 (divide both numbers by 5)
Step 3: Convert to cents
1/2 dollar = 50¢
Or think: 5 dimes = 1/2 dollar!
$5 ÷ 10 = $0.50
Fantastic! Did you notice they all equal $0.50? ✓
How much does 1 slice cost?
Step 1: Find the price per slice
Price per slice = $6 ÷ 12
Step 2: Write as a fraction and simplify
$6 ÷ 12 = 6/12
6/12 = 1/2 (divide both by 6)
Step 3: Convert to cents
1/2 dollar = 50¢
Each slice costs $0.50
You nailed it! Even with bigger numbers, fractions make it easier! 🍕 ✓
Choose all that apply:
A) 3 quarters:
3 × 25¢ = 75¢ ✓ CORRECT!
B) 7 dimes + 1 nickel:
(7 × 10¢) + (1 × 5¢) = 70¢ + 5¢ = 75¢ ✓ CORRECT!
C) 15 nickels:
15 × 5¢ = 75¢ ✓ CORRECT!
D) 1 half dollar + 1 quarter:
50¢ + 25¢ = 75¢ ✓ CORRECT!
Amazing! All four are correct!
They all equal 75¢, which is 3/4 of a dollar! ✓
Step 1: Write as a fraction
$3 ÷ 6 = 3/6 dollars
Step 2: Simplify the fraction
3/6 = 1/2 (divide both numbers by 3)
Step 3: Convert to cents
1/2 dollar = 50¢
$3 ÷ 6 = $0.50
Perfect! You're a fraction and money expert! ✓
Always simplify your fraction before converting to cents. It's much easier to work with 1/2 than 6/12!
If a fraction simplifies to 1/2, 1/4, or 1/10, you can immediately know the cent value because of your coin knowledge!
Write out each step: fraction → simplify → convert to cents. This helps you catch mistakes!
Does your answer make sense? If you divided $2 by 2 people, each person should get about $1, not $10!
When you divide money, you're really asking: "What fraction does each person/item get?"
Example: $6 ÷ 12 = 6/12 = 1/2 = 50¢
In our next unit, we'll learn about decimals — a special way to write fractions when the denominator is 10, 100, or 1000.
You already know that:
Soon you'll learn that we can also write these as:
The decimal point is just another way to show fractions of a dollar!
Amazing work! You're ready for decimals! 🌟💵