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:

1/30 of a ton

Step-by-step 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  =   $\frac{1}{3}+ \frac{1}{2}- \frac{4}{5}$

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

$(\frac{1}{3}+ \frac{1}{2})- \frac{4}{5}$       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.

$(\frac{2}{6}+ \frac{3}{6})- \frac{4}{5}$

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

$\frac{5}{6}- \frac{4}{5}$

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.

$\frac{25}{30}- \frac{24}{30}$

Subtract the numerators:

$\frac{1}{30}$                  Answer in tons

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