Free Math Guide
Learn how equivalent fractions work, how to use scale factors, how to solve missing-number problems, and how to check your answers.
Equivalent fractions are fractions that look different but represent the same amount. Once you understand how the numerator and denominator change together, finding and recognizing equivalent fractions becomes much easier.
Equivalent fractions have different numerators or denominators but represent the same portion of a whole.
Each fraction above represents one-half. The number of pieces changes, but the amount represented does not.
One out of two equal parts is selected.
Two out of four equal parts still represents one-half of the whole.
Three out of six equal parts also represents one-half.
Ten out of twenty equal parts is another way to represent one-half.
Equivalent fractions may use different numbers, but their overall values are equal.
A scale factor tells you what number was used to multiply or divide both parts of a fraction.
Multiply or divide the numerator and denominator by exactly the same nonzero number.
Choose a scale factor and apply it to both the numerator and denominator.
Select a nonzero whole number, such as 2, 3, 4, or 5.
Multiply the top number by the selected scale factor.
Multiply the bottom number by the same scale factor.
Confirm that both numbers changed using the same operation and factor.
First compare the denominators. Determine the scale factor, then apply that same factor to the numerator.
Find how the denominators changed, then make the numerators change in exactly the same way.
Compare the numerators to find the scale factor. Then apply that same scale factor to the denominator.
Find how the numerators changed, then make the denominators change in the same way.
You can check equivalent fractions using scale factors, cross products, or simplified forms.
Determine whether the numerator and denominator changed by the same factor.
Multiply diagonally. Equivalent fractions have equal cross products.
If both fractions simplify to the same fraction, they are equivalent.
Dividing each numerator by its denominator can confirm whether the values are equal.
Compare the cross products:
The cross products are equal, so the fractions are equivalent.
Compare the cross products:
The cross products are not equal, so the fractions are not equivalent.
For fractions a/b and c/d, the fractions are equivalent when a × d = b × c.
Simplifying a fraction means dividing the numerator and denominator by a common factor. The simplified fraction remains equivalent to the original fraction.
Divide the numerator and denominator by the same common factor until they have no common factor greater than 1.
Multiplying only the numerator changes the value of the fraction. The denominator must be multiplied by the same factor.
The numerator was multiplied by 3, but the denominator was multiplied by 4. Because the factors do not match, the fractions are not equivalent.
Adding the same number to the numerator and denominator does not usually create an equivalent fraction.
Fractions cannot be compared using only their numerators. The denominator determines the size of each part.
Pay attention to the direction of the change. Going from 4 to 20 uses multiplication by 5, while going from 20 to 4 uses division by 5.
Use these questions before submitting your answer.
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