# Which is the smallest of 3/5, 10/17, 15/54, 60/121 ?

Nov 21, 2017

$\frac{15}{54}$

#### Explanation:

Decreasing the numerator and/or increasing the denominator decreases the fraction.

So:

$\frac{3}{5} > \frac{2}{6} = \frac{1}{3}$

$\frac{10}{17} > \frac{6}{18} = \frac{1}{3}$

$\frac{60}{121} > \frac{41}{123} = \frac{1}{3}$

$\frac{15}{54} < \frac{15}{45} = \frac{1}{3}$

So: $\frac{15}{54}$ is the smallest, being the only one smaller than $\frac{1}{3}$

Nov 21, 2017

$\frac{15}{54}$ is the smallest

#### Explanation:

Often the easiest way to compare amounts is to give them all a common denominator.
Usually the easiest common denominator is a decimal, which you can find on a calculator.

$\frac{3}{5} = 0.600$

$\frac{10}{17} = 0.588$

$\frac{15}{54} = 0.278$ $\leftarrow$ smallest

$\frac{60}{121} = 0.496$
......................

In order from smallest to largest:
$\frac{15}{54} = 0.278$ $\leftarrow$ smallest

$\frac{60}{121} = 0.496$

$\frac{10}{17} = 0.588$

$\frac{3}{5} = 0.600$
...........................

Sometimes even the decimals themselves are confusing.
One thing that helps is to put each answer as MONEY.
Most people understand money very well! LOL!

(These values have been rounded to the nearest cent.)

$\frac{3}{5} = 0.600$ $\leftarrow$ 60ȼ

$\frac{10}{17} = 0.588$ $\leftarrow$ 59ȼ

$\frac{15}{54} = 0.278$ $\leftarrow$ 28ȼ$\leftarrow$ smallest

$\frac{60}{121} = 0.496$ $\leftarrow$ 50ȼ

Now it is easy to see which one is the smallest and which one is the largest, and it's easy to put them in order.