Question

Juans three math quizzes this week took him 1/3?4/6?and1/5 hour to complete. List all the fraction from least to greatest

Answer 1

Answer:

$\frac{1}{5}$ ,  $\frac{1}{3}$ , $\frac{4}{6}$.

Step-by-step explanation:

Given fractions $\frac{1}{3}$, $\frac{4}{6}$, $\frac{1}{5}$.

We need to list them from least to greatest.

In order to arrange them from least to greatest, we need to find the least common denominator of  $\frac{1}{3}$, $\frac{4}{6}$, $\frac{1}{5}$.

We have 3, 6 and 5 in denominators.

Least common multiple of 3, 6 and 5 is = 30, because 30 is least number that can be divided by all three number 3, 6 and 5.

Let us covert each denominator as 30.

Multiplying first fraction $\frac{1}{3}$ by 10 in top and bottom, we get

$\frac{1}{3} = \frac{1\times10}{3\times10}=\frac{10}{30}$

Multiplying first fraction $\frac{4}{6}$ by 5 in top and bottom, we get

$\frac{4}{6} = \frac{4\times5}{6\times5}=\frac{20}{30}$

Multiplying first fraction  $\frac{1}{5}$ by 6 in top and bottom, we get

$\frac{1}{5} = \frac{1\times6}{5\times6}=\frac{6}{30}.$

Now, we can check $\frac{10}{30}, \frac{20}{30} \ and \ \frac{6}{30}.$

$\frac{6}{30}$ is the smallest, $\frac{10}{30}$ is greater and $\frac{20}{30}$ is the greatest.

Therefore, we can arrange fractions$\frac{6}{30}, \frac{10}{30} \ and \ \frac{20}{30}.$

Writing original fractions in place of equivalent fractions, we can write

$\frac{1}{5}$ ,  $\frac{1}{3}$ and  $\frac{4}{6}$.

Therefore, the order the amounts of paint from least to greatest is:

$\frac{1}{5}$ ,  $\frac{1}{3}$ , $\frac{4}{6}$.