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

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Question

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?

Answer

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

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Question

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?

Answer

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

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Question

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?

Answer

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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Question

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?

Answer

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

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Question

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?

Answer

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

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Question

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?

Answer

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 $5\ miles$

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Question

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?

Answer

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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Question

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?

Answer

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

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Question

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?

Answer

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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Question

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?

Answer

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

Compare your answer with the correct one above

Question

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?

Answer

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

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Question

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?

Answer

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

Compare your answer with the correct one above

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