Multiply and Divide Mixed Numbers and Complex Fractions: example 4.46

Simplify: $\frac{2 \frac{3}{4}}{\frac{1}{8}} .$

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.

Your turn

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

Simplify: $\frac{\frac{5}{7}}{1 \frac{2}{5}} .$

How did it go?

	$\frac{2 \frac{3}{4}}{\frac{1}{8}}$
Rewrite as division.	$2 \frac{3}{4} \div \frac{1}{8}$
Change the mixed number to an improper fraction.	$\frac{11}{4} \div \frac{1}{8}$
Multiply the first fraction by the reciprocal of the second.	$\frac{11}{4} \cdot \frac{8}{1}$
Multiply.	$\frac{11 \cdot 8}{4 \cdot 1}$
Look for common factors.	$\frac{11 \cdot 4̸ \cdot 2}{4̸ \cdot 1}$
Remove common factors and simplify.	$22$

	$\frac{2 \frac{3}{4}}{\frac{1}{8}}$
Rewrite as division.	$2 \frac{3}{4} \div \frac{1}{8}$
Change the mixed number to an improper fraction.	$\frac{11}{4} \div \frac{1}{8}$
Multiply the first fraction by the reciprocal of the second.	$\frac{11}{4} \cdot \frac{8}{1}$
Multiply.	$\frac{11 \cdot 8}{4 \cdot 1}$
Look for common factors.	$\frac{11 \cdot 4̸ \cdot 2}{4̸ \cdot 1}$
Remove common factors and simplify.	$22$