Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: 7th Grade Math : Solve Multi-Step Problems with Positive and Negative Rational Numbers: CCSS.Math.Content.7.EE.B.3

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

Create An Account

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 #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

Report an Error

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

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

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

Report an Error

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

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

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

Report an Error

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

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

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

Report an Error

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

Report an Error

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 #1 : 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:

$\$6.80$

$\$6.60$

$\$6.20$

$\$7.00$

$\$6.40$

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

View Tutors

Ingy
Certified Tutor

University of Minnesota-Twin Cities, Bachelors, Mathematics with Actuarial Science Specialization.

View Tutors

Sarah
Certified Tutor

New York University, Bachelor of Fine Arts, Drama.

View Tutors

Justin
Certified Tutor

University of Toledo, Bachelors, Environmental Science. University of Michigan, Masters, Natural Resource Management.

All Common Core: 7th Grade Math Resources

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

Popular Subjects

Spanish Tutors in San Diego, Algebra Tutors in Chicago, Biology Tutors in Philadelphia, Spanish Tutors in New York City, LSAT Tutors in Houston, Math Tutors in Denver, Statistics Tutors in Miami, Calculus Tutors in Houston, Algebra Tutors in San Francisco-Bay Area, Biology Tutors in Los Angeles

Popular Courses & Classes

LSAT Courses & Classes in Miami, LSAT Courses & Classes in Boston, SAT Courses & Classes in Atlanta, GRE Courses & Classes in Chicago, ISEE Courses & Classes in Atlanta, SAT Courses & Classes in Miami, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Denver

Popular Test Prep

SSAT Test Prep in Boston, ISEE Test Prep in Atlanta, SSAT Test Prep in Denver, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Dallas Fort Worth, LSAT Test Prep in Houston, GRE Test Prep in Boston, GRE Test Prep in Miami, GRE Test Prep in Los Angeles, SAT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Common Core: 7th Grade Math : Solve Multi-Step Problems with Positive and Negative Rational Numbers: CCSS.Math.Content.7.EE.B.3

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

All Common Core: 7th Grade Math Resources

Example Questions

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

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 #1 : 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

All Common Core: 7th Grade Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: