# Common Core: 6th Grade Math : Ratios & Proportional Relationships

## Example Questions

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### Example Question #1 : Grade 6

If candidate A receives  vote for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  vote cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #2 : Ratios & Proportional Relationships

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #3 : Ratios & Proportional Relationships

If candidate A receives  vote for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  vote cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #21 : How To Find A Ratio

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #2 : Grade 6

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Reduce.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #3 : Grade 6

If candidate A receives  vote for every  votes that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  vote cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #7 : Ratios & Proportional Relationships

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #4 : Grade 6

If candidate A receives  votes for every  vote that candidate B receives. At the end of the election candidate B has  votes. How many votes did candidate A get?

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  vote. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify and solve.

### Example Question #5 : Grade 6

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

### Example Question #2 : Grade 6

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every  votes cast for candidate A, candidate B got  votes. We can write the following ratio.

Now substitute in the given numbers.

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

Cross multiply and solve for .

Simplify.

Divide both sides of the equation by .

Solve.

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