Equivalent Fractions
Equivalent fractions are different fractions that represent the same value. They're created by multiplying or dividing both the numerator and denominator by the same non-zero number.
Rule
a/b = (axn) / (bxn) where n != 0
Creating Equivalent Fractions
- Choose any non-zero number
- Multiply both numerator and denominator by that number
- The result is an equivalent fraction
Examples
Example 1: Find equivalents of 1/2
1/2 = 2/4 = 3/6 = 4/8 = 5/10...
Example 2: Find equivalents of 2/3
2/3 = 4/6 = 6/9 = 8/12...
Visual Understanding
Imagine a pizza: 1/2 of a pizza is the same amount as 2/4 or 4/8 - you're just cutting it into more pieces.
Uses
- Finding common denominators
- Comparing fractions
- Simplifying complex fractions
- Scaling recipes
Key Insight
Multiplying by n/n is the same as multiplying by 1, so the value doesn't change - only the representation.
Quick Tips
- Double-check your inputs for accurate results
- Use parentheses to clarify order of operations
- Results are rounded — consider significant figures
Frequently Asked Questions
Fractions that represent the same value but look different.
Multiply (or divide) both numerator and denominator by the same number.
Yes, they represent the same value.
Infinitely many for any fraction.
They help with comparing, adding, and subtracting fractions.