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Common Core: 6th Grade Math : Interpret and Compute Quotients of Fractions: CCSS.Math.Content.6.NS.A.1

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

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All Common Core: 6th Grade Math Resources

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Example Questions

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

Possible Answers:

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

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

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

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

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

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

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Example Question #542 : 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 $\frac{1}{3}\textup{ miles}$ in length and occupies an area of $\frac{7}{9}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

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

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

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

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

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

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

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Common Core: 6th Grade Math : Interpret and Compute Quotients of Fractions: CCSS.Math.Content.6.NS.A.1

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

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #541 : Numbers And Operations

Example Question #542 : Numbers And Operations

All Common Core: 6th Grade Math Resources

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