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SSAT Middle Level Math : Numbers and Operations

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Example Questions

Example Question #83 : Grade 6

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 $\frac{1}{5}\ miles$ $\displaystyle \frac{1}{5}\ miles$ in length and occupies an area of $\frac{35}{41}\ miles^2$ $\displaystyle \frac{35}{41}\ miles^2$. How wide is this particular site?

Possible Answers:

$2\tfrac{11}{41}\ miles$ $\displaystyle 2\tfrac{11}{41}\ miles$

$11\tfrac{4}{41}\ miles$ $\displaystyle 11\tfrac{4}{41}\ miles$

$4\tfrac{21}{41}\ miles$ $\displaystyle 4\tfrac{21}{41}\ miles$

$4\tfrac{11}{41}\ miles$ $\displaystyle 4\tfrac{11}{41}\ miles$

$5\tfrac{11}{41}\ miles$ $\displaystyle 5\tfrac{11}{41}\ miles$

Correct answer:

$4\tfrac{11}{41}\ miles$ $\displaystyle 4\tfrac{11}{41}\ miles$

Explanation:

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

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

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

$\frac{35}{41}\ miles^2=\frac{1}{5}\ miles\times Width$ $\displaystyle \frac{35}{41}\ miles^2=\frac{1}{5}\ miles\times Width$

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

$\frac{\frac{35}{41}\ miles^2}{\frac{1}{5}\ miles}=\frac{\frac{1}{5}\ miles \times Width}{\frac{1}{5}\ miles}$ $\displaystyle \frac{\frac{35}{41}\ miles^2}{\frac{1}{5}\ miles}=\frac{\frac{1}{5}\ miles \times Width}{\frac{1}{5}\ miles}$

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

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

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

Simplify and rewrite.

$Width=\frac{5}{1} \times \frac{35}{41}$ $\displaystyle Width=\frac{5}{1} \times \frac{35}{41}$

Multiply and solve.

$Width=\frac{175}{41}$ $\displaystyle Width=\frac{175}{41}$

Reduce.

$Width=4\tfrac{11}{41}\ miles$ $\displaystyle Width=4\tfrac{11}{41}\ miles$

The width of the fracking site is $4\tfrac{11}{41}\ miles$ $\displaystyle 4\tfrac{11}{41}\ miles$

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Example Question #551 : Numbers And Operations

How many $\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$ servings are in $\displaystyle 3$ cups of chocolate chips?

Possible Answers:

$\displaystyle 6$

$\displaystyle 3$

$\displaystyle 4$

$\displaystyle 12$

$\displaystyle 9$

Correct answer:

$\displaystyle 6$

Explanation:

Because we want to know how many $\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$ servings are in $\displaystyle 3$ cups, we are dividing $\displaystyle 3$ by $\frac{1}{2}$ $\displaystyle \frac{1}{2}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{3}{1}\times\frac{2}{1}=\frac{6}{1}=6$ $\displaystyle \frac{3}{1}\times\frac{2}{1}=\frac{6}{1}=6$

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Example Question #1 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

How many $\frac{1}{3}\ cup$ $\displaystyle \frac{1}{3}\ cup$ servings are in $\displaystyle 3$ cups of chocolate chips?

Possible Answers:

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 12$

$\displaystyle 9$

$\displaystyle 3$

Correct answer:

$\displaystyle 9$

Explanation:

Because we want to know how many $\frac{1}{3}\ cup$ $\displaystyle \frac{1}{3}\ cup$ servings are in $\displaystyle 3$ cups, we are dividing $\displaystyle 3$ by $\frac{1}{3}$ $\displaystyle \frac{1}{3}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{3}{1}\times\frac{3}{1}=\frac{9}{1}=9$ $\displaystyle \frac{3}{1}\times\frac{3}{1}=\frac{9}{1}=9$

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Example Question #4 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

How many $\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$ servings are in $\displaystyle 4$ cups of chocolate chips?

Possible Answers:

$\displaystyle 20$

$\displaystyle 8$

$\displaystyle 16$

$\displaystyle 12$

$\displaystyle 4$

Correct answer:

$\displaystyle 16$

Explanation:

Because we want to know how many $\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$ servings are in $\displaystyle 4$ cups, we are dividing $\displaystyle 4$ by $\frac{1}{4}$ $\displaystyle \frac{1}{4}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{4}{1}\times\frac{4}{1}=\frac{16}{1}=16$ $\displaystyle \frac{4}{1}\times\frac{4}{1}=\frac{16}{1}=16$

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Example Question #1 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

How many $\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$ servings are in $\displaystyle 4$ cups of chocolate chips?

