# How to Write Two Fractions That Are Equivalent to a Given Fraction

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Equivalent fractions are fractions that have the same value as each other. Finding equivalent fractions is a number-sense lesson that requires knowledge of basic multiplication and division. You can manipulate a fraction to find two equivalent fractions by dividing the fraction down into simplest form or by multiplying the fraction by a chosen number. The key to finding equivalent fractions is to manipulate the numerator and denominator by the same digit.

Look at the numerator and denominator of the given fraction. Write a list of common factors that divide into both the numerator and denominator evenly, to find an equivalent fraction in a simpler form (or its simplest form).

Divide the numerator and denominator by the same factor. For example, for the fraction 4/8, the factors 2 and 4 both divide evenly into the numerator and denominator. This solves the problem for two equivalent fractions, as in (4/8 ÷ 2 = 2/4) and (4/8 ÷ 4 = 1/2).

Multiply the numerator and denominator of a fraction by the same number to find an equivalent fraction. For instance, 4/8 x 2 = 8/16 and 4/8 x 4 = 16/32. These fractions are equivalent because when divided by the greatest common factor (GCF) into simplest form, they all equal 1/2.

Find equivalent fractions on a multiple choice quiz or test by writing them as diagrams. An example question might be: “What fractions are equivalent to 1/2?” Draw one circle and label it 1/2. Split the circle into the number of parts, as indicated by the denominator, which in this case is two parts. Color in the number indicated by the numerator, which in this case is one part.

Draw and label same-sized circles for the equivalent fraction options. Use the numerator and denominator of each choice to figure out how many parts to divide the circle into and how many parts to shade. Compare the shaded part of the circle to find equivalent fractions with the same amount shaded as the given fraction.