Equivalent fractions
Equivalent fractions represent the same value even though they use different numerators and denominators. In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students confirm equivalence by cross-multiplying (a/b = c/d when a times d = b times c) and create equivalent fractions by multiplying or dividing both parts by the same nonzero integer. For example, 6/12 = 1/2 because both are divisible by 6. Equivalent fractions are foundational for adding unlike fractions, comparing fractions, and reducing to simplest form.
Key Concepts
Property $\frac{6}{12}$ and $\frac{1}{2}$ are called equivalent fractions or equal fractions .
Examples Is $\frac{4}{6}$ equivalent to $\frac{2}{3}$? Yes, because $\frac{4 \div 2}{6 \div 2} = \frac{2}{3}$. Find a fraction equivalent to $\frac{3}{5}$: $\frac{3 \times 4}{5 \times 4} = \frac{12}{20}$. The fractions $\frac{8}{10}$, $\frac{4}{5}$, and $\frac{16}{20}$ are all equivalent.
Explanation Equivalent fractions are like twins in different outfits. The fractions $\frac{1}{2}$ and $\frac{2}{4}$ might look different, but they represent the exact same amount of stuff. Whether you eat 1 out of 2 giant cookies or 2 out of 4 small cookies, you still ate half! They have the same value, just different numbers.
Common Questions
What are equivalent fractions?
Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, 3/6, and 4/8 are all equivalent.
How do you verify that 6/12 and 1/2 are equivalent?
Cross-multiply: 6 x 2 = 12 and 12 x 1 = 12. Since both products are equal, the fractions are equivalent.
Create an equivalent fraction for 3/5 with denominator 20.
20 divided by 5 = 4. Multiply both parts by 4: 3 x 4 = 12 and 5 x 4 = 20. Equivalent fraction: 12/20.
How are equivalent fractions used when adding unlike fractions?
Rename each fraction as an equivalent fraction sharing the LCD before adding the numerators.
What is the simplest form of 8/20?
GCF of 8 and 20 is 4. Divide both by 4: 8/20 = 2/5.