Dividing Fractions and Mixed Numbers

Flashcards covering concepts, rules, and example problems for dividing fractions and mixed numbers.

In a division problem, what do the dividend (first number) and divisor (second number) represent?

The dividend represents what you have, and the divisor represents how many groups of.

What is the definition of a reciprocal?

A reciprocal is when the numerator is moved to the denominator position and the denominator is moved to the numerator position.

What are the two main steps when dividing fractions?

Find the reciprocal of the divisor and then multiply by that reciprocal.

What is cross canceling when multiplying fractions?

Looking across diagonals for common factors and dividing them out before multiplying, allowing for a simplified answer at the end.

What is the result of $\frac{5}{6} \div \frac{2}{3}$ written as a mixed number?

$$1\frac{1}{4}$$

What is the result of $\frac{6}{7} \div \frac{1}{2}$ written as a mixed number?

$$1\frac{5}{7}$$

What must you always do before dividing or multiplying mixed numbers?

Change any mixed number into an improper fraction first.

How are the mixed numbers $6\frac{1}{4}$ and $1\frac{1}{8}$ converted into improper fractions?

$6\frac{1}{4}$ converts to $\frac{25}{4}$ and $1\frac{1}{8}$ converts to $\frac{9}{8}$.

What is the result of $6\frac{1}{4} \div 1\frac{1}{8}$ written as a mixed number?

$$5\frac{5}{9}$$

How should a whole number such as $5$ be rewritten when setting up a fraction division problem?

It should be rewritten as a fraction over one: $\frac{5}{1}$.

What is the result of $5 \div 2\frac{2}{5}$ written as a mixed number?

$$2\frac{1}{12}$$

What are the three recap steps for dividing fractions and mixed numbers?

1. Convert any mixed numbers to improper fractions. 2. Find the reciprocal of the divisor (the second number). 3. Multiply the dividend by that reciprocal.