Possible Answers:

$\displaystyle 20$

$\displaystyle 4$

$\displaystyle 12$

$\displaystyle 8$

$\displaystyle 16$

Correct answer:

$\displaystyle 8$

Explanation:

Because we want to know how many $\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$ servings are in $\displaystyle 4$ cups, we are dividing $\displaystyle 4$ by $\frac{1}{2}$ $\displaystyle \frac{1}{2}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{4}{1}\times\frac{2}{1}=\frac{8}{1}=8$ $\displaystyle \frac{4}{1}\times\frac{2}{1}=\frac{8}{1}=8$

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Example Question #5 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

How many $\frac{1}{3}\ cup$ $\displaystyle \frac{1}{3}\ cup$ servings are in $\displaystyle 4$ cups of chocolate chips?

Possible Answers:

$\displaystyle 12$

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 16$

$\displaystyle 20$

Correct answer:

$\displaystyle 12$

Explanation:

Because we want to know how many $\frac{1}{3}\ cup$ $\displaystyle \frac{1}{3}\ cup$ servings are in $\displaystyle 4$ cups, we are dividing $\displaystyle 4$ by $\frac{1}{3}$ $\displaystyle \frac{1}{3}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

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

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Example Question #1213 : Ssat Middle Level Quantitative (Math)

How many $\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$ servings are in $\displaystyle 5$ cups of chocolate chips?

Possible Answers:

$\displaystyle 5$

$\displaystyle 20$

$\displaystyle 10$

$\displaystyle 15$

$\displaystyle 25$

Correct answer:

$\displaystyle 20$

Explanation:

Because we want to know how many $\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$ servings are in $\displaystyle 5$ cups, we are dividing $\displaystyle 5$ by $\frac{1}{4}$ $\displaystyle \frac{1}{4}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

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

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Example Question #71 : Fractions

How many $\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$ servings are in $\displaystyle 5$ cups of chocolate chips?

Possible Answers:

$\displaystyle 15$

$\displaystyle 10$

$\displaystyle 5$

$\displaystyle 20$

$\displaystyle 25$

Correct answer:

$\displaystyle 10$

Explanation:

Because we want to know how many $\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$ servings are in $\displaystyle 5$ cups, we are dividing $\displaystyle 5$ by $\frac{1}{2}$ $\displaystyle \frac{1}{2}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{5}{1}\times\frac{2}{1}=\frac{10}{1}=10$ $\displaystyle \frac{5}{1}\times\frac{2}{1}=\frac{10}{1}=10$

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Example Question #72 : Fractions

How many $\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$ servings are in $\displaystyle 6$ cups of chocolate chips?

Possible Answers:

$\displaystyle 12$

$\displaystyle 26$

$\displaystyle 24$

$\displaystyle 18$

$\displaystyle 36$

Correct answer:

$\displaystyle 24$

Explanation:

Because we want to know how many $\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$ servings are in $\displaystyle 6$ cups, we are dividing $\displaystyle 6$ by $\frac{1}{4}$ $\displaystyle \frac{1}{4}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

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

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Example Question #73 : Fractions

How many $\frac{1}{3}\ cup$ $\displaystyle \frac{1}{3}\ cup$ servings are in $\displaystyle 6$ cups of chocolate chips?

Possible Answers:

$\displaystyle 36$

$\displaystyle 6$

$\displaystyle 12$

$\displaystyle 18$

$\displaystyle 24$

Correct answer:

$\displaystyle 18$

Explanation:

Because we want to know how many $\frac{1}{3}\ cup$ $\displaystyle \frac{1}{3}\ cup$ servings are in $\displaystyle 6$ cups, we are dividing $\displaystyle 6$ by $\frac{1}{3}$ $\displaystyle \frac{1}{3}$.

Remember, whenever we divide by a fraction, we multiply by the reciprocal

$\frac{6}{1}\times\frac{3}{1}=\frac{18}{1}=18$ $\displaystyle \frac{6}{1}\times\frac{3}{1}=\frac{18}{1}=18$

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #83 : Grade 6

Example Question #551 : Numbers And Operations

Example Question #1 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #4 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #1 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #5 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #1213 : Ssat Middle Level Quantitative (Math)

Example Question #71 : Fractions

Example Question #72 : Fractions

Example Question #73 : Fractions

All SSAT Middle Level Math Resources

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