Equivalent Fractions
Learn how different fractions can represent the same amount and how to find equivalent fractions.
Definition
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Worked Examples
Find a fraction equivalent to with a denominator of 12.
Identify what to multiply the denominator by
, so → Multiply by 4
Multiply both numerator and denominator by the same number
→
Verify the fractions are equivalent
(both equal approximately 0.667) → Confirmed equivalent
Answer:
Common Mistakes
Adding the same number to both numerator and denominator
Why it's wrong: . Adding doesn't preserve the ratio between parts and whole.
Correct: Always multiply or divide both by the same number:
Only changing the numerator or only the denominator
Why it's wrong: Changing just one number changes the value of the fraction entirely.
Correct: Both numerator AND denominator must be multiplied (or divided) by the same number.
Thinking larger numbers always mean larger fractions
Why it's wrong: looks bigger than but they're equal! The relationship between numerator and denominator matters.
Correct: Compare by finding common denominators or simplifying first.
Interactive Visual
Click on the bar to change the fraction
Fraction Number Line
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
18 problemsWhich fraction is equivalent to ?
Why It Matters
- Cooking: A recipe calls for cup, but your measuring cup shows - they're the same!
- Sharing fairly: Cutting a pizza into 4 or 8 slices - and are both half the pizza
- Money: Half a dollar () equals two quarters () equals 50 cents
- Comparing: Deciding if is more or less than (they're equal!)
Real World Applications
Cooking and Recipes
Recipes often need to be scaled up or down, requiring equivalent fractions.
Example:
If a recipe calls for cup of flour and you want to double it, you need or cups.
Your recipe needs cup of sugar, but your measuring cup only shows sixths.
How many sixths equal ?
Step 1: Write the mathematical expression
Convert to sixths:
Pizza and Fair Sharing
Understanding that different slices can represent equal amounts helps with fair sharing.
Example:
A pizza cut into 8 slices: 4 slices () equals half the pizza ().
You ate 3 slices of a pizza cut into 6 pieces. Your friend ate 4 slices of a pizza cut into 8 pieces.
Who ate more pizza?
Step 1: Write the mathematical expression
Compare and
Money and Coins
Coins represent fractional parts of a dollar in equivalent ways.
Example:
Half a dollar () = 2 quarters () = 5 dimes () = 50 cents ()
You have 3 quarters. What fraction of a dollar is this?
Express 3 quarters as a simplified fraction of a dollar.
Step 1: Write the mathematical expression
3 quarters out of 4 quarters in a dollar =
Key Takeaways
- 1Equivalent fractions represent the same value but look different ()
- 2To find an equivalent fraction, multiply or divide both numerator and denominator by the same number
- 3A fraction is in lowest terms when numerator and denominator share no common factors except 1
- 4Cross multiplication can verify if two fractions are equivalent: if , then
Frequently Asked Questions
Glossary
- Equivalent fractions
- Fractions that represent the same value (e.g., and )
- Numerator
- The top number of a fraction, showing how many parts you have
- Denominator
- The bottom number of a fraction, showing how many equal parts the whole is divided into
- Lowest terms
- A fraction where numerator and denominator share no common factors except 1
- Greatest Common Factor (GCF)
- The largest number that divides evenly into two or more numbers
Formula Card
Creating equivalent fractions
Multiply both parts by the same number n (equivalent to multiplying by $\frac{n}{n}$)
Simplifying fractions
Divide both parts by the greatest common factor to get lowest terms
Cross multiplication test
If cross products are equal, fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent