How to Multiply and Divide Mixed Fractions

By Jon Zamboni
Mixed fractions can represent positive or negative numbers larger than 1.

Mixed fractions are composed of a whole number and a fraction, and represent the total of the two -- 3 1/4, for instance, represents 3 and one-fourth. To multiply or divide a mixed fraction, convert it into a an improper fraction such as 13/4. You can then multiply or divide it like any other fraction.

Convert Mixed Fractions to Improper Fractions

Before you can multiply or divide mixed fractions, you must convert the mixed fractions to improper fractions. An improper fraction, such as 7/4, is a fraction whose numerator is larger than its denominator. The numerator is the top number in the fraction, and the denominator is the bottom number. To convert a mixed fraction to an improper fraction, multiply the whole number part of the mixed fraction by the fraction's denominator, then add it to the numerator. For example, to convert the mixed fraction 8 1/3, multiply the whole number, 8, by the denominator, 3, getting the product 24. Add 24 to the numerator to find the equivalent improper fraction: 25/3. So 8 1/3 = 25/3.

Multiply Numerator and Denominator

Once you've converted the mixed numbers to improper fractions, you can multiply two fractions together. Say you're multiplying 3 1/2 by 1 1/3: 3 1/2 is equal to 7/2, and 1 1/3 is equal to 4/3, so you're multiplying 7/2 by 4/3. To multiply two fractions, multiply the numerators together to find the new numerator, then multiply the denominators together to find the new denominator. The numerators of the fractions are 7 and 4; multiplied together they produce the new numerator, 28. The denominators, 2 and 3, are multiplied together to produce the new denominator, 6. So the product of multiplying 7/2 by 4/3 is 28/6.

Divide Fractions

When you divide one fraction by another fraction, you switch the numerator and denominator of the divisor fraction, then multiply. Say instead of multiplying 7/2 by 4/3, you're dividing 7/2 by 4/3. Switch the numerator and denominator of 4/3, getting 3/4, then multiply: 7/2 x 3/4 = (7 x 3)/(2 x 4) = 21/8.

Simplify Fractions

Once you've divided or multiplied your fractions, check to see if the result can be simplified. You can simplify a fraction if both the numerator and denominator can be evenly divided by the same number. For instance, in 28/6, both 28 and 6 are divisible by two. Simplify the fraction by dividing both numerator and denominator by 2, getting 14/3. There is no number by which both 14 and 3 can be evenly divided, so you cannot further simplify it.

Convert Back to Mixed Fraction

Once you've simplified, if you still have an improper fraction, convert the fraction back into a mixed fraction. To do this, divide the numerator by the denominator. The result of the division will be the mixed fraction's whole number, and the remainder will be the new numerator. For example, to convert 14/3 into a mixed fraction, divide 14 by 3: 3 goes into 14 four times, with a remainder of 2. So 14/3 is equal to the mixed fraction 4 2/3.

About the Author

Jon Zamboni began writing professionally in 2010. He has previously written for The Spiritual Herald, an urban health care and religious issues newspaper based in New York City, and online music magazine eBurban. Zamboni has a Bachelor of Arts in religious studies from Wesleyan University.