Equivalent Fractions

Learn how different fractions can represent the same amount and how to find equivalent fractions.

Elementary25 minLesson
Printable worksheet

Definition

Equivalent fractions are fractions that look different but represent the same value.
For example, 12\frac{1}{2} and 24\frac{2}{4} are equivalent because they both represent half of a whole.
12=24=36=48\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}
To find an equivalent fraction, multiply (or divide) both the numerator and denominator by the same number:
12×22=24\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}

Try it now

Which fraction is equivalent to 12\frac{1}{2}?

Worked Examples

Find a fraction equivalent to 23\frac{2}{3} with a denominator of 12.
1

Identify what to multiply the denominator by

3×?=123 \times ? = 12, so 3×4=123 \times 4 = 12 → Multiply by 4
2

Multiply both numerator and denominator by the same number

23×44=2×43×4\frac{2}{3} \times \frac{4}{4} = \frac{2 \times 4}{3 \times 4} → 812\frac{8}{12}
3

Verify the fractions are equivalent

23=812\frac{2}{3} = \frac{8}{12} (both equal approximately 0.667) → Confirmed equivalent

Common Mistakes

Adding the same number to both numerator and denominator

Why it's wrong: Adding 1 to the top and bottom of 12\frac{1}{2} gives 1+12+1=23\frac{1+1}{2+1} = \frac{2}{3}, but 23≠12\frac{2}{3} \neq \frac{1}{2}. Adding doesn't keep the ratio between the part and the whole.

Correct: Always multiply or divide both by the same number: 12×22=24\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}

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: 612\frac{6}{12} looks bigger than 12\frac{1}{2} but they're equal! The relationship between numerator and denominator matters.

Correct: Compare by finding common denominators or simplifying first.

Interactive Visual

3
3/4= 75%

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Fraction Number Line

02/41

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Practice Problems

18 problems
Problem 1 of 18
Easy
Which fraction is equivalent to 12\frac{1}{2}?

Why It Matters

Equivalent fractions are essential in everyday life:
  • Cooking: A recipe calls for 12\frac{1}{2} cup, but your measuring cup shows 24\frac{2}{4} - they're the same!
  • Sharing fairly: Cutting a pizza into 4 or 8 slices - 24\frac{2}{4} and 48\frac{4}{8} are both half the pizza
  • Money: Half a dollar (12\frac{1}{2}) equals two quarters (24\frac{2}{4}) equals 50 cents
  • Comparing: Deciding if 34\frac{3}{4} is more or less than 68\frac{6}{8} (they're equal!)
Understanding equivalent fractions helps you simplify, compare, and add fractions!

Real World Applications

Cooking and Recipes

Recipes often need to be scaled up or down, requiring equivalent fractions.

Example:

If a recipe calls for 34\frac{3}{4} cup of flour and you want to double it, you need 64\frac{6}{4} or 32\frac{3}{2} cups.

1Try It Yourself

Your recipe needs 13\frac{1}{3} cup of sugar, but your measuring cup only shows sixths.

How many sixths equal 13\frac{1}{3}?

Step 1: Write the mathematical expression

Convert 13\frac{1}{3} to sixths: 13×??\frac{1}{3} \times \frac{?}{?}

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 (48\frac{4}{8}) equals half the pizza (12\frac{1}{2}).

2Try It Yourself

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: Choose the right answer

Compare 36\frac{3}{6} and 48\frac{4}{8}: which sign is correct?

Money and Coins

Coins represent fractional parts of a dollar in equivalent ways.

Example:

Half a dollar (12\frac{1}{2}) = 2 quarters (24\frac{2}{4}) = 5 dimes (510\frac{5}{10}) = 50 cents (50100\frac{50}{100})

3Try It Yourself

You have 75 cents. What fraction of a dollar is this?

Express 75 cents as a simplified fraction of a dollar.

Step 1: Choose the right answer

75 cents out of 100 cents in a dollar = 75100\frac{75}{100}. Which fraction is 75100\frac{75}{100} in lowest terms?

Key Takeaways

  • 1Equivalent fractions represent the same value but look different (12=24=36\frac{1}{2} = \frac{2}{4} = \frac{3}{6})
  • 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 a×d=b×ca \times d = b \times c, then ab=cd\frac{a}{b} = \frac{c}{d}

Frequently Asked Questions

A fraction is in lowest terms when the numerator and denominator share no common factors except 1. For example, 34\frac{3}{4} is in lowest terms, but 68\frac{6}{8} is not (both divisible by 2).
A fraction is in lowest terms when the numerator and denominator share no common factors except 1. For example, 34\frac{3}{4} is in lowest terms, but 68\frac{6}{8} is not (both divisible by 2).
Yes! You can multiply the numerator and denominator by any number: 12=24=36=100200\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{100}{200} and so on forever.
Because 22=1\frac{2}{2} = 1, and multiplying by 1 never changes a number's value. It just changes how the number looks.

Glossary

Equivalent fractions
Fractions that represent the same value (e.g., 12\frac{1}{2} and 24\frac{2}{4})
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

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Multiply both parts by the same number n (equivalent to multiplying by $\frac{n}{n}$)

Simplifying fractions

ab=a÷GCFb÷GCF\frac{a}{b} = \frac{a \div \text{GCF}}{b \div \text{GCF}}

Divide both parts by the greatest common factor to get lowest terms

Cross multiplication test

a×d=b×ca \times d = b \times c

If cross products are equal, fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent

Today's challengeOne problem, three tries

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