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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 #33 : How To Find A Ratio

A motorcycle travels $750\textup{ miles}$ $\displaystyle 750\textup{ miles}$ in $10\textup{ hours}$ $\displaystyle 10\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$750\textup{ mph}$ $\displaystyle 750\textup{ mph}$

$75\textup{ mph}$ $\displaystyle 75\textup{ mph}$

$60\textup{ mph}$ $\displaystyle 60\textup{ mph}$

$100\textup{ mph}$ $\displaystyle 100\textup{ mph}$

$57\textup{ mph}$ $\displaystyle 57\textup{ mph}$

Correct answer:

$75\textup{ mph}$ $\displaystyle 75\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$750\ miles: 10\ hours=\frac{750\ miles}{10\ hours}$ $\displaystyle 750\ miles: 10\ hours=\frac{750\ miles}{10\ hours}$

Reduce and solve.

75mph $\displaystyle 75mph$

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Example Question #34 : How To Find A Ratio

A motorcycle travels $3828\textup{ miles}$ $\displaystyle 3828\textup{ miles}$ in $58\textup{ hours}$ $\displaystyle 58\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$76\textup{ mph}$ $\displaystyle 76\textup{ mph}$

$55\textup{ mph}$ $\displaystyle 55\textup{ mph}$

$66\textup{ mph}$ $\displaystyle 66\textup{ mph}$

$68\textup{ mph}$ $\displaystyle 68\textup{ mph}$

$72\textup{ mph}$ $\displaystyle 72\textup{ mph}$

Correct answer:

$66\textup{ mph}$ $\displaystyle 66\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$3828\ miles: 58\ hours=\frac{3828\ miles}{58\ hours}$ $\displaystyle 3828\ miles: 58\ hours=\frac{3828\ miles}{58\ hours}$

Reduce and solve.

66mph $\displaystyle 66mph$

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Example Question #21 : Grade 6

A motorcycle travels $567\textup{ miles}$ $\displaystyle 567\textup{ miles}$ in $9\textup{ hours}$ $\displaystyle 9\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$36\textup{ mph}$ $\displaystyle 36\textup{ mph}$

$69\textup{ mph}$ $\displaystyle 69\textup{ mph}$

$66\textup{ mph}$ $\displaystyle 66\textup{ mph}$

$63\textup{ mph}$ $\displaystyle 63\textup{ mph}$

$72\textup{ mph}$ $\displaystyle 72\textup{ mph}$

Correct answer:

$63\textup{ mph}$ $\displaystyle 63\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$567\ miles: 9\ hours=\frac{567\ miles}{9\ hours}$ $\displaystyle 567\ miles: 9\ hours=\frac{567\ miles}{9\ hours}$

Reduce and solve.

63mph $\displaystyle 63mph$

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Example Question #22 : Grade 6

A motorcycle travels $1296\textup{ miles}$ $\displaystyle 1296\textup{ miles}$ in $18\textup{ hours}$ $\displaystyle 18\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$66\textup{ mph}$ $\displaystyle 66\textup{ mph}$

$75\textup{ mph}$ $\displaystyle 75\textup{ mph}$

$77\textup{ mph}$ $\displaystyle 77\textup{ mph}$

$72\textup{ mph}$ $\displaystyle 72\textup{ mph}$

$80\textup{ mph}$ $\displaystyle 80\textup{ mph}$

Correct answer:

$72\textup{ mph}$ $\displaystyle 72\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$1296\ miles: 18\ hours=\frac{1296\ miles}{18\ hours}$ $\displaystyle 1296\ miles: 18\ hours=\frac{1296\ miles}{18\ hours}$

Reduce and solve.

72mph $\displaystyle 72mph$

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Example Question #23 : Grade 6

At a local microchip factory, there are $\displaystyle 2$ managers for every $\displaystyle 5$ workers. How many managers are needed for $\displaystyle 25$ workers?

Possible Answers:

$12\ \text{managers}$ $\displaystyle 12\ \text{managers}$

$6\ \text{managers}$ $\displaystyle 6\ \text{managers}$

$8\ \text{managers}$ $\displaystyle 8\ \text{managers}$

$10\ \text{managers}$ $\displaystyle 10\ \text{managers}$

$2\ \text{managers}$ $\displaystyle 2\ \text{managers}$

Correct answer:

$10\ \text{managers}$ $\displaystyle 10\ \text{managers}$

Explanation:

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$ $\displaystyle 2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $25\ \text{workers}$ $\displaystyle 25\ \text{workers}$ .

Table

The factory will need $10\ \text{managers}$ $\displaystyle 10\ \text{managers}$ .

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Example Question #24 : Grade 6

At a local microchip factory, there are $\displaystyle 2$ managers for every $\displaystyle 5$ workers. How many managers are needed for $\displaystyle 5$ workers?

