How to Multiply Mixed Numbers

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Do you need two and a half dozen cookies, but a recipe only makes one dozen? Don't let the daunting task of multiplying mixed numbers get in the way.

Step 1: Write the numbers down
Write your mixed numbers down on a piece of paper to convert them to improper fractions.

Step 2: Convert to improper fraction
Multiply the denominator – the bottom number of the fraction – by the whole number, and then add the top number of the fraction – the numerator. Write the product on top of the denominator.

Tip
For example, the mixed numbers in two and a half times three and two-fifths convert to the improper fractions five halves and seventeen-fifths.

Step 3: Write the improper fractions
Write the improper fractions side-by-side on your paper.

Step 4: Multiply the numerators
Multiply the numerators and write the product as the numerator of your solution.

Tip
The product of five halves times seventeen-fifths will have a numerator of 85.

Step 5: Multiply the denominators
Multiply the denominators and write the product as the denominator of your solution.

Tip
The product of five halves × seventeen-fifths will have a denominator of 10.

Step 6: Simplify
Simplify the resulting fraction and write the solution as a mixed number.

Did You Know?
The Rhind Mathematical Papyrus, from around 1650 B.C.E., contains 84 mathematical problems involving administrative and building works.