# Is 2/5 the same as 5/8 ?

Apr 6, 2017

No

#### Explanation:

Convert $\frac{2}{5}$ and $\frac{5}{8}$ to fractions with the same denominator. The least common multiple of $5$ and $8$ is $40$.

$\frac{2}{5} \cdot \frac{8}{8} = \frac{16}{40}$

$\frac{5}{8} \cdot \frac{5}{5} = \frac{25}{40}$

Clearly, $\frac{5}{8} > \frac{2}{5}$.

Apr 8, 2017

No

#### Explanation:

When $b$ and $d$ are non-zero:

$\frac{a}{b} = \frac{c}{d} \text{ }$ if and only if $\text{ } a d = b c$

In our example:

$2 \cdot 8 = 16 \ne 25 = 5 \cdot 5$

So:

$\frac{2}{5} \ne \frac{5}{8}$

Apr 8, 2017

A sort of cheat way:

$\frac{5}{8}$ is bigger so the answer is no

#### Explanation:

If $\frac{2}{5}$ was equal to $\frac{5}{8}$ then dividing one into the other will give the answer of 1

Consider $\frac{2}{5} \div \frac{5}{8}$

If the answer is less than 1 then 5/8 is bigger.
If the answer is more that 1 the 5/8 is maller.

$\frac{2}{5} \div \frac{5}{8} \to \frac{2}{5} \times \frac{8}{5} \text{ "=" } \frac{16}{25}$ which is less than 1

So $\frac{5}{8}$ is bigger