ACT Math : How to find the part from the whole with fractions

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Whole And Part

On Friday night, Maria sells \(\displaystyle \frac{1}{5}\) of her stock of apples.  On Saturday, she sells \(\displaystyle \frac{1}{4}\) of the remaining apples.  What fraction of her original stock of apples does Maria have left for sale on Sunday?

Possible Answers:

\(\displaystyle \frac{3}{5}\)

\(\displaystyle \frac{9}{20}\)

\(\displaystyle \frac{2}{5}\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle \frac{1}{2}\)

Correct answer:

\(\displaystyle \frac{3}{5}\)

Explanation:

Friday:  \(\displaystyle \frac{1}{5}\) apples sold

Saturday:  This means that \(\displaystyle \frac{4}{5}\) of her stock is remaining at this point. 

\(\displaystyle \frac{1}{4}\cdot \frac{4}{5}= \frac{1}{5}\) of her stock of apples was sold on Saturday.

By the end of Saturday, \(\displaystyle \frac{2}{5}\) of her stock has been sold \(\displaystyle (\frac{1}{5}+\frac{1}{5})\).  If \(\displaystyle \frac{2}{5}\) of her stock has been sold, \(\displaystyle \frac{3}{5}\) remains to be sold on Sunday.

Example Question #102 : Fractions

Michael Phelps’ workout program consists of Aerobics, Bench Presses, and Cycling.  Aerobics and Bench Presses take a total of 24 minutes, Bench Press and Cycling take a total of 40 minutes, and the entire workout takes a total of 56 minutes.  How many minutes are required for the Bench Press portion of his workout?  

 

Possible Answers:

40 minutes

16 minutes

8 minutes

32 minutes

4 minutes

Correct answer:

8 minutes

Explanation:

To find your answer, we would use substitution within a system of equations.  If (A+B) +C = 56, we can replace (A+B )= 24 to get (24) + C = 56, Thus making C = 32.  Then we can replace C with 32 in the equation      B+C = 40, thus making B + (32) = 40 to get an answer of 8.

 

 

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