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Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : How To Divide Fractions

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:

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

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

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

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

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

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 #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 $\frac{1}{4}\ miles$ in length and occupies an area of $\frac{7}{9}\ miles^2$ . How wide is this particular site?

Possible Answers:

$3\tfrac{5}{9}\ miles$

$9\tfrac{5}{9}\ miles$

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

$9\tfrac{1}{3}\ miles$

$3\tfrac{1}{9}\ miles$

Correct answer:

$3\tfrac{1}{9}\ miles$

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 $\text{Width}$ .

$\frac{7}{9}\ miles^2=\frac{1}{4}\ miles\times Width$

Divide both sides by $\frac{1}{4}\ miles$

$\frac{\frac{7}{9}\ miles^2}{\frac{1}{4}\ miles}=\frac{\frac{1}{4}\ miles \times Width}{\frac{1}{4}\ miles}$

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

Find the reciprocal of $\frac{1}{4}\ miles$

$\frac{1}{4}\ miles\rightarrow \frac{4}{1}\ miles$

Simplify and rewrite.

$Width=\frac{4}{1} \times \frac{7}{9}$

Multiply and solve.

$Width=\frac{28}{9}$

Reduce.

$Width=3\tfrac{1}{9}\ miles$

The width of the fracking site is $3\tfrac{1}{9}\ miles$

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 $\frac{1}{4}\ miles$ in length and occupies an area of $\frac{7}{8}\ miles^2$ . How wide is this particular site?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $\text{Width}$ .

$\frac{7}{8}\ miles^2=\frac{1}{4}\ miles\times Width$

Divide both sides by $\frac{1}{4}\ miles$

$\frac{\frac{7}{8}\ miles^2}{\frac{1}{4}\ miles}=\frac{\frac{1}{4}\ miles \times Width}{\frac{1}{4}\ miles}$

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

Find the reciprocal of $\frac{1}{4}\ miles$

$\frac{1}{4}\ miles\rightarrow \frac{4}{1}\ miles$

Simplify and rewrite.

$Width=\frac{4}{1} \times \frac{7}{8}$

Multiply and solve.

$Width=\frac{28}{8}$

Reduce.

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

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

Report an Error

Example Question #62 : How To Divide Fractions

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:

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

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

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

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

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

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

Report an Error

Example Question #1321 : Ssat Middle Level Quantitative (Math)

Hydraulic fracturing is a process used by gas companies to rupture and collect pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{3}{4}\textup{ miles}$ in length and occupies an area of $\frac{1}{2}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

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

$\frac{6}{7}\textup{ miles}$

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

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

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

Correct answer:

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

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 $\text{Width}$ .

$\frac{1}{2}\ miles^2=\frac{3}{4}\ miles\times Width$

Divide both sides by $\frac{3}{4}\ miles$

$\frac{\frac{1}{2}\ miles^2}{\frac{3}{4}\ miles}=\frac{\frac{3}{4}\ miles \times Width}{\frac{3}{4}\ miles}$

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

Find the reciprocal of $\frac{3}{4}\ miles$

$\frac{3}{4}\ miles\rightarrow \frac{4}{3}\ miles$

Simplify and rewrite.

$Width=\frac{4}{3} \times \frac{1}{2}$

Multiply and solve.

$Width=\frac{4}{6}$

Reduce.

$Width=\frac{2}{3}\ miles$

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

Report an Error

Example Question #53 : Fractions

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:

$4\textup{ miles}$

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

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

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

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

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 #7 : 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:

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

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

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

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

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

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

Report an Error

Example Question #8 : 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 $\frac{5}{7}\textup{ miles}$ in length and occupies an area of $\frac{3}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

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

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

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

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

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

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 #1202 : Ssat Middle Level Quantitative (Math)

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:

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

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

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

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

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

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 #62 : Fractions

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:

$4\textup{ miles}$

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

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

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

$5\textup{ miles}$

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

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All Common Core: 6th Grade Math Resources

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Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #61 : How To Divide Fractions

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 #62 : How To Divide Fractions

Example Question #1321 : Ssat Middle Level Quantitative (Math)

Example Question #53 : Fractions

Example Question #7 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #8 : Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #1202 : Ssat Middle Level Quantitative (Math)

Example Question #62 : Fractions

All Common Core: 6th Grade Math Resources

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