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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.
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?
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).
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.
Multiplying Mixed Numbers
To multiply mixed numbers, first write them as improper fractions, and then multiply as you do with fractions.
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.
Dividing Mixed Numbers
To divide mixed numbers, rewrite them as improper fractions.
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