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Common Core: 7th Grade Math : Expressions & Equations

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

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #6 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Elizabeth is going to buy concert tickets. The concert tickets costs $\$200$ plus a $10\%$ sales tax. What is the total price that Elizabeth will pay for her concert tickets?

Possible Answers:

$\$220$

$\$210$

$\$225$

$\$215$

$\$230$

Correct answer:

$\$220$

Explanation:

We know that Elizabeth is going to pay $100\%$ of the $\$200$ concert because that is the total cost. Plus, she is going to pay $10\%$ of the $\$200$ 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:

$1.00(\$200)+0.10(\$200)=1.10(\$200)$

$\$200+\$20=\$220$

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

Laura is going to buy a new TV. The TV costs $\$400$ plus a $8\%$ sales tax. What is the total price that Laura will pay for her new TV?

Possible Answers:

$\$430$

$\$434$

$\$438$

$\$432$

$\$436$

Correct answer:

$\$432$

Explanation:

We know that Laura is going to pay $100\%$ of the $\$400$ TV because that is the total cost. Plus, she is going to pay $8\%$ of the $\$400$ because that is the sales tax.

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

$100\%\rightarrow1.00$

$8\%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00(\$400)+0.08(\$400)=1.08(\$400)$

$\$400+\$32=\$432$

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Example Question #8 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Kara is going to buy concert tickets. The tickets cost $\$325$ plus a $8\%$ sales tax. What is the total price that Kara will pay for her concert tickets?

Possible Answers:

$\$349$

$\$348$

$\$347$

$\$351$

$\$350$

Correct answer:

$\$351$

Explanation:

We know that Kara is going to pay $100\%$ of the $\$325$ concert tickets because that is the total cost. Plus, she is going to pay $8\%$ of the $\$325$ because that is the sales tax.

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

$100\%\rightarrow1.00$

$8\%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00(\$325)+0.08(\$325)=1.08(\$325)$

$\$325+\$26=\$351$

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Example Question #9 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Liz is going to buy a new coat. The coat costs $\$55$ plus an $8\%$ sales tax. What is the total price that Liz will pay for her new coat?

Possible Answers:

$\$59.40$

$\$60.20$

$\$52$

$\$58.60$

$\$64$

Correct answer:

$\$59.40$

Explanation:

We know that Liz is going to pay $100\%$ of the $\$55$ coat because that is the total cost. Plus, she is going to pay $8\%$ of the $\$55$ because that is the sales tax.

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

$100\%\rightarrow1.00$

$8\%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00(\$55)+0.08(\$55)=1.08(\$55)$

$\$55+\$4.40=\$59.40$

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Example Question #10 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Tamara is going to buy a new cell phone. The cell phone costs $\$170$ plus an $8\%$ sales tax. What is the total price that Tamara will pay for her new cell phone?

Possible Answers:

$\$183.60$

$\$185.20$

$\$182.20$

$\$180.60$

$\$178.40$

Correct answer:

$\$183.60$

Explanation:

We know that Tamara is going to pay $100\%$ of the $\$170$ cell phone because that is the total cost. Plus, she is going to pay $8\%$ of the $\$170$ because that is the sales tax.

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

$100\%\rightarrow1.00$

$8\%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00(\$170)+0.08(\$170)=1.08(\$170)$

$\$170+\$13.60=\$183.60$

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Example Question #31 : Expressions & Equations

Christina is going to buy a new camera. The camera costs $\$220$ plus an $8\%$ sales tax. What is the total price that Christina will pay for her new camera?

Possible Answers:

$\$239.60$

$\$237.60$

$\$245.20$

$\$230$

$\$240.20$

Correct answer:

$\$237.60$

Explanation:

We know that Christina is going to pay $100\%$ of the $\$220$ camera because that is the total cost. Plus, she is going to pay $8\%$ of the $\$220$ because that is the sales tax.

