# How do you solve a/10=2/5?

Mar 18, 2017

$a = 4$

#### Explanation:

For this problem, we need to find the LCD (least common denominator). In this case, it is $10$ as

$5 \cdot 2 = 10$

If we multiply the denominator by $2$, then we also need to multiply the numerator by $2$

$2 \cdot 2 = 4$

So

$\frac{a}{10} = \frac{2 \cdot 2}{5 \cdot 2}$

$\frac{a}{10} = \frac{4}{10}$

$a = 4$

Mar 18, 2017

$a = 4$

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

You need to manipulate the equation so that you have $a$ on its own on one side of the equals sign and everything else on the other side.

The left side we have $\frac{1}{10} \times a$ So if we can change the $\frac{1}{10}$ into 1 we have: $1 \times a$ which is the same as just $a$
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$\textcolor{b l u e}{\text{Answering the question}}$

Multiply both sides by $\textcolor{red}{10}$

$\textcolor{g r e e n}{\frac{a}{10} \textcolor{red}{\times 10} \text{ "=" } \frac{2}{5} \textcolor{red}{\times 10}}$

$\textcolor{g r e e n}{a \textcolor{red}{\times} \frac{\textcolor{red}{10}}{10} \text{ "=" } \frac{2}{5} \textcolor{red}{\times 10}}$

But $\frac{10}{10} = 1$

$a = 4$