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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

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

Example Questions

Example Question #4 : 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:

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

$a \bigstar (-1) = 1$ . What is the value of ?

Possible Answers:

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

a= 2

a= -2

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

Correct answer:

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

Explanation:

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

and

$a \bigstar (-1) = 1$

$\frac{a+(-1)}{a(-1)}=1$

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

$\frac{a-1}{-a} \cdot (-a) = 1 \cdot (-a)$

a- 1 = -a

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

2a= 1

$2a \div 2 = 1 \div 2$

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

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Example Question #5 : 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:

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

$a \bigstar 1= -1$ . What is the value of ?

Possible Answers:

a = -0.5

a = -2

No real value of makes this true.

a = -1

Correct answer:

a = -0.5

Explanation:

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

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

Set this equal to :

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

$\frac{a }{a+1} \cdot (a+1) = -1 \cdot (a+1)$

a = -a - 1

a + a = -a - 1 + a

2a = - 1

$2a \div 2= - 1 \div 2$

a = -0.5

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Example Question #6 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

If a server at a restaurant gets a $20\%$ tip on a bill of $\$29$ , then what will be the amount of the tip?

Possible Answers:

$\$5.40$

$\$5.80$

$\$5.60$

$\$5.20$

$\$5.00$

Correct answer:

$\$5.80$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $20\%$ of $\$29$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20\%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}29\\ \times\ .20\end{array}}{ \ \ \space 5.80}$

The server's tip will be $\$5.80$

Report an Error

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

If a server at a restaurant gets a $20\%$ tip on a bill of $\$17$ , then what will be the amount of the tip?

Possible Answers:

$\$3.20$

$\$3.80$

$\$3.60$

$\$4.00$

$\$3.40$

Correct answer:

$\$3.40$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $20\%$ of $\$17$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20\%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}17\\ \times\ .20\end{array}}{ \ \ \space 3.40}$

The server's tip will be $\$3.40$

Report an Error

Example Question #8 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

If a server at a restaurant gets a $20\%$ tip on a bill of $\$33$ , then what will be the amount of the tip?

Possible Answers:

$\$6.80$

$\$6.60$

$\$7.00$

$\$6.40$

$\$6.20$

Correct answer:

$\$6.60$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $20\%$ of $\$33$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20\%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}33\\ \times\ .20\end{array}}{ \ \ \space 6.60}$

The server's tip will be $\$6.60$

Report an Error

Example Question #4 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

If a server at a restaurant gets a $20\%$ tip on a bill of $\$35$ , then what will be the amount of the tip?

Possible Answers:

$\$7.80$

$\$7.00$

$\$7.20$

$\$7.60$

$\$7.40$

Correct answer:

$\$7.00$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $20\%$ of $\$35$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20\%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}35\\ \times\ .20\end{array}}{ \ \ \space 7.00}$

The server's tip will be $\$7.00$

Report an Error

Example Question #5 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

If a server at a restaurant gets a $20\%$ tip on a bill of $\$46$ , then what will be the amount of the tip?

Possible Answers:

$\$9.00$

$\$8.40$

$\$8.60$

$\$8.80$

$\$9.20$

Correct answer:

$\$9.20$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $20\%$ of $\$46$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$20\%\rightarrow0.20$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}46\\ \times\ .20\end{array}}{ \ \ \space 9.20}$

The server's tip will be $\$9.20$

Report an Error

Example Question #41 : Expressions & Equations

If a server at a restaurant gets a $15\%$ tip on a bill of $\$25$ , then what will be the amount of the tip?

Possible Answers:

$\$3.00$

$\$3.50$

$\$3.75$

$\$3.25$

$\$3.55$

Correct answer:

$\$3.75$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $15\%$ of $\$25$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$15\%\rightarrow0.15$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}25\\ \times\ .15\end{array}}{ \ \ \space 3.75}$

The server's tip will be $\$3.75$

Report an Error

Example Question #42 : Expressions & Equations

If a server at a restaurant gets a $15\%$ tip on a bill of $\$38$ , then what will be the amount of the tip?

Possible Answers:

$\$5.60$

$\$5.90$

$\$5.70$

$\$5.50$

$\$5.80$

Correct answer:

$\$5.70$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $15\%$ of $\$38$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$15\%\rightarrow0.15$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}38\\ \times\ .15\end{array}}{ \ \ \space 5.70}$

The server's tip will be $\$5.70$

Report an Error

Example Question #43 : Expressions & Equations

If a server at a restaurant gets a $15\%$ tip on a bill of $\$50$ , then what will be the amount of the tip?

Possible Answers:

$\$7.50$

$\$7.60$

$\$7.70$

$\$7.90$

$\$7.80$

Correct answer:

$\$7.50$

Explanation:

The first step to solving this problem is determining what operation we are going to use.

Think:we know that the tip is going to be $15\%$ of $\$50$ . The keyword "of" gives us a clue and indicates that we are going to multiply.

As we have learned in previous lessons, we need to convert our percentage into a decimal before we are able to multiply:

$15\%\rightarrow0.15$

Next, we can perform the multiplication operation and find the tip:

$\frac{\begin{array}[b]{r}50\\ \times\ .15\end{array}}{ \ \ \space 7.50}$

The server's tip will be $\$7.50$

Report an Error

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All Common Core: 7th Grade Math Resources

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

Example Question #5 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #6 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

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

Example Question #8 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #4 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #5 : Solve Multi Step Problems With Positive And Negative Rational Numbers: Ccss.Math.Content.7.Ee.B.3

Example Question #41 : Expressions & Equations

Example Question #42 : Expressions & Equations

Example Question #43 : Expressions & Equations

All Common Core: 7th Grade Math Resources

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