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Common Core: 7th Grade Math : Grade 7

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

7 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #17 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{3}(a+6)$

Possible Answers:

$\frac{a}{3}+3$

$\frac{a}{3}+2$

a+2

$\frac{a}{3}+18$

a+18

Correct answer:

$\frac{a}{3}+2$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

First, we will need to use the distributive property, which tells us to multiply each component inside the parenthesis by the value outside the parenthesis. In this case we will multiply by the and the by the following fraction:

$\frac{1}{3}$

For the variable ,

$\frac{1}{3}\times a=\frac{a}{3}$

For the number ,

$\frac{1}{3}\times\frac{6}{1}=\frac{6}{3}=2$

Next, we put our products together:

$\frac{a}{3}+2$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{a}{3}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

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Example Question #18 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{3}(y+21)$

Possible Answers:

y+7

$\frac{y}{3}+21$

y+14

$\frac{y}{3}+7$

$\frac{y}{3}+14$

Correct answer:

$\frac{y}{3}+7$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{3}$

For the variable ,

$\frac{1}{3}\times y=\frac{y}{3}$

For the number ,

$\frac{1}{3}\times\frac{21}{1}=\frac{21}{3}=7$

Next, we put our products together:

$\frac{y}{3}+7$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{y}{3}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #19 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{3}(m+36)$

Possible Answers:

$\frac{m}{3}+10$

$\frac{m}{3}+12$

m+10

m+18

$\frac{m}{3}+18$

Correct answer:

$\frac{m}{3}+12$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{3}$

For the variable ,

$\frac{1}{3}\times m=\frac{m}{3}$

For the number ,

$\frac{1}{3}\times\frac{36}{1}=\frac{36}{3}=12$

Next, we put our products together:

$\frac{m}{3}+12$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{m}{3}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #21 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{4}(a+24)$

Possible Answers:

$\frac{a}{4}+6$

a+8

$\frac{a}{4}+8$

a+6

$\frac{a}{4}+12$

Correct answer:

$\frac{a}{4}+6$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{4}$

For the variable ,

$\frac{1}{4}\times a=\frac{a}{4}$

For the number ,

$\frac{1}{4}\times\frac{24}{1}=\frac{24}{4}=6$

Next, we put our products together:

$\frac{a}{4}+6$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{a}{4}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #22 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{4}(x+40)$

Possible Answers:

$\frac{x}{4}+10$

$\frac{x}{4}+8$

x+10

x+12

$\frac{x}{4}+4$

Correct answer:

$\frac{x}{4}+10$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{4}$

For the variable ,

$\frac{1}{4}\times x=\frac{x}{4}$

For the number ,

$\frac{1}{4}\times\frac{40}{1}=\frac{40}{4}=10$

Next, we put our products together:

$\frac{x}{4}+10$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{x}{4}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #23 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{4}(p+100)$

Possible Answers:

$\frac{p}{4}+75$

p+25

$\frac{p}{4}+25$

p+75

$\frac{p}{4}+100$

Correct answer:

$\frac{p}{4}+25$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{4}$

For the variable ,

$\frac{1}{4}\times p=\frac{p}{4}$

For the number 100 ,

$\frac{1}{4}\times\frac{100}{1}=\frac{100}{4}=25$

Next, we put our products together:

$\frac{p}{4}+25$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{p}{4}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #24 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Which of the answer choices is equivalent to the following expression:

$\frac{1}{5}(a+5)$

Possible Answers:

$\frac{a}{5}+5$

$\frac{a}{5}$

a+5

$\frac{a}{5}+1$

$\frac{a}{5}+25$

Correct answer:

$\frac{a}{5}+1$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{5}$

For the variable ,

$\frac{1}{5}\times a=\frac{a}{5}$

For the number ,

$\frac{1}{5}\times\frac{5}{1}=\frac{5}{5}=1$

Next, we put our products together:

$\frac{a}{5}+1$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{a}{5}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #21 : Expressions & Equations

Which of the answer choices is equivalent to the following expression:

$\frac{1}{5}(n+45)$

Possible Answers:

n+7

n+9

$\frac{n}{5}+8$

$\frac{n}{5}+7$

$\frac{n}{5}+9$

Correct answer:

$\frac{n}{5}+9$

Explanation:

In order to answer this question, we need to write the given expression is standard form.

$\frac{1}{5}$

For the variable ,

$\frac{1}{5}\times n=\frac{n}{5}$

For the number ,

$\frac{1}{5}\times\frac{45}{1}=\frac{45}{5}=9$

Next, we put our products together:

$\frac{n}{5}+9$

This expression is considered to be simplified because we are not able to perform any other operations on its constituent components.

In other words, we can't add the $\frac{n}{5}$ to because the rules of operations tell us that these are unlike terms due to the presence of the variable, , in the enumerator and we cannot add unlike terms.

Report an Error

Example Question #22 : Expressions & Equations

Sarah is going to buy a new cell phone. The cell phone costs $\$175$ plus a $10\%$ sales tax. What is the total price that Sarah will pay for her new cell phone?

Possible Answers:

$\$196.25$

$\$192.50$

$\$200.00$

$\$190.50$

$\$225.50$

Correct answer:

$\$192.50$

Explanation:

We know that Sarah is going to pay $100\%$ of the $\$175$ cell phone because that is the total cost. Plus, she is going to pay $10\%$ of the $\$175$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100\%\rightarrow1.00$

$10\%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00(\$175)+0.10(\$175)=1.10(\$175)$

$\$175+\$17.50=\$192.50$

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Example Question #2 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Megan is going to buy a new TV. The TV costs $\$375$ plus a $10\%$ sales tax. What is the total price that Megan will pay for her new TV?

Possible Answers:

$\$400.20$

$\$408.25$

$\$417.50$

$\$412.50$

$\$404.75$

Correct answer:

$\$412.50$

Explanation:

We know that Megan is going to pay $100\%$ of the $\$375$ TV because that is the total cost. Plus, she is going to pay $10\%$ of the $\$375$ because that is the sales tax.

First, we need to convert our percentages into decimals in order to multiply.

$100\%\rightarrow1.00$

$10\%\rightarrow0.10$

Next, we can write a numeric expression and solve:

$1.00(\$375)+0.10(\$375)=1.10(\$375)$

$\$375+\$37.50=\$412.50$

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Common Core: 7th Grade Math : Grade 7

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #17 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #18 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #19 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #21 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #22 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #23 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #24 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Example Question #21 : Expressions & Equations

Example Question #22 : Expressions & Equations

Example Question #2 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

All Common Core: 7th Grade Math Resources

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