How to Multiply Fractions

Let’s look at an example. Imagine finding one-quarter of half a cake.

This is the same as multiplying \( \frac{1}{4} \) by \( \frac{1}{2} \).

$$ \frac{1}{4} \cdot \frac{1}{2} $$

To calculate the product, multiply the numerators together, then do the same for the denominators.

$$ \frac{1}{4} \cdot \frac{1}{2} = \frac{1 \cdot 1}{4 \cdot 2} $$

The numerator is \( 1 \cdot 1 = 1 \), and the denominator is \( 4 \cdot 2 = 8 \).

$$ \frac{1}{4} \cdot \frac{1}{2} = \frac{1 \cdot 1}{4 \cdot 2} = \frac{1}{8} $$

So, the result \( \frac{1}{8} \) tells us that one-quarter of a half equals one-eighth of the entire cake.

As you can see, multiplying fractions is easy to understand—and with a little practice, it becomes second nature.

Don’t forget to simplify. Sometimes, the result can be simplified further. For example, take this multiplication: $$ \frac{6}{8} \cdot \frac{2}{3} $$ Multiply the numerators and denominators: $$ \frac{6}{8} \cdot \frac{2}{3}= \frac{6 \cdot 2}{8 \cdot 3} = \frac{12}{24} $$ The fraction \( \frac{12}{24} \) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (12): $$ \frac{12}{24} = \frac{1}{2} $$ Simplifying the result makes it clearer and easier to interpret.

A helpful tip: always simplify fractions before multiplying.

Here’s an example involving larger numbers:

$$ \frac{32}{12} \cdot \frac{27}{15} $$

$$ \frac{32}{12} \cdot \frac{27}{15} = \frac{32 \cdot 27}{12 \cdot 15} $$

Instead of jumping straight into the multiplication, reduce both fractions to their simplest forms first.

$$ \frac{32 \div 2}{12 \div 2} \cdot \frac{27 \div 3}{15 \div 3} $$

$$ \frac{16 \div 2}{6 \div 2} \cdot \frac{9}{5} $$

$$ \frac{8}{3} \cdot \frac{9}{5} $$

By simplifying the fractions, you work with smaller, more manageable numbers while solving the problem.

$$ \frac{8}{3} \cdot \frac{9}{5} = \frac{8 \cdot 9}{3 \cdot 5} = \frac{72}{15} $$

Since both 72 and 15 are divisible by 3, you can simplify the result even further:

$$ \frac{72 \div 3}{15 \div 3} = \frac{24}{5} $$

So, the final result of this multiplication is \( \frac{24}{5} \). 

Understanding these concepts will make solving math problems much easier and less time-consuming.