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Common Core: 6th Grade Math : Grade 6

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 Find The Solution To An Equation

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

Possible Answers:

$24\ \text{turnips}$

$21\ \text{turnips}$

$26\ \text{turnips}$

$62\ \text{turnips}$

$12\ \text{turnips}$

Correct answer:

$26\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{6\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{6\ \text{corn}}{T}$

Cross multiply and solve for .

$6\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=78

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{78}{3}$

Solve.

T=26

The farmer can get $26\ \text{turnips}$ .

Report an Error

Example Question #62 : How To Find The Solution To An Equation

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

Possible Answers:

$57\ \text{turnips}$

$56\ \text{turnips}$

$52\ \text{turnips}$

$60\ \text{turnips}$

$65\ \text{turnips}$

Correct answer:

$52\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{12\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{12\ \text{corn}}{T}$

Cross multiply and solve for .

$12\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=156

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{156}{3}$

Solve.

T=52

The farmer can get $52\ \text{turnips}$ .

Report an Error

Example Question #51 : Ratios & Proportional Relationships

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has 210 ears of corn, then how many turnips can he get?

Possible Answers:

$980\ \text{turnips}$

$2100\ \text{turnips}$

$910\ \text{turnips}$

$180\ \text{turnips}$

$1009\ \text{turnips}$

Correct answer:

$910\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 210 ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{210\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{210\ \text{corn}}{T}$

Cross multiply and solve for .

$210\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=2730

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{2730}{3}$

Solve.

T=910

The farmer can get $910\ \text{turnips}$ .

Report an Error

Example Question #63 : How To Find The Solution To An Equation

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has 150 ears of corn, then how many turnips can he get?

Possible Answers:

$750\ \text{turnips}$

$560\ \text{turnips}$

$650\ \text{turnips}$

$860\ \text{turnips}$

$550\ \text{turnips}$

Correct answer:

$650\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 150 ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{150\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{150\ \text{corn}}{T}$

Cross multiply and solve for .

$150\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=1950

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{1950}{3}$

Solve.

T=650

The farmer can get $650\ \text{turnips}$ .

Report an Error

Example Question #52 : Ratios & Proportional Relationships

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has 180 ears of corn, then how many turnips can he get?

Possible Answers:

$878\ \text{turnips}$

$780\ \text{turnips}$

$877\ \text{turnips}$

$870\ \text{turnips}$

$787\ \text{turnips}$

Correct answer:

$780\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 180 ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{180\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{180\ \text{corn}}{T}$

Cross multiply and solve for .

$180\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=2340

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{2340}{3}$

Solve.

T=780

The farmer can get $780\ \text{turnips}$ .

Report an Error

Example Question #64 : How To Find The Solution To An Equation

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

Possible Answers:

$449\ \text{turnips}$

$429\ \text{turnips}$

$924\ \text{turnips}$

$483\ \text{turnips}$

$249\ \text{turnips}$

Correct answer:

$429\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{99\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{99\ \text{corn}}{T}$

Cross multiply and solve for .

$99\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=1287

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{1287}{3}$

Solve.

T=429

The farmer can get $429\ \text{turnips}$ .

Report an Error

Example Question #65 : How To Find The Solution To An Equation

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

Possible Answers:

$165\ \text{turnips}$

$516\ \text{turnips}$

$159\ \text{turnips}$

$166\ \text{turnips}$

$156\ \text{turnips}$

Correct answer:

$156\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{36\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{36\ \text{corn}}{T}$

Cross multiply and solve for .

$36\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=468

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{468}{3}$

Solve.

T=156

The farmer can get $156\ \text{turnips}$ .

Report an Error

Example Question #53 : Ratios & Proportional Relationships

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has 3000 ears of corn, then how many turnips can he get?

Possible Answers:

$13113\ \text{turnips}$

$13013\ \text{turnips}$

$13000\ \text{turnips}$

$33000\ \text{turnips}$

$31000\ \text{turnips}$

Correct answer:

$13000\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 3000 ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{3000\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{3000\ \text{corn}}{T}$

Cross multiply and solve for .

$3000\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=39000

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{39000}{3}$

Solve.

T=13000

The farmer can get $13000\ \text{turnips}$ .

Report an Error

Example Question #67 : How To Find The Solution To An Equation

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

Possible Answers:

$353\ \text{turnips}$

$531\ \text{turnips}$

$351\ \text{turnips}$

$153\ \text{turnips}$

$533\ \text{turnips}$

Correct answer:

$351\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{81\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{81\ \text{corn}}{T}$

Cross multiply and solve for .

$81\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=1053

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{1053}{3}$

Solve.

T=351

The farmer can get $351\ \text{turnips}$ .

Report an Error

Example Question #54 : Ratios & Proportional Relationships

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has 126 ears of corn, then how many turnips can he get?

Possible Answers:

$645\ \text{turnips}$

$654\ \text{turnips}$

$456\ \text{turnips}$

$546\ \text{turnips}$

$564\ \text{turnips}$

Correct answer:

$546\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 126 ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{126\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{126\ \text{corn}}{T}$

Cross multiply and solve for .

$126\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=1638

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{1638}{3}$

Solve.

T=546

The farmer can get $546\ \text{turnips}$ .

Report an Error

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All Common Core: 6th Grade Math Resources

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Common Core: 6th Grade Math : Grade 6

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 Find The Solution To An Equation

Example Question #62 : How To Find The Solution To An Equation

Example Question #51 : Ratios & Proportional Relationships

Example Question #63 : How To Find The Solution To An Equation

Example Question #52 : Ratios & Proportional Relationships

Example Question #64 : How To Find The Solution To An Equation

Example Question #65 : How To Find The Solution To An Equation

Example Question #53 : Ratios & Proportional Relationships

Example Question #67 : How To Find The Solution To An Equation

Example Question #54 : Ratios & Proportional Relationships

All Common Core: 6th Grade Math Resources

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