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

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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

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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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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 $\$5.80$

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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

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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 #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

All Common Core: 7th Grade Math Resources

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