Question

miss gupta is planning a project for the art class that she teaches. in her classroom, she already has $25\frac{3}{8}$ pounds of gray clay and $9\frac{7}{8}$ pounds of tan clay. for the art project that miss gupta has planned, the color of the clay doesnt matter, but she needs 40 pounds in all. how much more clay does miss gupta need to get?

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(25\frac{3}{8}\) to an improper fraction: \(25\frac{3}{8}=\frac{25\times8 + 3}{8}=\frac{200+3}{8}=\frac{203}{8}\)
Then, convert \(9\frac{7}{8}\) to an improper fraction: \(9\frac{7}{8}=\frac{9\times8 + 7}{8}=\frac{72 + 7}{8}=\frac{79}{8}\)

Step2: Find the total clay already available

Add the two amounts of clay: \(\frac{203}{8}+\frac{79}{8}=\frac{203 + 79}{8}=\frac{282}{8}\)
Simplify \(\frac{282}{8}\) to a mixed number: \(\frac{282}{8}=35\frac{2}{8}=35\frac{1}{4}\)

Step3: Calculate the additional clay needed

Subtract the total available clay from the required 40 pounds.
First, write 40 as a fraction with denominator 4: \(40=\frac{160}{4}\)
\(35\frac{1}{4}=\frac{35\times4+1}{4}=\frac{140 + 1}{4}=\frac{141}{4}\)
Now subtract: \(\frac{160}{4}-\frac{141}{4}=\frac{160 - 141}{4}=\frac{19}{4}=4\frac{3}{4}\)

Answer:

\(4\frac{3}{4}\) pounds