How do you simplify 3/5 times 10/12?

2 Answers
Jul 16, 2016

$\frac{1}{2}$

Explanation:

Multiplying fractions is dead easy! ..

$\left(\text{top x top")/("bottom x bottom}\right)$

However, just multiplying can lead to big numbers which might be awkward to simplify to the simplest form.

Check if there are common factors in the numerator and denominator and cancel them first.

$\frac{\cancel{3}}{\cancel{5}} \times {\cancel{10}}^{\cancel{2}} / {\cancel{12}}^{{\cancel{4}}^{2}} = \frac{1}{2}$

If you cancel as far as possible, the answer should not require further simplfying'

Jul 16, 2016

$\frac{1}{2}$

Explanation:

Method One:

First, we can cross simplify by finding factors to divide out from the numbers diagonal from each other ($3$ and $12$, $5$ and $10$).

$\frac{3}{5} \times \frac{10}{12}$

$\frac{1 \cancel{3}}{1 \cancel{5}} \times \frac{2 \cancel{10}}{4 \cancel{12}}$

*In the pair of numbers diagonal left going down ($3$ and $12$), we took out a $3$. The $3$ on the left numerator became $1$ and the $12$ on the bottom denominator became $4$. The same procedure took place in the other diagonal pair of numbers, but we took out a $5$ instead. *

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

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

$\frac{2}{4}$

$\frac{2 \div i \mathrm{de} 2}{4 \div i \mathrm{de} 2}$

$\frac{1}{2}$

In the last few steps, we multiplied the two simplified fractions and ended up with $\frac{2}{4}$ (remember that $\frac{1}{1}$ is the same as $1$ and multiplying a number by $1$ is itself). We simplified $\frac{2}{4}$ by dividing out a $2$, which was a common factor in both fractions and ended up with $\frac{1}{2}$. This cannot be simplified anymore and is thus the final answer.

Method 2:

This method is more simple. We can multiply the fractions the traditional way, just multiplying across the numerator and across the denominator.

$\frac{3}{5} \times \frac{10}{12}$

$\frac{3 \times 10}{5 \times 12}$

$\frac{30}{60}$

We end up with a different fraction than the one above. Do not fear, this can be simplified. $30$ and $60$ both have $30$ as the biggest common factor (greatest common factor, GCF). We can divide both the numerator and denominator by $30$.

$\frac{30 \div i \mathrm{de} 30}{60 \div i \mathrm{de} 30}$

$\frac{1}{2}$

*We got the same answer using both methods, $\frac{1}{2}$.