Equivalent Fractions & Simplifying
Learn how to find equivalent fractions, use the greatest common factor (GCF) to simplify, and express fractions in their lowest terms.
What Are Equivalent Fractions?
Equivalent fractions are different fractions that represent the same value. You create them by multiplying or dividing both the numerator and denominator by the same number.
Visual Example
1⁄2
2⁄4
4⁄8
All three fractions show exactly the same amount — one half!
The Rule
Multiply or divide the numerator AND denominator by the same number (not zero). The fraction stays equal.
2⁄3 = 2×4⁄3×4 = 8⁄12
Greatest Common Factor (GCF)
The greatest common factor (GCF) is the largest number that divides evenly into both the numerator and denominator. You use it to simplify fractions to their lowest terms.
Finding the GCF of 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6
GCF = 6
Simplifying Fractions
To simplify (or reduce) a fraction, divide both the numerator and denominator by their GCF. When you cannot simplify any further, the fraction is in its lowest terms.
Example: Simplify 12⁄18
Step 1: Find the GCF of 12 and 18 → 6
Step 2: Divide both: 12 ÷ 6 = 2, 18 ÷ 6 = 3
Answer: 12⁄18 = 2⁄3
Using Equivalent Fractions to Compare
To compare fractions with different denominators, find equivalent fractions with a common denominator, then compare the numerators.
Example: Which is larger, 3⁄4 or 5⁄6?
Step 1: Common denominator of 4 and 6 = 12
Step 2: 3⁄4 = 9⁄12 and 5⁄6 = 10⁄12
Answer: 10⁄12 > 9⁄12, so 5⁄6 is larger.
Key Vocabulary
Equivalent Fractions
Different fractions that represent the same value (e.g. 1⁄2 = 3⁄6).
Simplify
Reducing a fraction by dividing both parts by their greatest common factor.
GCF (Greatest Common Factor)
The largest number that divides evenly into two or more numbers.
Lowest Terms
A fraction where the numerator and denominator share no common factor other than 1.
Worked Examples
Find an equivalent fraction: 3⁄5 = ?⁄20
Step 1: What was 5 multiplied by to get 20? 5 × 4 = 20
Step 2: Multiply the numerator by the same number: 3 × 4 = 12
Answer: 3⁄5 = 12⁄20
Simplify 15⁄25 to lowest terms.
Step 1: Find GCF of 15 and 25 → 5
Step 2: 15 ÷ 5 = 3, 25 ÷ 5 = 5
Answer: 15⁄25 = 3⁄5
Simplify 24⁄36
Step 1: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Step 2: Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 3: GCF = 12. Divide: 24 ÷ 12 = 2, 36 ÷ 12 = 3
Answer: 24⁄36 = 2⁄3
Knowledge Check
Select the correct answer for each question. Click “Check Answer” to see if you are right.
Question 1
Which fraction is equivalent to 2⁄3?
Question 2
Simplify 10⁄15 to lowest terms.
Question 3
What is the GCF of 16 and 24?
Question 4
Complete: 5⁄8 = ?⁄24
Question 5
Simplify 18⁄30 to lowest terms.
Key Concepts Summary
- ●Equivalent fractions represent the same value.
- ●Multiply or divide both parts by the same number to find equivalents.
- ●The GCF is the largest number that divides both numerator and denominator.
- ●A fraction is in lowest terms when the GCF of numerator and denominator is 1.