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SSAT Upper Level Math : How to add fractions

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Example Questions

Example Question #1 : How To Add Fractions

Find the arithmetic mean of the following five numbers.

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

Possible Answers:

$\frac{2}{5}$

$\frac{9}{25}$

$\frac{7}{25}$

$\frac{6}{25}$

$\frac{3}{5}$

Correct answer:

$\frac{9}{25}$

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.

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

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Example Question #2 : How To Add Fractions

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?

Possible Answers:

$\frac{7}{12}$

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{5}{12}$

Correct answer:

$\frac{5}{12}$

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.

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

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

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

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Example Question #1304 : Ssat Upper Level Quantitative (Math)

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?

Possible Answers:

$\frac{19}{28}$

$\frac{11}{28}$

$\frac{5}{28}$

$\frac{4}{11}$

Correct answer:

$\frac{19}{28}$

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.

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

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Example Question #181 : Fractions

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?

Possible Answers:

$\frac{17}{21}$

$\frac{12}{21}$

$\frac{3}{10}$

$\frac{11}{21}$

Correct answer:

$\frac{17}{21}$

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.

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

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Example Question #5 : How To Add Fractions

Timothy spends $\frac{2}{9}$ of his weekly allowance on comic books and $\frac{1}{5}$ of his weekly allowance on candy. What fraction of his weekly allowance does he spend on comic books and candy?

Possible Answers:

$\frac{19}{45}$

$\frac{44}{45}$

$\frac{2}{45}$

$\frac{3}{14}$

Correct answer:

$\frac{19}{45}$

Explanation:

To find out how much of his weekly allowance Timothy spends on candy and comic books, add $\frac{2}{9}$ and $\frac{1}{5}$ together.

To do so, you need to first convert both fractions so that they have the same denominator.

$\frac{2}{9}=\frac{10}{45}$

$\frac{1}{5}=\frac{9}{45}$

Now you can add together the fractions.

$\frac{2}{9}+\frac{1}{5}=\frac{10}{45}+\frac{9}{45}=\frac{19}{45}$

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Example Question #53 : Operations With Fractions

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?

Possible Answers:

$\frac{11}{25}$

$\frac{13}{30}$

$\frac{7}{25}$

$\frac{17}{25}$

Correct answer:

$\frac{17}{25}$

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.

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

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Example Question #182 : Rational Numbers

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?

Possible Answers:

$\frac{9}{26}$

$\frac{5}{26}$

$\frac{4}{39}$

$\frac{1}{26}$

Correct answer:

$\frac{5}{26}$

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.

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

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Example Question #2 : How To Add Fractions

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?

Possible Answers:

$\frac{3}{5}$

$\frac{1}{6}$

$\frac{2}{10}$

$\frac{2}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

You will need to add together $\frac{1}{10}$ and $\frac{1}{2}$ .

Since is a multiple of , we can use as the common denominator.

Then, $\frac{1}{2}=\frac{5}{10}$

$\frac{1}{10}+\frac{1}{2}=\frac{1}{10}+\frac{5}{10}=\frac{6}{10}=\frac{3}{5}$

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Example Question #8 : How To Add Fractions

Michael ate $\frac{5}{8}$ of a cake for breakfast, and then $\frac{1}{6}$ of the same cake for dinner. How much of the cake did Michael eat?

Possible Answers:

$\frac{11}{24}$

$\frac{5}{14}$

$\frac{19}{24}$

$\frac{3}{7}$

Correct answer:

$\frac{19}{24}$

Explanation:

To figure out how much cake Michael ate, you will need to add the two fractions given in the question.

First, find the common denominator of both fractions and convert them so that they have that denominator.

$\frac{5}{8}=\frac{15}{24}$

$\frac{1}{6}=\frac{4}{24}$

Now, add the fractions.

$\frac{5}{8}+\frac{1}{6}=\frac{15}{24}+\frac{4}{24}=\frac{19}{24}$

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Example Question #182 : Fractions

On a certain game show, the audience is polled. $\frac{29}{100}$ of the audience enjoys playing football, and $\frac{1}{5}$ of the audience enjoys playing basketball. What fraction of the audience enjoys playing football and basketball?

Possible Answers:

$\frac{19}{100}$

$\frac{49}{100}$

$\frac{3}{10}$

$\frac{59}{100}$

Correct answer:

$\frac{49}{100}$

Explanation:

Add the fractions together. In order to do so, you will need to convert $\frac{1}{5}$ so that it shares the same denominator as $\frac{29}{100}$ .

$\frac{1}{5}=\frac{20}{100}$

Now, add the fractions.

$\frac{1}{5}+\frac{29}{100}=\frac{20}{100}+\frac{29}{100}=\frac{49}{100}$

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SSAT Upper Level Math : How to add fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Add Fractions

Example Question #2 : How To Add Fractions

Example Question #1304 : Ssat Upper Level Quantitative (Math)

Example Question #181 : Fractions

Example Question #5 : How To Add Fractions

Example Question #53 : Operations With Fractions

Example Question #182 : Rational Numbers

Example Question #2 : How To Add Fractions

Example Question #8 : How To Add Fractions

Example Question #182 : Fractions

All SSAT Upper Level Math Resources

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