ACT Math : Fractions

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

Example Question #3 : How To Simplify A Fraction

Simplify the following fraction:

\(\displaystyle \small \frac{315}{825}\)

Possible Answers:

\(\displaystyle \small \frac{105}{275}\)

\(\displaystyle \small \small \small \frac{21}{55}\)

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

\(\displaystyle \small \frac{7}{11}\)

\(\displaystyle \small \small \frac{63}{165}\)

Correct answer:

\(\displaystyle \small \small \small \frac{21}{55}\)

Explanation:

First, begin by noticing that both numerator and denominator contain a \(\displaystyle \small 5\). Dividing this out gives you:

\(\displaystyle \small \small \frac{63}{165}\)

Now, \(\displaystyle \small 1+6+5=12\) and \(\displaystyle \small 6+3=9\).  Since each of these are true, we know that both numerator and denominator contain a \(\displaystyle \small 3\).  Dividing this out, you get:

\(\displaystyle \small \small \small \frac{21}{55}\)

This is the simplest possible form of the fraction.

Example Question #2 : Simplifying Fractions

Maria owns an art studio and spent \(\displaystyle \$1850\) in supplies.  She sells her paintings for \(\displaystyle \$150\) each.  How many paintings does Maria need to sell until she makes a profit? 

Possible Answers:

\(\displaystyle 13\)

\(\displaystyle 12\)

\(\displaystyle 11\)

\(\displaystyle 10\)

\(\displaystyle 14\)

Correct answer:

\(\displaystyle 13\)

Explanation:

Divide the total money spent by the cost of each painting.  

\(\displaystyle \frac{\$1850}{\$150}=12.33333\) 

Therefore, to make a profit, she needs to sell more than this amount.  Since she can't sell a portion of a painting, the answer has to be the next nearest whole number (\(\displaystyle 13\)).  

Learning Tools by Varsity Tutors