Multiplying and Dividing Fractions

Multiplying Fractions

When multiplying and dividing fractions, it is easiest to work with proper or improper fractions. If the fraction is mixed, simply convert it to an improper fraction before you start. There are three simple steps to multiplying fractions. 

• Step 1: Multiply the numerators.
• Step 2: Multiply the denominators
• Step 3: Simplify the fraction (if needed).

Example: \(\frac{3}{4}\times\frac{2}{5}\)

Solution:

\(\frac{3}{4}\times\frac{2}{5} = \frac{3\cdot2}{4\cdot5}=\frac{6}{20}\)

Now, simplify the fraction:

\(\frac{6}{20} = \frac{3}{10}\)

Dividing Fractions

• Step 1: Turn the second fraction (the one you want to divide by) upside-down (this is now a reciprocal).
• Step 2: Multiply the first fraction by that reciprocal.
• Step 3: Simplify the fraction (if needed)

Example: \(\frac{2}{8} \div 3\frac{2}{5}\)

Solution: 

First convert the mixed fraction into an improper fraction: \(3 \frac{2}{5} = \frac{5\cdot3+2}{5} = \frac{17}{5}\)

Now, turn the second fraction (\(\frac{17}{5}\)) upside-down: \(\frac{5}{17}\)

Multiply the first fraction by the reciprical: \(\frac{2}{8}\times\frac{5}{17} = \frac{2\cdot5}{8\cdot17} = \frac{10}{136}\)

Simplify the fraction: \(\frac{10}{136}= \frac{5}{68}\)