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SSAT Upper Level Math : Number Concepts and Operations

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #211 : Number Concepts And Operations

Simplify the expression $\frac{4}{3}\times(-\frac{3}{4})$ .

Possible Answers:

$\frac{9}{16}$

$-\frac{16}{9}$

$\frac{16}{9}$

Correct answer:

Explanation:

Multiplying across the numerators and denominators of both terms and simplifying:

$\frac{4}{3}\times(-\frac{3}{4})=-\frac{12}{12}=-1$

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Example Question #3 : How To Multiply Fractions

Simplify the expression $\frac{12}{5}\times\frac{10}{20}$ .

Possible Answers:

$\frac{6}{5}$

$\frac{22}{25}$

$-\frac{5}{6}$

$-\frac{6}{5}$

$\frac{5}{6}$

Correct answer:

$\frac{6}{5}$

Explanation:

$\frac{12}{5}\times\frac{10}{20}$

First, multiply straight across. Multiply the numerators together and then multiply the denominators together.

$=\frac{12\times 10}{5\times 20}$

$=\frac{120}{100}$

From here, simplify the expression by factoring out the Greatest Common Factor.

In this case the Greatest Common Factor is 20.

$=\frac{120\div 20}{100\div 20}$

$=\frac{6}{5}$

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Example Question #4 : How To Multiply Fractions

Steven runs a pizza shop. On Monday, he used $\frac{4}{5}$ of a bag of flour. On Tuesday, he used $\frac{1}{6}$ the amount he used on Monday. How much of a bag of flour did he use on Tuesday?

Possible Answers:

$\frac{2}{15}$

$\frac{4}{10}$

$\frac{1}{10}$

$\frac{4}{15}$

Correct answer:

$\frac{2}{15}$

Explanation:

To find how many bags of flour he used on Tuesday, multiply $\frac{4}{5}$ by $\frac{1}{6}$ .

To multiply fractions, multiply the numerators together, then multiply the denominators together.

$\frac{4}{5}\times \frac{1}{6}=\frac{4\times1}{5\times6}=\frac{4}{30}=\frac{2}{15}$

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Example Question #5 : How To Multiply Fractions

In Mary's class, $\frac{1}{12}$ of the class owns a dog, and of those in the class that own a dog, $\frac{2}{7}$ also owns a cat. What fraction of the class owns both a dog and a cat?

Possible Answers:

$\frac{3}{19}$

$\frac{1}{10}$

$\frac{1}{47}$

$\frac{1}{42}$

Correct answer:

$\frac{1}{42}$

Explanation:

Multiply $\frac{1}{12}$ by $\frac{2}{7}$ to find out how much of the class have both a cat and a dog.

$\frac{1}{12}\times \frac{2}{7}=\frac{1\times2}{12\times7}=\frac{2}{84}=\frac{1}{42}$

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Example Question #3 : How To Multiply Fractions

A certain recipe for a batch of chocolate cookies calls for $\frac{9}{10}$ of a cup of sugar to be used. If Mike only wants to make $\frac{3}{4}$ of a batch, how much of a cup of sugar should he use?

Possible Answers:

$\frac{27}{40}$

$\frac{9}{10}$

$\frac{6}{7}$

$\frac{1}{9}$

Correct answer:

$\frac{27}{40}$

Explanation:

Multiply $\frac{9}{10}$ by $\frac{3}{4}$ to find out how much sugar he needs to use.

$\frac{9}{10}\times \frac{3}{4}=\frac{9\times3}{10\times4}=\frac{27}{40}$

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Example Question #6 : How To Multiply Fractions

A poll was conducted at a high school. The poll found that $\frac{2}{3}$ of the students at the school had siblings, and that $\frac{4}{5}$ of the students who had siblings also had a dog at home. What fraction of the students have siblings and a dog?

Possible Answers:

$\frac{9}{14}$

$\frac{1}{5}$

$\frac{2}{5}$

$\frac{8}{15}$

Correct answer:

$\frac{8}{15}$

Explanation:

To find what fraction of the students have siblings and a dog, multiply $\frac{2}{3}$ by $\frac{4}{5}$ .

$\frac{2}{3}\times \frac{4}{5}=\frac{2\times4}{3\times5}=\frac{8}{15}$

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Example Question #4 : How To Multiply Fractions

Louis gave away $\frac{7}{8}$ of his comic books to his sister. Of the ones he gave to his sister, $\frac{1}{8}$ were Superman comics. What fraction of the comics that Louis gave away are Superman comics?

Possible Answers:

$\frac{1}{8}$

$\frac{7}{64}$

$\frac{3}{16}$

$\frac{2}{5}$

Correct answer:

$\frac{7}{64}$

Explanation:

Multiply $\frac{7}{8}$ by $\frac{1}{8}$ to figure out what fraction of the comics are Superman comics.

$\frac{7}{8}\times \frac{1}{8}=\frac{7\times1}{8\times8}=\frac{7}{64}$

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Example Question #2 : How To Multiply Fractions

$\frac{1}{3}$ of the students in an elementary school owns their own computer. Of those that own their own computer, $\frac{2}{5}$ also owned their own cell phone. What fraction of the students owned both a computer and a cell phone?

Possible Answers:

$\frac{4}{15}$

$\frac{2}{15}$

$\frac{3}{8}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{15}$

Explanation:

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ to find what fraction of the students own a computer and a cell phone.

$\frac{1}{3}\times\frac{2}{5}=\frac{1\times2}{3\times5}=\frac{2}{15}$

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Example Question #152 : Rational Numbers

In Timothy's 3rd grade class, $\frac{1}{5}$ of the students enjoy eating vegetables. Of the ones who enjoy eating vegetables, $\frac{5}{6}$ say that spinach is their favorite vegetable. What fraction of the class say spinach is their favorite vegetable?

Possible Answers:

$\frac{1}{6}$

$\frac{5}{11}$

$\frac{2}{5}$

$\frac{3}{10}$

Correct answer:

$\frac{1}{6}$

Explanation:

Multiply $\frac{1}{5}$ by $\frac{5}{6}$ to find out what fraction of the students say spinach is their favorite vegetable.

$\frac{1}{5}\times \frac{5}{6}=\frac{1\times5}{5\times6}=\frac{5}{30}=\frac{1}{6}$

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Example Question #32 : Operations With Fractions

At an arcade, $\frac{1}{6}$ of the games are fighting games. Of those games, $\frac{3}{7}$ are Japanese games. What fraction of the games at the arcade are Japanese fighting games?

Possible Answers:

$\frac{1}{21}$

$\frac{4}{13}$

$\frac{1}{14}$

$\frac{5}{42}$

Correct answer:

$\frac{1}{14}$

Explanation:

To find what fraction of the games are Japanese fighting ones, multiply $\frac{1}{6}$ by $\frac{3}{7}$ .

$\frac{1}{6}\times \frac{3}{7}=\frac{1\times3}{6\times7}=\frac{3}{42}=\frac{1}{14}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #211 : Number Concepts And Operations

Example Question #3 : How To Multiply Fractions

Example Question #4 : How To Multiply Fractions

Example Question #5 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #6 : How To Multiply Fractions

Example Question #4 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #152 : Rational Numbers

Example Question #32 : Operations With Fractions

All SSAT Upper Level Math Resources

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