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How to Subtract Mixed Fractions with Unlike Denominators

Instructor: Mia Primas

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

In this lesson, you will learn how to subtract mixed fractions with unlike denominators. The mixed fractions will be converted to improper fractions, then changed so that they have the same denominator.

Steps for Subtracting Mixed Fractions with Unlike Denominators


Example of subtracting mixed fractions with unlike denominators
subfrac1

  • Step 1: Convert the mixed fractions to improper fractions.

Multiply the whole number by the denominator of the fraction and then add the numerator. This number becomes the numerator of the improper fraction. The denominator of the improper fraction remains the same as the denominator of the mixed fraction.


subfrac2


subfrac3

  • Step 2: Change the fractions so that they have the same denominator

We can make a common denominator by determining a common multiple of the denominators, 6 and 9. The multiples of 6 are 6, 12, 18, etc. The multiples of 9 are 9, 18, 27, etc. They have a common multiple of 18 which will be the new denominator for the fractions.

Multiplying the first fraction by 3/3 and the second fraction by 2/2 will result in 18 for both denominators. Note that 3/3 and 2/2 are equal to 1, so we are actually multiplying both fractions by 1 and not changing the value of the fractions in any way.


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  • Step 3: Subtract the fractions

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