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Exercises Numbers, fractions and percents

Example 4.37 from Prealgebra, 4.3 Multiply and Divide Mixed Numbers and Complex Fractions

Multiply and Divide Mixed Numbers and Complex Fractions: example 4.37

Multiply: $\frac{2̸ \cdot 5 \cdot 5}{3 \cdot 2̸ \cdot 4}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

$3 \frac{1}{3} \cdot \frac{5}{8}$

Convert $3 \frac{1}{3}$ to an improper fraction. $\frac{10}{3} \cdot \frac{5}{8}$

Multiply. $\frac{10 \cdot 5}{3 \cdot 8}$

Look for common factors. $\frac{2̸ \cdot 5 \cdot 5}{3 \cdot 2̸ \cdot 4}$

Remove common factors. $\frac{5 \cdot 5}{3 \cdot 4}$

Simplify. $\frac{25}{12}$

Notice that we left the answer as an improper fraction, $\frac{25}{12},$ and did not convert it to a mixed number. In algebra, it is preferable to write answers as improper fractions instead of mixed numbers. This avoids any possible confusion between $2 \frac{1}{12}$ and $2 \cdot \frac{1}{12} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Multiply, and write your answer in simplified form: $5 \frac{2}{3} \cdot \frac{6}{17} .$

How did it go?

PreviousMultiply and Divide Fractions: example 4.36 Next Multiply and Divide Mixed Numbers and Complex Fractions: example 4.38

From Prealgebra (1st edition) by OpenStax (Rice University), section 4.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.