Equivalent Fractions

Grade 4 · Math · Study Guide

Discover how different fractions can represent the same amount using multiplication and division.

Equivalent fractions are fractions that look different but have the same value. For example, 1/2 and 2/4 and 4/8 all represent the same amount — half of something.

To create an equivalent fraction, multiply or divide both the numerator (top number) and the denominator (bottom number) by the same number. For example, to find a fraction equivalent to 2/3, multiply both parts by 2: (2 × 2)/(3 × 2) = 4/6. Since you multiplied by 2/2 which equals 1, you did not change the value.

To simplify a fraction (find its lowest terms), divide both the numerator and denominator by their greatest common factor (GCF). For 6/8, the GCF of 6 and 8 is 2, so 6 ÷ 2 = 3 and 8 ÷ 2 = 4, giving you 3/4.

You can also use a number line or fraction models to check if two fractions are equivalent. On a number line, equivalent fractions land on the same point. In a fraction bar model, the shaded portions cover the same area even if they are split into different numbers of pieces.

Key terms

Equivalent fractions: Fractions that represent the same value, even though they use different numerators and denominators.
Numerator: The top number of a fraction; it tells how many parts are being considered.
Denominator: The bottom number of a fraction; it tells how many equal parts the whole is divided into.
Simplify: To rewrite a fraction using the smallest possible numerator and denominator while keeping the same value.
Greatest Common Factor (GCF): The largest number that divides evenly into both the numerator and denominator.
Lowest terms: A fraction where the numerator and denominator share no common factor other than 1.

Flashcards

Equivalent fractions: Fractions with the same value; made by multiplying or dividing both numerator and denominator by the same number
1/2 equivalent fractions: 2/4, 3/6, 4/8, 5/10 — all equal one half
Simplifying 6/9: Divide numerator and denominator by GCF of 3: 6 ÷ 3 = 2 and 9 ÷ 3 = 3, so 6/9 = 2/3
Why multiply top AND bottom?: Multiplying both by the same number is the same as multiplying by 1 (e.g., 2/2 = 1), so the value does not change
GCF of 4 and 8: 4 — because 4 divides evenly into both 4 and 8; used to simplify 4/8 to 1/2
Fraction comparison using equivalents: Rewrite both fractions with the same denominator to compare; e.g., 1/2 = 3/6 and 2/3 = 4/6, so 2/3 > 1/2
Is 3/5 equivalent to 6/10?: Yes — multiply numerator and denominator of 3/5 by 2: (3 × 2)/(5 × 2) = 6/10
Lowest terms: A fraction simplified so numerator and denominator share no common factor other than 1; e.g., 3/4 is in lowest terms

Questions

Which fraction is equivalent to 3/4?
1. 6/10
2. 9/12
3. 6/9
4. 4/5
Show answer
Answer: 9/12
3/4: multiply both by 3 → (3 × 3)/(4 × 3) = 9/12. Check: 9 ÷ 3 = 3 and 12 ÷ 3 = 4. ✓
To create an equivalent fraction, you can add the same number to both the numerator and denominator.
Show answer
Answer: False
Adding the same number to both parts changes the value. You must multiply or divide both parts by the same number.
To simplify 8/12, divide both the numerator and denominator by 4 to get _____.
Show answer
Answer: 2/3
8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 simplifies to 2/3. The GCF of 8 and 12 is 4.
What number do you multiply both the numerator and denominator of 1/3 by to get 4/12?
1. 2
2. 3
3. 4
4. 5
Show answer
Answer: 4
1 × 4 = 4 and 3 × 4 = 12, so you multiply by 4 to get 4/12.
2/5 and 4/10 are equivalent fractions.
Show answer
Answer: True
2/5 × (2/2) = 4/10. Since both fractions simplify to the same value, they are equivalent.

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