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

## 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  on the set of real numbers as follows:

If , then what is ?

Explanation:

,

so

.

If

then

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

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

.

If , evaluate .

Explanation:

so

Equivalently

, so set this equal to :

### Example Question #31 : Expressions & Equations

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

.

If ,  then evaluate .

Explanation:

,

so

Set this equal to 0.1:

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

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

.

. What is the value of  ?

Explanation:

and

so

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

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

. What is the value of  ?

No real value of  makes this true.

Explanation:

, so

Set this equal to :

### 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  tip on a bill of , then what will be the amount of the tip?

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  of .  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:

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

The server's tip will be

### 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  tip on a bill of , then what will be the amount of the tip?

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  of .  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:

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

The server's tip will be

### 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  tip on a bill of , then what will be the amount of the tip?

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  of .  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:

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

The server's tip will be

### Example Question #9 : 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  tip on a bill of , then what will be the amount of the tip?

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  of .  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:

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

The server's tip will be

### Example Question #10 : 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  tip on a bill of , then what will be the amount of the tip?