Lesson 29: Multiplying Fractions

New Concept

When we multiply fractions, we multiply the numerators to find the numerator of the product, and we multiply the denominators to find the denominator of the product.

What’s next

Next, you’ll work through examples of multiplying simple fractions, whole numbers by fractions, and reducing the resulting products to their simplest form.

Property

When we multiply fractions, we multiply the numerators to find the numerator of the product, and we multiply the denominators to find the denominator of the product.

Examples

Find $\frac{2}{5}$ of $\frac{3}{7}$: $\frac{2}{5} \times \frac{3}{7} = \frac{2 \times 3}{5 \times 7} = \frac{6}{35}$
Multiply $\frac{1}{4}$ and $\frac{5}{9}$: $\frac{1}{4} \times \frac{5}{9} = \frac{1 \times 5}{4 \times 9} = \frac{5}{36}$
Calculate $\frac{7}{8} \times \frac{1}{2}$: $\frac{7}{8} \times \frac{1}{2} = \frac{7 \times 1}{8 \times 2} = \frac{7}{16}$

Explanation

Imagine a pizza party! If you have $\frac{3}{4}$ of a pizza left and you eat $\frac{1}{2}$ of that, you're not eating half the whole pizza—just half of the leftovers. Multiplying fractions tells you exactly what portion of the original, entire pizza you just devoured. It keeps track of the pieces for you!

Property

The 'of' in '$\frac{1}{2}$ of $\frac{1}{2}$' means to multiply.

Examples

• '$\frac{1}{2}$ of $\frac{4}{5}$' is a secret code for $\frac{1}{2} \times \frac{4}{5} = \frac{4}{10}$, which reduces to $\frac{2}{5}$.
• '$\frac{2}{3}$ of $\frac{3}{4}$' simply means $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12}$, which reduces to $\frac{1}{2}$.
• '$\frac{1}{4}$ of 20 dollars' means $\frac{1}{4} \times \frac{20}{1} = \frac{20}{4}$, which equals 5 dollars.

Explanation

In the world of math, the word 'of' is a secret agent with one mission: to tell you to multiply. When you read a phrase like 'one-half OF three-quarters,' that 'of' is your cue to set up a multiplication problem. It's the dictionary's way of saying 'take a piece of that other piece,' so you multiply to find out how big it is.

Property

We can reduce fractions by dividing the numerator and the denominator by a factor of both numbers. To reduce $\frac{6}{12}$, we will divide both the numerator and the denominator by 6.

Examples

Reduce $\frac{15}{25}$ by dividing by the GCF, 5: $\frac{15 \div 5}{25 \div 5} = \frac{3}{5}$
Reduce $\frac{12}{18}$ by dividing by the GCF, 6: $\frac{12 \div 6}{18 \div 6} = \frac{2}{3}$
Reduce $\frac{24}{32}$ by dividing by the GCF, 8: $\frac{24 \div 8}{32 \div 8} = \frac{3}{4}$

Explanation

Think of reducing fractions like simplifying a super-long text message. You want to say the same thing, but with fewer characters. By dividing the top and bottom by their greatest common factor (GCF), you get the simplest, cleanest version of the fraction without changing its value. Less is more, and it's easier to read!