Multiplying & Dividing Fractions Flashcards

All 6 cards in this deck

How do you multiply two fractions?
e.g. $\frac{2}{3}\times\frac{4}{5}$

Multiply the numerators, multiply the denominators, then simplify.
$\frac{2\times4}{3\times5}=\frac{8}{15}$

What is the reciprocal of a fraction $\frac{a}{b}$?
e.g. $\frac{3}{4}$

$\frac{b}{a}$ — turn the fraction upside down.
The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.

What is the rule for dividing by a fraction?
e.g. $\frac{2}{5}\div\frac{3}{4}$

Multiply by the reciprocal of the second fraction.
$\frac{2}{5}\times\frac{4}{3}=\frac{8}{15}$

What are the steps to divide with mixed numbers, giving the answer as a mixed number?
e.g. $1\frac{3}{4}\div\frac{3}{4}$

1. Convert to improper fractions: $\frac{7}{4}\div\frac{3}{4}$
2. Multiply by the reciprocal: $\frac{7}{4}\times\frac{4}{3}=\frac{28}{12}$
3. Simplify and write as a mixed number: $\frac{7}{3}=2\frac{1}{3}$

What are the steps to multiply two mixed numbers?
e.g. $2\frac{1}{3}\times3\frac{3}{4}$

1. Convert to improper fractions: $\frac{7}{3}\times\frac{15}{4}$
2. Multiply numerators and denominators: $\frac{105}{12}=\frac{35}{4}$
3. Write as a mixed number: $8\frac{3}{4}$

True or false? You need a common denominator before you can multiply two fractions.

False. A common denominator is only needed for adding and subtracting; to multiply, just multiply numerators and denominators.