Possible Answers:

$6\ \text{managers}$ $\displaystyle 6\ \text{managers}$

$2\ \text{managers}$ $\displaystyle 2\ \text{managers}$

$4\ \text{managers}$ $\displaystyle 4\ \text{managers}$

$8\ \text{managers}$ $\displaystyle 8\ \text{managers}$

$1\ \text{manager}$ $\displaystyle 1\ \text{manager}$

Correct answer:

$2\ \text{managers}$ $\displaystyle 2\ \text{managers}$

Explanation:

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$ $\displaystyle 2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $5\ \text{workers}$ $\displaystyle 5\ \text{workers}$ .

Table

The factory will need $2\ \text{managers}$ $\displaystyle 2\ \text{managers}$ .

Report an Error

Example Question #21 : Grade 6

At a local microchip factory, there are $\displaystyle 2$ managers for every $\displaystyle 5$ workers. How many managers are needed for $\displaystyle 15$ workers?

Possible Answers:

$4\ \text{managers}$ $\displaystyle 4\ \text{managers}$

$3\ \text{managers}$ $\displaystyle 3\ \text{managers}$

$8\ \text{managers}$ $\displaystyle 8\ \text{managers}$

$5\ \text{managers}$ $\displaystyle 5\ \text{managers}$

$6\ \text{managers}$ $\displaystyle 6\ \text{managers}$

Correct answer:

$6\ \text{managers}$ $\displaystyle 6\ \text{managers}$

Explanation:

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$ $\displaystyle 2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $15\ \text{workers}$ $\displaystyle 15\ \text{workers}$ .

Table

The factory will need $6\ \text{managers}$ $\displaystyle 6\ \text{managers}$ .

Report an Error

Example Question #22 : Grade 6

At a local microchip factory, there are $\displaystyle 2$ managers for every $\displaystyle 5$ workers. How many managers are needed for $\displaystyle 10$ workers?

Possible Answers:

$1\ \text{manager}$ $\displaystyle 1\ \text{manager}$

$4\ \text{managers}$ $\displaystyle 4\ \text{managers}$

$6\ \text{managers}$ $\displaystyle 6\ \text{managers}$

$3\ \text{managers}$ $\displaystyle 3\ \text{managers}$

$2\ \text{managers}$ $\displaystyle 2\ \text{managers}$

Correct answer:

$4\ \text{managers}$ $\displaystyle 4\ \text{managers}$

Explanation:

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$ $\displaystyle 2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $10\ \text{workers}$ $\displaystyle 10\ \text{workers}$ .

Table

The factory will need $4\ \text{managers}$ $\displaystyle 4\ \text{managers}$ .

Report an Error

Example Question #23 : Grade 6

At a local microchip factory, there are $\displaystyle 2$ managers for every $\displaystyle 5$ workers. How many managers are needed for $\displaystyle 60$ workers?

Possible Answers:

$23\ \text{managers}$ $\displaystyle 23\ \text{managers}$

$24\ \text{managers}$ $\displaystyle 24\ \text{managers}$

$20\ \text{managers}$ $\displaystyle 20\ \text{managers}$

$18\ \text{managers}$ $\displaystyle 18\ \text{managers}$

$26\ \text{managers}$ $\displaystyle 26\ \text{managers}$

Correct answer:

$24\ \text{managers}$ $\displaystyle 24\ \text{managers}$

Explanation:

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$ $\displaystyle 2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $60\ \text{workers}$ $\displaystyle 60\ \text{workers}$ .

Table

The factory will need $24\ \text{managers}$ $\displaystyle 24\ \text{managers}$ .

Report an Error

Example Question #24 : Grade 6

At a local microchip factory, there are $\displaystyle 2$ managers for every $\displaystyle 5$ workers. How many managers are needed for $\displaystyle 45$ workers?

Possible Answers:

$17\ \text{managers}$ $\displaystyle 17\ \text{managers}$

$18\ \text{managers}$ $\displaystyle 18\ \text{managers}$

$14\ \text{managers}$ $\displaystyle 14\ \text{managers}$

$13\ \text{managers}$ $\displaystyle 13\ \text{managers}$

$16\ \text{managers}$ $\displaystyle 16\ \text{managers}$

Correct answer:

$18\ \text{managers}$ $\displaystyle 18\ \text{managers}$

Explanation:

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$ $\displaystyle 2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $45\ \text{workers}$ $\displaystyle 45\ \text{workers}$ .

Table

The factory will need $18\ \text{managers}$ $\displaystyle 18\ \text{managers}$ .

Report an Error

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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

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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 #33 : How To Find A Ratio

Example Question #34 : How To Find A Ratio

Example Question #21 : Grade 6

Example Question #22 : Grade 6

Example Question #23 : Grade 6

Example Question #24 : Grade 6

Example Question #21 : Grade 6

Example Question #22 : Grade 6

Example Question #23 : Grade 6

Example Question #24 : Grade 6

All Common Core: 6th Grade Math Resources

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