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}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%2B%20%5Cfrac%7B1%7D%7B2%7D-%20%5Cfrac%7B4%7D%7B5%7D)
Solve the equation by finding <u>common denominators</u> (when the bottom numbers are the same).
Focus on the first part. The least common multiple (LCM) of 3 and 2 is "6", which will become the denominator.
For <u>1/3 to become ?/6</u>, multiply top and bottom by 2.
For <u>1/2 to become ?/6</u>, multiply top and bottom by 3.
![(\frac{2}{6}+ \frac{3}{6})- \frac{4}{5}](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B6%7D%2B%20%5Cfrac%7B3%7D%7B6%7D%29-%20%5Cfrac%7B4%7D%7B5%7D)
Now we can add the numerators together over the same denominator.
![\frac{5}{6}- \frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D-%20%5Cfrac%7B4%7D%7B5%7D)
Do the same thing as before and change the denominators. The LCM of 6 and 5 is "30".
For <u>5/6 to become ?/30</u>, multiply top and bottom by 5.
For <u>4/5 to become ?/30</u>, multiply top and bottom by 6.
![\frac{25}{30}- \frac{24}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B30%7D-%20%5Cfrac%7B24%7D%7B30%7D)
Subtract the numerators:
Answer in tons
Therefore there was 1/30 of a ton of rock left at the construction site.