Question

# Solve each problem. Show your work and be sure to label your answer. The cook in the school cafeteria made 47(1/2) cups of mashed potatoes. If there are 1(1/4) cups of mashed potatoes in a serving, how many servings did she make?

Math Word Problem
Solve each problem. Show your work and be sure to label your answer. The cook in the school cafeteria made 47(1/2) cups of mashed potatoes. If there are 1(1/4) cups of mashed potatoes in a serving, how many servings did she make?

Convert to improper fractions $$\displaystyle{47}\frac{{\frac{1}{{2}}}}{{1}}{\left(\frac{1}{{4}}\right)}=\frac{{{47}{\left({2}\right)}+{1}}}{{2}}/\frac{{{1}{\left({4}\right)}+{1}}}{{4}}=\frac{95}{{2}}/\frac{5}{{4}}$$
Change to multiplication by the reciprocal $$\displaystyle\frac{95}{{2}}/\frac{5}{{4}}=\frac{95}{{2}}\cdot\frac{4}{{5}}$$
We can simplify before multiplying. 95 and 5 are divisible by 5, 4 and 2 are divisible by 2. $$\displaystyle\frac{95}{{2}}\cdot\frac{4}{{5}}=\frac{19}{{1}}\cdot\frac{2}{{1}}={38}$$