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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

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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:

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

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

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

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

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

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

Report an Error

Example Question #91 : 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 $\frac{1}{3}\textup{ miles}$ in length and occupies an area of $\frac{7}{9}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

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

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

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

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

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

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

Report an Error

Example Question #11 : The Number System

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 93\\ 3{\overline{\smash{)}279}}\\ -\ 27 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{9\ \ }\\ -\ \ \ 9\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$3\times 93$

$3\times 90$

$3\times 279$

$3\times 3$

$3\times 99$

Correct answer:

$3\times 93$

Explanation:

The computation shows that $279\div3=93$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 93}\\ {\color{Green} 3}{\overline{\smash{)}279}}\\ -\ 27 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 9\ \ }\\ -\ \ \ 9\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$3\times93=279+0$

Simplify.

$3\times93=279$

The correct answer is $3\times 93$

Report an Error

Example Question #1 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 72\\ 2{\overline{\smash{)}144}}\\ -\ 14 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{4\ \ }\\ -\ \ \ 4\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$2\times 70$

$2\times 92$

$2\times 73$

$2\times 12$

$2\times 72$

Correct answer:

$2\times 72$

Explanation:

The computation shows that $144\div2=72$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 72}\\ {\color{Green} 2}{\overline{\smash{)}144}}\\ -\ 14 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 4\ \ }\\ -\ \ \ 4\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$2\times72=144+0$

Simplify.

$2\times72=144$

The correct answer is $2\times 72$

Report an Error

Example Question #11 : The Number System

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 61\\ 4{\overline{\smash{)}244}}\\ -\ 24 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{4\ \ }\\ -\ \ \ 4\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$4\times 18$

$4\times 60$

$4\times 64$

$4\times 61$

$4\times 46$

Correct answer:

$4\times 61$

Explanation:

The computation shows that $244\div4=61$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 61}\\ {\color{Green} 4}{\overline{\smash{)}244}}\\ -\ 24 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 4\ \ }\\ -\ \ \ 4\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$4\times61=244+0$

Simplify.

$4\times61=244$

The correct answer is $4\times 61$

Report an Error

Example Question #4 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 11\\ 11{\overline{\smash{)}121}}\\ -\ 11 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}01{1\ \ }\\ -\ \ \ 11\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$11\times 21$

$12\times 12$

$11\times 10$

$11\times 13$

$11\times 11$

Correct answer:

$11\times 11$

Explanation:

The computation shows that $121\div11=11$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 11}\\ {\color{Green} 11}{\overline{\smash{)}121}}\\ -\ 11 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}01{ 1\ \ }\\ -\ \ \ 11\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$11\times11=121+0$

Simplify.

$11\times11=121$

The correct answer is $11\times 11$

Report an Error

Example Question #5 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 54\\ 2{\overline{\smash{)}108}}\\ -\ 10 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{8\ \ }\\ -\ \ \ 8\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$2\times 46$

$2\times 64$

$4\times 44$

$2\times 54$

$2\times 56$

Correct answer:

$2\times 54$

Explanation:

The computation shows that $108\div2=54$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 54}\\ {\color{Green} 2}{\overline{\smash{)}108}}\\ -\ 10 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 8\ \ }\\ -\ \ \ 8\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$2\times54=108+0$

Simplify.

$2\times54=108$

The correct answer is $2\times 54$

Report an Error

Example Question #6 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 61\\ 2{\overline{\smash{)}122}}\\ -\ 12 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{2\ \ }\\ -\ \ \ 2\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$2\times 76$

$2\times 68$

$2\times 61$

$3\times 36$

$2\times 63$

Correct answer:

$2\times 61$

Explanation:

The computation shows that $122\div2=61$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 61}\\ {\color{Green} 2}{\overline{\smash{)}122}}\\ -\ 12 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 2\ \ }\\ -\ \ \ 2\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$2\times61=122+0$

Simplify.

$2\times61=122$

The correct answer is $2\times 61$

Report an Error

Example Question #7 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 51\\ 3{\overline{\smash{)}153}}\\ -\ 15 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{3\ \ }\\ -\ \ \ 3\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$3\times 53$

$3\times 36$

$3\times 35$

$3\times 51$

$3\times 61$

Correct answer:

$3\times 51$

Explanation:

The computation shows that $153\div3=61$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 51}\\ {\color{Green} 3}{\overline{\smash{)}153}}\\ -\ 15 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 3\ \ }\\ -\ \ \ 3\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$3\times51=153+0$

Simplify.

$3\times51=153$

The correct answer is $3\times 51$

Report an Error

Example Question #101 : Grade 6

Use the computation shown to find the products:

$\frac{\begin{array}[b]{r} \ 61\\ 3{\overline{\smash{)}183}}\\ -\ 18 \ \smash \ \end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{3\ \ }\\ -\ \ \ 3\ \ \end{array}}{ \ \ \ \space} }$

Possible Answers:

$3\times 61$

$3\times 63$

$3\times 68$

$3\times 42$

$3\times 36$

Correct answer:

$3\times 61$

Explanation:

The computation shows that $183\div3=61$ with a remainder of .

$\frac{\begin{array}[b]{r} \ {\color{Green} 61}\\ {\color{Green} 3}{\overline{\smash{)}183}}\\ -\ 18 \smash{\downarrow}\end{array}}{ \ \ \ \space \frac{\begin{array}[b]{r}00{ 3\ \ }\\ -\ \ \ 3\ \ \end{array}}{ \ \ \ \space} }$

So it must be that:

$3\times61=183+0$

Simplify.

$3\times61=183$

The correct answer is $3\times 61$

Report an Error

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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 #541 : Numbers And Operations

Example Question #91 : Grade 6

Example Question #11 : The Number System

Example Question #1 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Example Question #11 : The Number System

Example Question #4 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Example Question #5 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Example Question #6 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Example Question #7 : Fluently Divide Multi Digit Numbers: Ccss.Math.Content.6.Ns.B.2

Example Question #101 : Grade 6

All Common Core: 6th Grade Math Resources

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