Question

A dump truck brought 1⁄3 of a ton of rock on the first trip, 1⁄2 of a ton on the second trip, but on the third trip, had to take back 4⁄5 of a ton. What was the total weight of the rock left at the construction site?

Answer 1

Answer:1/3

Explanation:

1+1+1=3

so the answer is 1/3

Answer 2

1/30 of a ton

Explanation:

Write this as an expression:

1/3 of a ton and 1/2 of a ton were taken to the site.

4/5 of a ton were remove from the site.

Amount of a ton at the site =
`(1)/(3)+ (1)/(2)- (4)/(5)`

Solve the equation by finding common denominators (when the bottom numbers are the same).

`((1)/(3)+ (1)/(2))- (4)/(5)` Focus on the first part. The least common multiple (LCM) of 3 and 2 is "6", which will become the denominator.

For 1/3 to become ?/6, multiply top and bottom by 2.

For 1/2 to become ?/6, multiply top and bottom by 3.

`((2)/(6)+ (3)/(6))- (4)/(5)`

Now we can add the numerators together over the same denominator.

`(5)/(6)- (4)/(5)`

Do the same thing as before and change the denominators. The LCM of 6 and 5 is "30".

For 5/6 to become ?/30, multiply top and bottom by 5.

For 4/5 to become ?/30, multiply top and bottom by 6.

`(25)/(30)- (24)/(30)`

Subtract the numerators:

`(1)/(30)` Answer in tons

Therefore there was 1/30 of a ton of rock left at the construction site.