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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

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10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #33 : Number & Operations With Fractions

$\small 6$ people are sharing a $\small \small 35$ pould bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 9$ and $\small 10$

$\small 8$ and $\small 9$

$\small 5$ and $\small 6$

$\small 7$ and $\small 8$

$\small 6$ and $\small 7$

Correct answer:

$\small 5$ and $\small 6$

Explanation:

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{35}{6}=5\frac{5}{6}$

$\small 6$ can be divided into $\small 35$ only $\small 5$ times with $\small \frac{5}{6}$ left over.

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Example Question #1201 : Ssat Middle Level Quantitative (Math)

$\small 3$ people are sharing a $\small 13$ -pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

Possible Answers:

$\small 6$ and $\small 7$

$\small 3$ and $\small 4$

$\small 7$ and $\small 8$

$\small 4$ and $\small 5$

$\small 5$ and $\small 6$

Correct answer:

$\small 4$ and $\small 5$

Explanation:

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{13}{3}=4\frac{1}{3}$

$\small 3$ can go into $\small 13$ only $\small 4$ times with $\small \frac{1}{3}$ left over.

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Example Question #541 : Numbers And Operations

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{7}\textup{ miles}$ in length and occupies an area of $\frac{3}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$4\tfrac{4}{5}\textup{ miles}$

$4\textup{ miles}$

$4\tfrac{1}{5}\textup{ miles}$

$4\tfrac{2}{5}\textup{ miles}$

$4\tfrac{3}{5}\textup{ miles}$

Correct answer:

$4\tfrac{1}{5}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{3}{5}\ miles^2=\frac{1}{7}\ miles\times Width$

Divide both sides by $\frac{1}{7}\ miles$

$\frac{\frac{3}{5}\ miles^2}{\frac{1}{7}\ miles}=\frac{\frac{1}{7}\ miles \times Width}{\frac{1}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{7}\ miles$

$\frac{1}{7}\ miles\rightarrow \frac{7}{1}\ miles$

Simplify and rewrite.

$Width=\frac{7}{1} \times \frac{3}{5}$

Multiply and solve.

$Width=\frac{21}{5}$

Reduce.

$Width=4\tfrac{1}{5}\ miles$

The width of the fracking site is $4\tfrac{1}{5}\ miles$

Report an Error

Example Question #1 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{2}{7}\textup{ miles}$ in length and occupies an area of $\frac{2}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$1\tfrac{5}{7}\textup{ miles}$

$\frac{3}{5}\textup{ miles}$

$1\tfrac{2}{5}\textup{ miles}$

$2\tfrac{3}{5}\textup{ miles}$

$1\tfrac{3}{5}\textup{ miles}$

Correct answer:

$1\tfrac{2}{5}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{2}{5}\ miles^2=\frac{2}{7}\ miles\times Width$

Divide both sides by $\frac{2}{7}\ miles$

$\frac{\frac{2}{5}\ miles^2}{\frac{2}{7}\ miles}=\frac{\frac{2}{7}\ miles \times Width}{\frac{2}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{2}{7}\ miles$

$\frac{2}{7}\ miles\rightarrow \frac{7}{2}\ miles$

Simplify and rewrite.

$Width=\frac{7}{2} \times \frac{2}{5}$

Multiply and solve.

$Width=\frac{14}{10}$

Reduce.

$Width=1\tfrac{2}{5}\ miles$

The width of the fracking site is $1\tfrac{2}{5}\ miles$

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Example Question #1 : The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{5}{7}\textup{ miles}$ in length and occupies an area of $\frac{3}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{21}{27}\textup{ miles}$

$\frac{24}{25}\textup{ miles}$

$\frac{21}{25}\textup{ miles}$

$\frac{11}{15}\textup{ miles}$

$\frac{31}{35}\textup{ miles}$

Correct answer:

$\frac{21}{25}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{3}{5}\ miles^2=\frac{5}{7}\ miles\times Width$

Divide both sides by $\frac{5}{7}\ miles$

$\frac{\frac{3}{5}\ miles^2}{\frac{5}{7}\ miles}=\frac{\frac{5}{7}\ miles \times Width}{\frac{5}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{5}{7}\ miles$

$\frac{5}{7}\ miles\rightarrow \frac{7}{5}\ miles$

Simplify and rewrite.

$Width=\frac{7}{5} \times \frac{3}{5}$

Multiply and solve.

$Width=\frac{21}{25}$

The width of the fracking site is $\frac{21}{25}\ miles$

Report an Error

Example Question #2 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{8}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$5\tfrac{3}{4}\textup{ miles}$

$3\tfrac{5}{7}\textup{ miles}$

$3\tfrac{3}{4}\textup{ miles}$

$4\tfrac{1}{4}\textup{ miles}$

$3\tfrac{1}{3}\textup{ miles}$

Correct answer:

$3\tfrac{3}{4}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{8}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{8}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{8}$

Multiply and solve.

