Find Equivalent Fractions

Equivalent fractions look different but represent the same amount. Half a pizza cut into 2 slices and half a pizza cut into 8 slices are the same amount — 1/2 = 4/8. You can always find an equivalent fraction by multiplying or dividing both the numerator and denominator by the same non-zero number.

Finding Equivalent Fractions by Multiplying

• Multiply both the numerator and denominator by the same number.
• Example: 1/2 × 2/2 = 2/4 — double both top and bottom.
• Example: 1/2 × 4/4 = 4/8 — multiply both by 4.
• The value does not change because you are multiplying by 1 (in the form n/n).

Simplifying Fractions (Finding Lowest Terms)

• Divide both the numerator and denominator by their Greatest Common Factor (GCF).
• GCF of 6 and 8 is 2 — so 6/8 ÷ 2/2 = 3/4.
• A fraction is in its simplest form when the GCF of numerator and denominator is 1.
• Always divide by the SAME non-zero number — never add or subtract.

Checking if Two Fractions Are Equivalent

• Cross-multiply: if a/b = c/d, then a × d = b × c.
• Example: Is 3/4 = 9/12? Check: 3 × 12 = 36 and 4 × 9 = 36. Yes, they are equivalent.
• Or simplify both fractions — if they reduce to the same fraction, they are equivalent.