Russ and David have a dump truck full of mulch to spread in the yard. By lunchtime, Russ has spread 3/5 mulch, and David has spread 1/3 mulch. How much more mulch do the boys have to spread?
The Correct Answer and Explanation is:
To find how much more mulch Russ and David need to spread, we first need to calculate how much mulch they have already spread and subtract that from the total amount.
Let’s assume that the truck originally contained 1 full load of mulch.
Step 1: Calculate the total amount of mulch spread
- Russ has spread 3/5 of the mulch.
- David has spread 1/3 of the mulch.
To add these fractions, we need a common denominator. The denominators are 5 and 3, and the least common denominator (LCD) between 5 and 3 is 15.
- Convert 3/5 to have a denominator of 15: 35=3×35×3=915\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}53=5×33×3=159
- Convert 1/3 to have a denominator of 15: 13=1×53×5=515\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}31=3×51×5=155
Now we can add the fractions:915+515=1415\frac{9}{15} + \frac{5}{15} = \frac{14}{15}159+155=1514
This means that Russ and David together have spread 14/15 of the mulch.
Step 2: Calculate how much mulch is left
Since they started with a full load of mulch (1 whole), the amount left to spread is:1−1415=1515−1415=1151 – \frac{14}{15} = \frac{15}{15} – \frac{14}{15} = \frac{1}{15}1−1514=1515−1514=151
Final Answer:
The boys have 1/15 of the mulch left to spread.
In summary, after Russ and David have spread 14/15 of the mulch, there is only 1/15 remaining. They still have a small amount left to finish the job.
