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Common Core: 6th Grade Math : Expressions & Equations

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 #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 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) = (2x+30)

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

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

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

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 #441 : Expressions & Equations

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) + 2 (x - 10) = 360

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

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

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

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

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 #52 : Ssat Middle Level Quantitative (Math)

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 + (14-x) = 60

x + (x + 60) = 14

x + (x - 60) = 14

x + (x + 14) = 60

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 #81 : How To Do Other Word Problems

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 + 40) = 12

x + (x + 40) = 12

x + (x + 12) = 40

x - (x + 12) = 40

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 #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:

93=x-45

93>45-x

92<45-x

93<x-45

93>x-45

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 #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:

14=19-x

14=x-19

14<x-19

14>x-19

14<19-x

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

Report an Error

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 less than minus

Possible Answers:

13>21-x

13<21-x

13<x-21

13>x-21

13=x-21

Correct answer:

13<x-21

Explanation:

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

" is less than" can be written as 13< because we replace the words "less than" with the less than symbol.

Next, we have " minus ". This can be written as x-21 because minus means subtraction, so we replace the word "minus" with the subtraction symbol.

When we put these pieces together we have 13<x-21

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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 less than minus

Possible Answers:

57=19-x

57<x-19

57>19-x

57<19-x

57>x-19

Correct answer:

57<x-19

Explanation:

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

" is less than" can be written as 57< because we replace the words "less than" with the less 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 57<x-19

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Example Question #901 : Grade 6

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

is less than minus 100

Possible Answers:

66>x-100

66>100-x

66<x-100

66<100-x

66=x-100

Correct answer:

66<x-100

Explanation:

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

" is less than" can be written as 66< because we replace the words "less than" with the less than symbol.

Next, we have " minus 100 ". This can be written as x-100 because minus means subtraction, so we replace the word "minus" with the subtraction symbol.

When we put these pieces together we have 66<x-100

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All Common Core: 6th Grade Math Resources

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Common Core: 6th Grade Math : Expressions & Equations

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

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

Example Question #441 : Expressions & Equations

Example Question #52 : Ssat Middle Level Quantitative (Math)

Example Question #81 : How To Do Other Word Problems

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

Example Question #1 : 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

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

Example Question #901 : Grade 6

All Common Core: 6th Grade Math Resources

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