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Multiplying and Dividing Fractions and Mixed Numbers

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1 Multiplying and Dividing Fractions and Mixed Numbers
Today you will learn to: multiply fractions and mixed numbers. divide fractions and mixed numbers, M07.A-N.1.1.3: To apply properties of operations to multiply and divide rational numbers, including real-world contexts.

2 Warm-up Problem: Multiplying Fractions
A paper published in a medical journal reported that about 11/25 of girls ages 16 to 17 do not exercise at all. The entire study consisted of about 2,500 girls. About how many did not exercise?

3 Multiplying Fractions
When multiplying fractions and mixed numbers, you do not need a common denominator as you do when adding and subtracting fractions and mixed numbers. To multiply fractions, you multiply their numerators and multiply their denominators, then simplify (if necessary).

4 Multiplying a Fraction by a Whole Number
To multiply a fraction by a whole number, write the whole number as a fraction with a denominator of 1.

5 Multiplying Mixed Numbers
To multiply mixed numbers, first write them as improper fractions, and then multiply as you do with fractions.

6 Dividing Fractions To divide by a fraction, multiply by its reciprocal. Two numbers are reciprocals if their product is one. For example, the fractions 2/6 and 6/2 are reciprocals. To find the reciprocal of a fraction, interchange the numerator and denominator.

7 Dividing Mixed Numbers
To divide mixed numbers, rewrite them as improper fractions.

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