Find Equivalent Fractions
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What you will learn
- 1Explain that equivalent fractions represent the same amount using different denominators
- 2Find equivalent fractions by multiplying or dividing numerator and denominator by the same number
- 3Simplify a fraction to its lowest terms
- 4Identify whether two fractions are equivalent
Mini Lesson
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 (2/2 and 4/4 both equal 1).
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 divide the top and bottom by 2: 6/8 → 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.
Words to know
Equivalent fractions
Different fractions that name the same amount
e.g. 1/2 and 4/8 are equivalent fractions.
Simplify
To rewrite a fraction with smaller numerator and denominator
e.g. Simplify 6/8 to 3/4.
Common factor
A number that divides exactly into both numerator and denominator
e.g. 2 is a common factor of 6 and 8.
Lowest terms
A fraction whose numerator and denominator share no common factor besides 1
e.g. 3/4 is in lowest terms.
Cross-multiply
A check that multiplies the diagonals of two fractions to compare them
e.g. Cross-multiply to test if 3/4 equals 9/12.
Tip: To check if two fractions are equivalent, simplify both to lowest terms. If they match, they are equivalent.
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