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SSAT Middle Level Math : Numbers and Operations

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

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All SSAT Middle Level Math Resources

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Example Questions

Example Question #2 : 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 $\frac{35}{41}\ miles^2$ . How wide is this particular site?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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

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

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.

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

Multiply and solve.

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

Reduce.

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

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

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Example Question #551 : Numbers And Operations

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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Example Question #2 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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Example Question #3 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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Example Question #623 : Number & Operations With Fractions

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

Report an Error

Example Question #6 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

Report an Error

Example Question #631 : Number & Operations With Fractions

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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Example Question #632 : Number & Operations With Fractions

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

Possible Answers:

Correct answer:

Explanation:

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

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

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

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All SSAT Middle Level Math Resources

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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 #2 : The Number System

Example Question #551 : Numbers And Operations

Example Question #2 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #3 : 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 #623 : Number & Operations With Fractions

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

Example Question #6 : Solve Division Word Problems With Fractions And Whole Numbers: Ccss.Math.Content.5.Nf.B.7c

Example Question #631 : Number & Operations With Fractions

Example Question #632 : Number & Operations With Fractions

All SSAT Middle Level Math Resources

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