What Are Equivalent Fractions?
Equivalent fractions encompass different types of fractions that represent equal values, or portions, as a whole. Although they have different forms, both will yield the same results when compared. To create an equivalent fraction, multiply/divide both the numerator (top number) and denominator (bottom number) by the same non-zero number.
Key Points: ✔ Different looks with the same message. ✔ Created from scaling (multiplying or dividing). ✔ Allow for easier calculation and/or simplification of fractions.
Examples of Equivalent Fractions
Example 1: ½, 2⁄4, and 3⁄6 are all the same fraction. For the pizza example: ½ means 1 slice out of 2: 2 slices out of 4, and that is the same as ½; 3 slices out of 6, or ½. Example 2: ⅓, 2⁄6, and 3⁄9 are all the same fraction. For the cake example: ⅓ means 1 piece out of 3; 2 pieces out of 6 is the same as ⅓; 3 pieces out of 9 is still the same as ⅓. Example 3: ⅖ and 4⁄10 are equal fractions. Chocolate bar example: ⅖ means 2 squares out of 5; 4 squares out of 10, which are the same as ⅖.
How to Find Equivalent Fractions
Method 1: Multiply Numerator & Denominator To find an equivalent fraction, multiply both the numerator and denominator by the same number.
Example: Find a fraction equivalent to ¾.
Multiply numerator & denominator by 2:3×24×2=684×23×2=86→ ¾ = 6⁄8 Method 2: Divide Numerator & Denominator You can also divide both numbers by the same number (simplifying).
Example: Simplify 8⁄12.
Divide numerator & denominator by 4:8÷412÷4=2312÷48÷4=32→ 8⁄12 = ⅔
Exercises
Exercise 1: Identifying Equivalent Fractions Circle the fractions that are equivalent to 1/2:
2/4 3/6 4/8 2/5 5/10
Exercise 2: Fill in the Missing Number Fill in the blank to make the fractions equivalent:
1/3 = /6 2/5 = /10 3/4 = /8 5/6 = 10/ 2/3 = __/9
Exercise 3: Creating Equivalent Fractions Multiply the numerator and denominator by the same number to create equivalent fractions:
2/3 (Multiply by 2) = / 3/5 (Multiply by 3) = / 4/6 (Multiply by 4) = / 1/4 (Multiply by 5) = /
Exercise 4: True or False Determine if the following pairs of fractions are equivalent (True or False):
3/6 and 1/2 4/8 and 2/4 2/3 and 3/5 6/9 and 2/3 8/10 and 4/5