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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 #432 : Expressions & Equations

Which value for would make the inequality below true?

34<5+4x

Possible Answers:

All of the choices are correct

Correct answer:

Explanation:

We can use substitution to determine which value of makes the inequality true.

5+4(8)=37

$34<37\textup { TRUE}$

5+4(7)=33

$34<33\textup{ FALSE}$ , because 34>33

5+4(6)=29

$34<29\textup { FALSE}$ , because 34>29

5+4(5)=25

$34<25\textup { FALSE}$ , because 34>25

Because we are looking for a value of that makes the expression greater than , is our correct answer.

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Example Question #82 : Understand What Makes An Equation Or Inequality True And Why: Ccss.Math.Content.6.Ee.B.5

Which value for would make the equation below true?

19=12+x

Possible Answers:

Correct answer:

Explanation:

We can use substitution to determine the value of .

${\color{Teal} 12+7=19}$

12+8=20

12+9=21

12+10=22

12+11=23

Because we are looking for the number that when added to equals , our correct answer is

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Example Question #891 : Grade 6

James bought candy using a 10 dollar bill and received dollars in change. Which of the following describes how much James paid for the candy?

Possible Answers:

10/y

y/10

Correct answer:

Explanation:

The amount of change given after a purchase is the amount the customer pays minus the cost of the item. So the cost of the item is the amount the customer pays minus the amount of change received.

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Example Question #414 : Problem Solving

Call the three angles of a triangle $\angle 1, \angle 2, \angle 3$ .

The measure of $\angle2$ is twenty degrees greater than that of $\angle 1$ ; the measure of $\angle 3$ is thirty degrees less than twice that of $\angle 1$ . If is the measure of $\angle 1$ , then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

x + (x-20) + 2(x-30) = 360

x + (x-20) + 2(x-30) = 180

x + (x+20) + (2x-30) = 360

x + (x+20) = (2x+30)

x + (x+20) + (2x-30) = 180

Correct answer:

x + (x+20) + (2x-30) = 180

Explanation:

The measure of $\angle2$ is twenty degrees greater than the measure of $\angle 1$ , so its measure is 20 added to that of $\angle 1$ - that is, x + 2 0 .

The measure of $\angle 3$ is thirty degrees less than twice that of $\angle 1$ . Twice the measure of $\angle 1$ is , and thirty degrees less than this is 30 subtracted from - that is, 2x-30 .

The sum of the measures of the three angles of a triangle is 180, so, to solve for - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

x + (x+20) + (2x-30) = 180

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Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Call the three angles of a triangle $\angle 1, \angle 2, \angle 3$ .

The measure of $\angle2$ is forty degrees less than that of $\angle 1$ ; the measure of $\angle 3$ is ten degrees less than twice that of $\angle 1$ . If is the measure of $\angle 1$ , then which of the following equations would we need to solve in order to calculate the measures of the angles?

Possible Answers:

x + (x-40) = (2x - 10)

x + (x-40) + (2x - 10) = 180

x + (x-40) + (2x - 10) = 360

x + (x-40) + 2 (x - 10) = 180

x + (x-40) + 2 (x - 10) = 360

Correct answer:

x + (x-40) + (2x - 10) = 180

Explanation:

The measure of $\angle2$ is forty degrees less than the measure of $\angle 1$ , so its measure is 40 subtracted from that of $\angle 1$ - that is, x -40 .

The measure of $\angle 3$ is ten degrees less than twice that of $\angle 1$ . Twice the measure of $\angle 1$ is , and ten degrees less than this is 10 subtracted from - that is, 2x-10 .

x + (x-40) + (2x - 10) = 180

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Example Question #892 : Grade 6

Read the following scenario:

A barista has to make sixty pounds of a special blend of coffee at Moonbucks, using Hazelnut Happiness beans and Pecan Delight beans. If there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans, then how many pounds of each will she use?

If represents the number of pounds of Pecan Delight coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?

