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
ANSWERED 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. $$\displaystyle\frac{95}{{2}}\cdot\frac{4}{{5}}=\frac{19}{{1}}\cdot\frac{2}{{1}}={38}$$