Question

A dump truck brought 1⁄3 of a ton of rock on the first trip, 5⁄6 of a ton on the second trip, and 5⁄12 of a ton on the third trip. What was the total weight of the rock?

Answer 1

Weight =
`1 and (7)/(12)` Ton

Explanation:

The total weight of the rock is calculated by adding the three fractions.

Weight =
`(1)/(3)+(5)/(6)+(5)/(12)`

As they are different denominators, we look for a common denominator that is the Least Common Multiple (LCM).

Then, for each term, the LCM is divided by the denominator of the original fraction and multiplied by the numerator.

Weight =
`(1)/(3)+(5)/(6)+(5)/(12)`

Weight =
`((12/3*1) + (12/6*5) + (12/12*5))/(12)`

Weight =
`(4+10+5)/(12)`

Weight =
`(19)/(12)=1.5833` Ton

Or

Weight =
`(19)/(12)`

Weight =
`(12+7)/(12)`

Weight =
`(12)/(12)+(7)/(12)`

Weight =
`1+(7)/(12)`

Weight =
`1 and (7)/(12)` Ton

Hope this helps!

Answer 2

First convert the numbers to get the same denominator
1/3=4/12
5/6=10/12
5/12
Then add them all together
4/12+10/12+5/12= 19/12
Then reduce
1 7/12
Your answer is 1 ton and 7/12 of a ton