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

`(1)/(5)` ,
`(1)/(3)` ,
`(4)/(6)`.

Explanation:

Given fractions
`(1)/(3)`,
`(4)/(6)`,
`(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
`(1)/(3)`,
`(4)/(6)`,
`(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
`(1)/(3)` by 10 in top and bottom, we get

`(1)/(3) = (1*10)/(3*10)=(10)/(30)`

Multiplying first fraction
`(4)/(6)` by 5 in top and bottom, we get

`(4)/(6) = (4*5)/(6*5)=(20)/(30)`

Multiplying first fraction
`(1)/(5)` by 6 in top and bottom, we get

`(1)/(5) = (1*6)/(5*6)=(6)/(30).`

Now, we can check
`(10)/(30), (20)/(30) \ and \ (6)/(30).`

`(6)/(30)` is the smallest,
`(10)/(30)` is greater and
`(20)/(30)` is the greatest.

Therefore, we can arrange fractions
`(6)/(30), (10)/(30) \ and \ (20)/(30).`

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

`(1)/(5)` ,
`(1)/(3)` and
`(4)/(6)`.

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

`(1)/(5)` ,
`(1)/(3)` ,
`(4)/(6)`.