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

$100\%\rightarrow1.00$

$8\%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00(\$220)+0.08(\$220)=1.08(\$220)$

$\$220+\$17.60=\$237.60$

Report an Error

Example Question #32 : Expressions & Equations

Addison is going to buy a new computer. The computer costs $\$575$ plus an $8\%$ sales tax. What is the total price that Addison will pay for her new computer?

Possible Answers:

$\$619$

$\$621$

$\$622$

$\$620$

$\$618$

Correct answer:

$\$621$

Explanation:

We know that Addison is going to pay $100\%$ of the $\$575$ computer because that is the total cost. Plus, she is going to pay $8\%$ of the $\$575$ because that is the sales tax.

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

$100\%\rightarrow1.00$

$8\%\rightarrow0.08$

Next, we can write a numeric expression and solve:

$1.00(\$575)+0.08(\$575)=1.08(\$575)$

$\$575+\$46=\$621$

Report an Error

Example Question #1 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = a^{2}+ b$

If $6 \bigstar b = 100$ , then what is ?

Possible Answers:

$\sqrt{94}$

$\sqrt{106}$

Correct answer:

Explanation:

$a \bigstar b = a^{2}+ b$ ,

$6 \bigstar b = 6 ^{2} + b = 36 + b$ .

$6 \bigstar b = 100$

then

36 + b= 100

36+ b - 36 = 100 - 36

b = 64

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Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar \frac{1}{2} = -1$ , evaluate .

Possible Answers:

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

a = -3

a = 3

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

Correct answer:

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

Explanation:

$a \bigstar b = \frac{a+b}{ab}$

$a \bigstar \frac{1}{2} = \frac{a+ \frac{1}{2} }{a \cdot \frac{1}{2} } = \frac{\frac{2a}{2}+ \frac{1}{2} }{ \frac{a}{2} } = \frac{\frac{2a+1}{2} }{ \frac{a}{2} }$

Equivalently

$a \bigstar \frac{1}{2} = \frac{2a+1}{2} \div \frac{a}{2} = \frac{2a+1}{2} \cdot \frac{2}{a} = \frac{2a+1}{a}$

$a \bigstar \frac{1}{2} = -1$ , so set this equal to :

$\frac{2a+1}{a} = -1$

$\frac{2a+1}{a} \cdot a = -1 \cdot a$

2a+1 = -a

2a+1 + a - 1 = -a + a - 1

3a= - 1

$3a\div 3 = - 1 \div 3$

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

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Example Question #3 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Define an operation $\bigstar$ on the set of real numbers as follows:

$a \bigstar b = \frac{a+b}{ab}$ .

If $a \bigstar 0.5 = 0.1$ , then evaluate .

Possible Answers:

$a = \frac{ 19} {10}$

$a = - \frac{10}{19}$

$a = - \frac{ 19} {10}$

$a = \frac{10}{19}$

Correct answer:

$a = - \frac{10}{19}$

Explanation:

$a \bigstar b = \frac{a+b}{ab}$ ,

$a \bigstar 0.5 = \frac{a+0.5 }{a \cdot 0.5 } = \frac{a+0.5 }{0.5a }$

Set this equal to 0.1:

$\frac{a+0.5 }{0.5a } = 0.1$

$\frac{a+0.5 }{0.5a } \cdot 0.5 a = 0.1 \cdot 0.5 a$

a+0.5 = 0.05 a

$(a+0.5) \cdot 100 = 0.05 a \cdot 100$

$a \cdot 100 +0.5 \cdot 100 = 5 a$

100a +5 0= 5 a

100a +50 - 100a = 5 a - 100a

50 = -95a

$50 \div (-95) = -95a \div (-95)$

$a = -\frac{50}{95} = - \frac{10}{19}$

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Common Core: 7th Grade Math : Expressions & Equations

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

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #6 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

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

Example Question #8 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Example Question #9 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Example Question #10 : Rewrite An Expression: Ccss.Math.Content.7.Ee.A.2

Example Question #31 : Expressions & Equations

Example Question #32 : Expressions & Equations

Example Question #1 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #2 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #3 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

All Common Core: 7th Grade Math Resources

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