Multiply and Divide Mixed Numbers and Complex Fractions: example 4.40

Divide: $2 \frac{1}{2} \div 1 \frac{1}{4} .$

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.

Your turn

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

Divide, and write your answer in simplified form: $2 \frac{2}{3} \div 1 \frac{1}{3} .$

How did it go?

	$2 \frac{1}{2} \div 1 \frac{1}{4}$
Convert mixed numbers to improper fractions.	$\frac{5}{2} \div \frac{5}{4}$
Multiply the first fraction by the reciprocal of the second.	$\frac{5}{2} \cdot \frac{4}{5}$
Multiply.	$\frac{5 \cdot 4}{2 \cdot 5}$
Look for common factors.	$\frac{5̸ \cdot 2̸ \cdot 2}{2̸ \cdot 1 \cdot 5̸}$
Remove common factors.	$\frac{2}{1}$
Simplify.	$2$

	$2 \frac{1}{2} \div 1 \frac{1}{4}$
Convert mixed numbers to improper fractions.	$\frac{5}{2} \div \frac{5}{4}$
Multiply the first fraction by the reciprocal of the second.	$\frac{5}{2} \cdot \frac{4}{5}$
Multiply.	$\frac{5 \cdot 4}{2 \cdot 5}$
Look for common factors.	$\frac{5̸ \cdot 2̸ \cdot 2}{2̸ \cdot 1 \cdot 5̸}$
Remove common factors.	$\frac{2}{1}$
Simplify.	$2$