$Width=\frac{30}{8}$

Reduce.

$Width=3\tfrac{3}{4}\ miles$

The width of the fracking site is $3\tfrac{3}{4}\ miles$

Report an Error

Example Question #3 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{6}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$5\tfrac{3}{5}\textup{ miles}$

$4\textup{ miles}$

$5\tfrac{1}{5}\textup{ miles}$

$5\tfrac{2}{5}\textup{ miles}$

$5\textup{ miles}$

Correct answer:

$5\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{6}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{6}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{6}$

Multiply and solve.

$Width=\frac{30}{6}$

Reduce.

$Width=5\ miles$

The width of the fracking site is $5\ miles$

Report an Error

Example Question #11 : The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{5}{7}\textup{ miles}$ in length and occupies an area of $\frac{2}{3}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{13}{17}\textup{ miles}$

$\frac{14}{25}\textup{ miles}$

$\frac{13}{15}\textup{ miles}$

$\frac{14}{17}\textup{ miles}$

$\frac{14}{15}\textup{ miles}$

Correct answer:

$\frac{14}{15}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{2}{3}\ miles^2=\frac{5}{7}\ miles\times Width$

Divide both sides by $\frac{5}{7}\ miles$

$\frac{\frac{2}{3}\ miles^2}{\frac{5}{7}\ miles}=\frac{\frac{5}{7}\ miles \times Width}{\frac{5}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{5}{7}\ miles$

$\frac{5}{7}\ miles\rightarrow \frac{7}{5}\ miles$

Simplify and rewrite.

$Width=\frac{7}{5} \times \frac{2}{3}$

Multiply and solve.

$Width=\frac{14}{15}$

The width of the fracking site is $\frac{14}{15}\ miles$

Report an Error

Example Question #1 : The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{5}\ miles$ in length and occupies an area of $\frac{7}{8}\ miles^2$ . How wide is this particular site?

Possible Answers:

$4\tfrac{1}{8}\ miles$

$4\tfrac{5}{8}\ miles$

$3\tfrac{3}{8}\ miles$

$6\tfrac{3}{8}\ miles$

$4\tfrac{3}{8}\ miles$

Correct answer:

$4\tfrac{3}{8}\ miles$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{7}{8}\ miles^2=\frac{1}{5}\ miles\times Width$

Divide both sides by $\frac{1}{5}\ miles$

$\frac{\frac{7}{8}\ miles^2}{\frac{1}{5}\ miles}=\frac{\frac{1}{5}\ miles \times Width}{\frac{1}{5}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{5}\ miles$

$\frac{1}{5}\ miles\rightarrow \frac{5}{1}\ miles$

Simplify and rewrite.

$Width=\frac{5}{1} \times \frac{7}{8}$

Multiply and solve.

$Width=\frac{35}{8}$

Reduce.

$Width=4\tfrac{3}{8}\ miles$

The width of the fracking site is $4\tfrac{3}{8}\ miles$

Report an Error

Example Question #12 : The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{3}\textup{ miles}$ in length and occupies an area of $\frac{7}{9}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$3\tfrac{2}{3}\textup{ miles}$

$3\tfrac{1}{3}\textup{ miles}$

$2\tfrac{1}{3}\textup{ miles}$

$1\tfrac{1}{3}\textup{ miles}$

$2\tfrac{2}{3}\textup{ miles}$

Correct answer:

$2\tfrac{1}{3}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{7}{9}\ miles^2=\frac{1}{3}\ miles\times Width$

Divide both sides by $\frac{1}{3}\ miles$

$\frac{\frac{7}{9}\ miles^2}{\frac{1}{3}\ miles}=\frac{\frac{1}{3}\ miles \times Width}{\frac{1}{3}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{3}\ miles$

$\frac{1}{3}\ miles\rightarrow \frac{3}{1}\ miles$

Simplify and rewrite.

$Width=\frac{3}{1} \times \frac{7}{9}$

Multiply and solve.

$Width=\frac{21}{9}$

Reduce.

$Width=2\tfrac{1}{3}\ miles$

The width of the fracking site is $2\tfrac{1}{3}\ miles$

Report an Error

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #33 : Number & Operations With Fractions

Example Question #1201 : Ssat Middle Level Quantitative (Math)

Example Question #541 : Numbers And Operations

Example Question #1 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #1 : The Number System

Example Question #2 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #3 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #11 : The Number System

Example Question #1 : The Number System

Example Question #12 : The Number System

All SSAT Middle Level Math Resources

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