Answer:
,
,
.
Step-by-step explanation:
Given fractions
,
,
.
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
,
,
.
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
by 10 in top and bottom, we get
![\frac{1}{3} = \frac{1\times10}{3\times10}=\frac{10}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%3D%20%5Cfrac%7B1%5Ctimes10%7D%7B3%5Ctimes10%7D%3D%5Cfrac%7B10%7D%7B30%7D)
Multiplying first fraction
by 5 in top and bottom, we get
![\frac{4}{6} = \frac{4\times5}{6\times5}=\frac{20}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B6%7D%20%3D%20%5Cfrac%7B4%5Ctimes5%7D%7B6%5Ctimes5%7D%3D%5Cfrac%7B20%7D%7B30%7D)
Multiplying first fraction
by 6 in top and bottom, we get
![\frac{1}{5} = \frac{1\times6}{5\times6}=\frac{6}{30}.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%20%3D%20%5Cfrac%7B1%5Ctimes6%7D%7B5%5Ctimes6%7D%3D%5Cfrac%7B6%7D%7B30%7D.)
Now, we can check ![\frac{10}{30}, \frac{20}{30} \ and \ \frac{6}{30}.](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B30%7D%2C%20%5Cfrac%7B20%7D%7B30%7D%20%5C%20and%20%5C%20%5Cfrac%7B6%7D%7B30%7D.)
is the smallest,
is greater and
is the greatest.
Therefore, we can arrange fractions![\frac{6}{30}, \frac{10}{30} \ and \ \frac{20}{30}.](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B30%7D%2C%20%5Cfrac%7B10%7D%7B30%7D%20%5C%20and%20%5C%20%5Cfrac%7B20%7D%7B30%7D.)
Writing original fractions in place of equivalent fractions, we can write
,
and
.
Therefore, the order the amounts of paint from least to greatest is:
,
,
.