How to Multiply Fractions With Mixed Numbers

Mixed numbers require conversion before multiplying.
••• Jose Luis Pelaez Inc../Blend Images/Getty Images

Before multiplying fractions, you convert any mixed numbers to improper fractions. You then multiply all the fractions in your problem, simplify if possible and finally convert back into mixed number form.

Convert Mixed to Improper

To convert a mixed number to an improper fraction, multiply the denominator by the whole number and add the numerator. For example, in the fraction 5 3/8, multiply the denominator 8 and the whole number 5, then add the numerator 3:

(8 x 5) + 3 = 43

The answer becomes your new numerator. The denominator stays the same. In the example, the improper fraction is 43/8. Repeat this process for all mixed numbers in your equation.

Multiply the Fractions

Once you've converted all fractions to improper fraction form, multiply the fractions as you would in any fraction multiplication problem. First, multiply all the numerators. Then multiply all the denominators. Write the answers in fraction form with the numerator product on top and the denominator product on bottom. For the problem 10/3 x 3/4, multiply 10 and 3 to find the numerator of 30. Multiply 3 and 4 to find the denominator of 12. Your answer is 30/12.

Simplify the Answer

You might need to simplify your answer to its lowest terms. Simplifying at this point makes conversion back to a mixed number easier. Look at the numerator and denominator and determine if any number can divide into both of them. If they are both divisible by more than one number, look for the highest number. In 48/18, both numbers are divisible by 2, 3 and 6. Since 6 is the largest, divide both numbers by 6 to get 8/3.

Convert Back to Mixed Number

If your answer is an improper fraction, convert it back to a mixed number after simplifying. Instead of multiplying, this time you divide the top number by the bottom number. In the improper fraction 32/5, divide 32 by 5. Your answer is 6 plus a remainder of 2. The 6 becomes your whole number. The 2 becomes the numerator in the mixed number. Your denominator stays the same, so 32/5 becomes 6 2/5.

Related Articles

Miles Per Hour to Meters Per Second Conversion
How to Reduce Mixed Numbers & Improper Fractions to...
How to Add & Subtract Improper Fractions
Multiplying Fractions
How to Change Mixed Numbers Into Improper Fractions
How to Turn Improper Fractions Into Whole Numbers
Adding & Subtracting Fractions
How to Get a Remainder in Your Calculator
How to Find the Product of Fractions
How to Write a Fraction in the Simplest Form
How to Multiply and Divide Mixed Fractions
How to Turn a Negative Denominator into a Positive
How to Divide Fractions With Ease
Miles Per Hour to Meters Per Second Conversion
How to Subtract Mixed Numbers With Regrouping
How to Solve Math Problems With Fractions
How to Multiply Fractions by Percentages
How to Change Improper Fractions to Mixed Numbers in...
How to Simplify Fractions
How to Borrow When Adding & Subtracting Fractions

Dont Go!

We Have More Great Sciencing Articles!