Possible Answers:

x + (x - 60) = 14

x + (14-x) = 60

x + (x - 14) = 60

x + (x + 60) = 14

x + (x + 14) = 60

Correct answer:

x + (x - 14) = 60

Explanation:

Since there are fourteen fewer pounds of Hazelnut Happiness beans in the mixture than Pecan Delight beans , then the number of pounds of Hazelnut Happiness beans is fourteen subtracted from :

x -14 .

Add the number of pounds of Pecan Delight beans, , to the number of pounds of Hazelnut Happiness beans, x -14 , to get the number of pounds of the mixture, which is .

This translates to the following equation:

x + (x - 14) = 60

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Example Question #893 : Grade 6

Read the following scenario:

A barista has to make forty pounds of a special blend of coffee at Moonbucks, using Vanilla Dream beans and Strawberry Heaven beans. If there are twelve more pounds of Vanilla Dream beans in the mixture than Strawberry Heaven beans, then how many pounds of each will she use?

If represents the number of pounds of Strawberry Heaven coffee beans in the mixture, then which of the following equations could be set up in order to find the number of pounds of each variety of bean?

Possible Answers:

x + (x - 12) = 40

x + (x + 12) = 40

x - (x + 12) = 40

x - (x + 40) = 12

x + (x + 40) = 12

Correct answer:

x + (x + 12) = 40

Explanation:

Since there are twelve more pounds of Vanilla Dream beans in the mixture than Strawberry Heaven beans, then the number of pounds of Vanilla Dream beans is twelve added to :

x + 12 .

Add the number of pounds of Strawberry Heaven beans, , to the number of pounds of Vanilla Dream beans, x + 12 , to get the number of pounds of the mixture, which is .

This translates to the following equation:

x + (x + 12) = 40

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Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Select the equation or inequality that matches the number sentence below.

is greater than minus

Possible Answers:

93>x-45

93=x-45

93>45-x

93<x-45

92<45-x

Correct answer:

93>x-45

Explanation:

Our number sentence has the phrase "greater than" which means we have an inequality.

" is greater than" can be written as 93> because we replace the words "greater than" with the greater than symbol.

Next, we have " minus ". This can be written as x-45 because minus means subtraction, so we replace the word "minus" with the subtraction symbol.

When we put these pieces together we have 93>x-45

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Example Question #4 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Select the equation or inequality that matches the number sentence below.

is greater than minus

Possible Answers:

14>x-19

14=19-x

14<x-19

14<19-x

14=x-19

Correct answer:

14>x-19

Explanation:

Our number sentence has the phrase "greater than" which means we have an inequality.

" is greater than" can be written as 14> because we replace the words "greater than" with the greater than symbol.

Next, we have " minus ". This can be written as x-19 because minus means subtraction, so we replace the word "minus" with the subtraction symbol.

When we put these pieces together we have 14>x-19

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Example Question #3 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Select the equation or inequality that matches the number sentence below.

is greater than minus

Possible Answers:

72=31-x

72<x-31

72>x-31

72>31-x

72<31-x

Correct answer:

72>x-31

Explanation:

Our number sentence has the phrase "greater than" which means we have an inequality.

" is greater than" can be written as 72> because we replace the words "greater than" with the greater than symbol.

Next, we have " minus ". This can be written as x-31 because minus means subtraction, so we replace the word "minus" with the subtraction symbol.

When we put these pieces together we have 72>x-31

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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 #432 : Expressions & Equations

Example Question #82 : Understand What Makes An Equation Or Inequality True And Why: Ccss.Math.Content.6.Ee.B.5

Example Question #891 : Grade 6

Example Question #414 : Problem Solving

Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Example Question #892 : Grade 6

Example Question #893 : Grade 6

Example Question #1 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Example Question #4 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

Example Question #3 : Use Variables To Represent Numbers And Write Expressions: Ccss.Math.Content.6.Ee.B.6

All Common Core: 6th Grade Math Resources

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