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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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 #8 : How To Express A Fraction As A Ratio

A smoothie is made with cups of apple juice, cup of mango juice, cups of orange juice, and cups of blueberry juice. What is the ratio of the amount of orange juice to the amount of blueberry juice?

Possible Answers:

1:2

1:4

1:1

2:1

Correct answer:

2:1

Explanation:

The ratio of orange juice to blueberry juice can be expressed as a fraction:

$\frac{4}{2}=\frac{2}{1}$

That fraction can also be expressed as 2:1 .

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Example Question #1171 : Ssat Upper Level Quantitative (Math)

Express $\frac{10}{12}$ as a ratio in simplest terms.

Possible Answers:

2:3

5:6

10:12

6:5

Correct answer:

5:6

Explanation:

First, reduce the fraction.

$\frac{10}{12}=\frac{5}{6}$

Now, the simplified fraction can also be expressed as 5:6 .

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Example Question #42 : Rational Numbers

A pan of cupcakes had cupcakes on Monday. After one day, cupcakes were eaten. What is the ratio of cupcakes eaten to cupcakes remaining?

Possible Answers:

6:1

5:1

1:6

1:5

Correct answer:

1:5

Explanation:

First, find the number of cupcakes that remain.

$\text{Remaining cupcakes}=48-8=40$

Now, set up the ratio of cupcakes eaten to cupcakes remaining as a fraction:

$\frac{8}{40}=\frac{1}{5}$

That fraction is equivalent to 1:5 .

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Example Question #1172 : Ssat Upper Level Quantitative (Math)

In a group of dolphins, there are male dolphins for every female dolphins. What is the ratio of female dolphins to male dolphins in this group?

Possible Answers:

6:1

1:6

6:5

5:6

Correct answer:

6:1

Explanation:

The ratio of female to male dolphins can be expressed as the following fraction:

$\frac{30}{5}=\frac{6}{1}$

That fraction can be expressed using the colon form of a ratio as 6:1 .

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Example Question #14 : How To Express A Fraction As A Ratio

In an animal shelter, there are cats, birds, and dogs. What is the ratio of dogs to the total number of animals at the shelter?

Possible Answers:

3:5

10:23

1:5

5:3

Correct answer:

10:23

Explanation:

First, find the total number of animals at the shelter.

$\text{Total Number of Animals}=12+14+20=46$

The ratio of dogs to the total number of animals can be expressed as the following fraction:

$\frac{20}{46}=\frac{10}{23}$

That fraction can also be expressed as 10:23 .

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Example Question #104 : Number Concepts And Operations

There are marbles in a bag. In the bag, there are red marbles, blue marbles, and the rest of the marbles are yellow. What is the ratio of yellow marbles to red marbles?

Possible Answers:

1:2

2:1

1:1

4:5

Correct answer:

2:1

Explanation:

First, find the number of yellow marbles in the bag.

$\text{Number of yellow marbles}=30-12-6=12$

The ratio of yellow marbles to red marbles can be expressed as a fraction:

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

That fraction can then be expressed as 2:1 .

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Example Question #1173 : Ssat Upper Level Quantitative (Math)

A video store lent out videos during the fall semester. of the videos were lost, and the rest were returned. What is the ratio of lost videos to returned videos?

Possible Answers:

31:9

5:12

9:50

9:31

Correct answer:

9:31

Explanation:

First, find the number of videos that were returned.

$\text{Number of videos returned}=80-18=62$

Now, the ratio of videos lost to videos returned can be expressed as the following fraction:

$\frac{18}{62}=\frac{9}{31}$

This fraction can then be expressed as 9:31 .

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Example Question #1 : How To Multiply Complex Fractions

Simplify.

$\frac{5}{x}\cdot\frac{x^2}{10}$

Possible Answers:

$\frac{2}{x}$

$\frac{1}{2}$

$\frac{x^2}{2}$

$\frac{5x^2}{10x}$

$\frac{x}{2}$

Correct answer:

$\frac{x}{2}$

Explanation:

When multiplying fractions, find a way to reduce any of the fractions before multplying them out.

For example, since is a multiple of , you would cancel out the and that becomes a and the becomes a .

The same goes for x^2 and . The becomes and the x^2 goes to .

Overall, the fractions to multiply becomes

$\frac{1}{1}\cdot \frac{x}{2}$ . Answer should be $\frac{x}{2}$ .

$\frac{5x^2}{10x}$ is not correct because it's not reduced.

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Example Question #1 : Complex Fractions

Simplify.

$\frac{\frac{x}{3}}{\frac{x^2}{9}}$

Possible Answers:

$\frac{3}{x}$

$\frac{x}{3}$

$\frac{x^3}{27}$

$\frac{9x}{3x^2}$

Correct answer:

$\frac{3}{x}$

Explanation:

We need to get rid of that denominator to solve this problem easily.

Multiply top and bottom by the reciprocal of the denominator or $\frac{9}{x^2}$ .

This should leave you with $\frac{x}{3}\cdot \frac{9}{x^2}$ .

Now, find a way to reduce any of the fractions before multplying them out.

For example, since is a multiple of , you would cancel out the and that becomes a and the becomes a .

The same goes for x^2 and . The becomes and the x^2 goes to .

This leaves you with $\frac{1}{1}\cdot \frac{3}{x}$ . Answer is $\frac{3}{x}$ .

$\frac{9x}{3x^2}$ is not simplified.

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Example Question #2 : How To Multiply Complex Fractions

Simplify.

$\frac{36x^3y^2z^6}{216xy^5z^7}$

Possible Answers:

Can't be reduced.

$\frac{x^3}{6y^3z}$

$\frac{x^2}{6y^3z}$

$\frac{6x^2}{y^3z}$

$\frac{6y^3z}{x}$

Correct answer:

$\frac{x^2}{6y^3z}$

Explanation:

This involves a lot of dividing exponents with same base. When dividing exponents of the same base, all you have to do is take the exponent from the numerator and subtract it with the denominator.

For example, with the same base, , the numerator has a and denominator is . Take the diference which is . Same applies and . Since their differences are negative, it means there were mor and in the denominators.

So far, the overall fraction is $\frac{36x^2}{216y^3z}$ .

216 divides into , times.

Now with that simplification, answer is shown.

$\frac{x^2}{6y^3z}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #8 : How To Express A Fraction As A Ratio

Example Question #1171 : Ssat Upper Level Quantitative (Math)

Example Question #42 : Rational Numbers

Example Question #1172 : Ssat Upper Level Quantitative (Math)

Example Question #14 : How To Express A Fraction As A Ratio

Example Question #104 : Number Concepts And Operations

Example Question #1173 : Ssat Upper Level Quantitative (Math)

Example Question #1 : How To Multiply Complex Fractions

Example Question #1 : Complex Fractions

Example Question #2 : How To Multiply Complex Fractions

All SSAT Upper Level Math Resources

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