Equivalent fractions
Equivalent fractions are different fractions that name the same value on the number line. In Grade 6 Saxon Math Course 1 (Chapter 5: Number and Operations), students create equivalent fractions by multiplying or dividing both numerator and denominator by the same nonzero number. For example, 1/2 = 2/4 = 3/6 = 4/8. Students use equivalent fractions to compare fractions, add or subtract fractions with unlike denominators, and reduce fractions to lowest terms by dividing both parts by their greatest common factor (GCF). Recognizing equivalence is foundational to all fraction operations in middle school math.
Key Concepts
Property Fractions with the same value but different names are called equivalent fractions . For example, the fractions $\frac{2}{4}$, $\frac{3}{6}$, and $\frac{4}{8}$ are all equivalent to $\frac{1}{2}$.
Examples To find an equivalent fraction for $\frac{1}{3}$: $\frac{1}{3} \times \frac{2}{2} = \frac{2}{6}$ To find an equivalent fraction for $\frac{2}{5}$: $\frac{2}{5} \times \frac{3}{3} = \frac{6}{15}$ To find a fraction equal to $\frac{1}{2}$ with a denominator of 20: $\frac{1}{2} \times \frac{10}{10} = \frac{10}{20}$.
Explanation Think of it like giving a fraction a disguise! By multiplying it by a special form of 1, like $\frac{2}{2}$ or $\frac{10}{10}$, you change its numerator and denominator but not its actual value. The fraction just gets a new name and look!
Common Questions
How do you create an equivalent fraction?
Multiply or divide both the numerator and the denominator by the same nonzero number. For example, 2/3 × 4/4 = 8/12, so 2/3 and 8/12 are equivalent.
How do you verify that two fractions are equivalent?
Cross-multiply: if a/b = c/d, then a×d = b×c. For 2/3 and 8/12: 2×12=24 and 3×8=24, so they are equivalent.
How are equivalent fractions used when adding fractions with unlike denominators?
Rewrite both fractions as equivalent fractions sharing a common denominator, then add the numerators.
What is simplifying a fraction and how does it relate to equivalent fractions?
Simplifying means finding the equivalent fraction with the smallest numerator and denominator by dividing both by their GCF. For 8/12, GCF=4, giving 2/3.
List three fractions equivalent to 3/4.
6/8, 9/12, and 12/16 are all equivalent to 3/4, formed by multiplying numerator and denominator by 2, 3, and 4 respectively.