Question

a plumber had a piece of pipe that was 27 7/8 in. long. he cut off a piece 3 3/4 in. long and used it to repair the sink. about how long was the remaining piece of pipe?
mario is training for the track team. he ran 4 1/4 mi on monday, 5 9/10 mi on wednesday, and 7 4/5 mi on friday. about how far did he run altogether on the three days?

Explanation:

Step1: Convert mixed numbers to improper fractions for pipe problem

The original length of the pipe is $27\frac{7}{8}=\frac{27\times8 + 7}{8}=\frac{216+7}{8}=\frac{223}{8}$ inches, and the cut - off length is $3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{12 + 3}{4}=\frac{15}{4}=\frac{30}{8}$ inches.

Step2: Subtract the cut - off length from the original length

The remaining length is $\frac{223}{8}-\frac{30}{8}=\frac{223 - 30}{8}=\frac{193}{8}=24\frac{1}{8}$ inches.

Step3: Convert mixed numbers to improper fractions for running problem

$4\frac{1}{4}=\frac{4\times4+1}{4}=\frac{17}{4}$, $5\frac{9}{10}=\frac{5\times10 + 9}{10}=\frac{59}{10}$, $7\frac{4}{5}=\frac{7\times5+4}{5}=\frac{39}{5}$.
Find a common denominator, which is 20. $\frac{17}{4}=\frac{17\times5}{4\times5}=\frac{85}{20}$, $\frac{59}{10}=\frac{59\times2}{10\times2}=\frac{118}{20}$, $\frac{39}{5}=\frac{39\times4}{5\times4}=\frac{156}{20}$.

Step4: Add the distances

$\frac{85}{20}+\frac{118}{20}+\frac{156}{20}=\frac{85 + 118+156}{20}=\frac{359}{20}=17\frac{19}{20}$ miles.

Answer:

For the pipe - related problem: $24\frac{1}{8}$
For the running - related problem: $17\frac{13}{20}$