SSAT Upper Level Quantitative - How to add fractions

Solve,

$\frac{2}{13}+\frac{4}{13}=?$

$\frac{6}{13}$

$\frac{6}{26}$

$\frac{3}{13}$

$\frac{2}{13}$

Explanation

Since the denominators for the fractions are the same, keep the denominator and add the numerators.

$\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}$

A poll was conducted in a class to see what fraction of the class plays sports. $\frac{3}{7}$ of the class plays basketball, and $\frac{1}{4}$ of the class plays soccer. The rest of the class do not play any sports. What fraction of the class plays a sport?

$\frac{19}{28}$

$\frac{4}{11}$

$\frac{5}{28}$

$\frac{11}{28}$

Explanation

To find what fraction of the class plays a sport, add together $\frac{3}{7}$ and $\frac{1}{4}$ .

First, convert both fractions so that the denominators are the same.

$\frac{3}{7}=\frac{12}{28}$

$\frac{1}{4}=\frac{7}{28}$

Now, you can add them together.

$\frac{3}{7}+\frac{1}{4}=\frac{12}{28}+\frac{7}{28}=\frac{19}{28}$

Peter ate $\frac{2}{3}$ of a pie for breakfast, then ate $\frac{1}{7}$ of the pie as a morning snack. How much of the pie did Peter eat?

$\frac{17}{21}$

$\frac{3}{10}$

$\frac{11}{21}$

$\frac{12}{21}$

Explanation

To find how much of the pie Peter ate, you will need to add together $\frac{2}{3}$ and $\frac{1}{7}$ .

Start by converting both fractions so that the denominators are the same.

$\frac{2}{3}=\frac{14}{21}$

$\frac{1}{7}=\frac{3}{21}$

Now, you can add the fractions.

$\frac{2}{3}+\frac{1}{7}=\frac{14}{21}+\frac{3}{21}=\frac{17}{21}$

On a given week, Jeremy spends $\frac{1}{5}$ of his time working on homework and $\frac{1}{4}$ of his time doing chores. What fraction of his time is spent doing homework and doing chores?

$\frac{9}{20}$

$\frac{2}{9}$

$\frac{1}{20}$

$\frac{3}{11}$

Explanation

To find how much time Jeremy spends doing his homework and his chores, add together $\frac{1}{5}$ and $\frac{1}{4}$ .

First, convert both fractions so that they have the same denominator.

$\frac{1}{5}=\frac{4}{20}$

$\frac{1}{4}=\frac{5}{20}$

Now, you can add the fractions together.

$\frac{1}{5}+\frac{1}{4}=\frac{4}{20}+\frac{5}{20}=\frac{9}{20}$

In a jar of marbles, $\frac{12}{25}$ of the marbles are red and $\frac{1}{5}$ of the marbles of blue. What fraction of the jar of marbles are red and blue marbles?

$\frac{17}{25}$

$\frac{13}{30}$

$\frac{11}{25}$

$\frac{7}{25}$

Explanation

To find out what fraction of the jar are red and blue marbles, add $\frac{12}{25}$ and $\frac{1}{5}$ together.

First, you need to convert the fractions so that they have the same denominator. Since is a multiple of , you only need to change one fraction.

$\frac{1}{5}=\frac{5}{25}$

Now, add the fractions together.

$\frac{12}{25}+\frac{1}{5}=\frac{12}{25}+\frac{5}{25}=\frac{17}{25}$

Jim baked two batches of cookies. In the first batch, he used $\frac{1}{13}$ cup of sugar. In his second batch, he used $\frac{3}{26}$ cups of sugar. In cups, how much sugar did he use in total?

$\frac{5}{26}$

$\frac{4}{39}$

$\frac{1}{26}$

$\frac{9}{26}$

Explanation

To find how much sugar he used in total, add $\frac{1}{13}$ and $\frac{3}{26}$ together.

First, make sure that both fractions have the same denominator before you add them. Since is a multiple of , you will need to convert $\frac{1}{13}$ into $\frac{2}{26}$ by multiplying both numerator and denominators by .

Now, add the fractions.

$\frac{1}{13}+\frac{3}{26}=\frac{2}{26}+\frac{3}{26}=\frac{5}{26}$

Scott gave $\frac{1}{4}$ of the chocolate chip cookies he made to Cindy, and he gave $\frac{1}{6}$ of the cookies to Stephanie. What fraction of his chocolate chip cookies did he give away?

$\frac{5}{12}$

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{7}{12}$

Explanation

This question wants you to add $\frac{1}{4}$ and $\frac{1}{6}$ . First, convert both fractions so that they share the same denominator.

$\frac{1}{4}=\frac{3}{12}$

$\frac{1}{6}=\frac{2}{12}$

$\frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{5}{12}$

Find the arithmetic mean of the following five numbers.

$\frac{2}{5}, \frac{1}{5},\frac{1}{2},\frac{3}{10}, \frac{2}{5}$

$\frac{9}{25}$

$\frac{7}{25}$

$\frac{2}{5}$

$\frac{6}{25}$

$\frac{3}{5}$

Explanation

Add the numbers, then divide by or, equivalently, multiply by $\frac{1}{5}$ .

$\frac{\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}}{5}$

$\frac{1}{5} \left(\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}\right )$

Find the common denominator of the terms we are adding.

$\frac{1}{5} \left(\frac{4}{10}+ \frac{2}{10}+\frac{5}{10}+\frac{3}{10}+ \frac{4}{10}\right )$

$\frac{1}{5} \left(\frac{4+2+5+3+4}{10} \right)$

Multiply and simplify.

$\frac{1}{5} \left(\frac{18}{10} \right)= \frac{1}{5} \left(\frac{9}{5} \right) = \frac{9}{25}$

Lucy gave away $\frac{1}{10}$ of her hair ribbons to Megan and $\frac{1}{2}$ of her hair ribbons to Patrice. What fraction of her hair ribbons did Lucy give away?