Summary: Equivalent fractions are different fractions that name the same number. We can now redefine the terms fraction and equivalent fraction as follows: In example 9, we multiplied the numerator AND the denominator by 5. Write the fraction three-eighths as an equivalent fraction with a numerator of 15. In example 8, we multiplied the numerator AND the denominator by 3. Write the fraction two-sevenths as an equivalent fraction with a denominator of 21. In example 7, we multiplied the numerator AND the denominator by 4. Write the fraction five-sixths as an equivalent fraction with a denominator of 24. However, the equivalent fractions found in each part all have the same value. Looking at each part of example 6, the answers vary, depending on the nonzero whole number chosen. Note that the procedure for finding equivalent fractions is the same for both types of fractions. In example 6, the fraction given in part a is a proper fraction whereas the fractions given in parts b and c are improper fractions. Let's look at some more examples: Example 5 Equal fractions may look different, but they have the same value, hence equal. Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equal fraction, but it will not change its value. So, multiplying a fraction by one does not change its value. In the last lesson, we learned that a fraction that has the same numerator and denominator is equal to one. The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equal fractions. But you cannot multiply the numerator by 4 and the denominator by 2. ![]() You can multiply the numerator and the denominator by 4, as shown in part B above. ![]() But you cannot multiply the numerator by 3 and the denominator by 5. You can multiply the numerator and the denominator of a fraction by any nonzero whole number, as long as you multiply both by the same whole number! For example, you can multiply the numerator and the denominator by 3, as shown in part A above. This procedure is used to solve example 4. ![]() Procedure: To find equivalent fractions, multiply the numerator AND denominator by the same nonzero whole number. We need an arithmetic method for finding equal fractions. What would happen if we did not have shapes such as circles and rectangles to refer to? Look at example 4 below. The fractions three-fourths, six-eighths, and nine-twelfths are equivalent. Let's look at some more examples: Example 2 These are equivalent fractions.ĭefinition: Equivalent fractions are different fractions that name the same number. What do the fractions in example 1 have in common?Įach fraction in example 1 represents the same number. Use the following examples and interactive exercises to learn about equivalent fractions. Learn About Equivalent Fractions With Example Problems And Interactive Exercises.
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