Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #25 : Percents

Convert  to a decimal.

Possible Answers:

Correct answer:

Explanation:

In order to convert any percent to a decimal, simply remove the percentage sign and move the decimal place back two spaces.

This can also be shown in fraction form.

Remove the percent sign and divide 1015 by 100, since a percent is a part out of 100.  Add a decimal at the end of the ones digits.

If we choose to move the decimal of the denominator two times to the left, we must also move the decimal place two times for the numerator.

The fraction becomes:

The decimal representation of  is .

Example Question #21 : Percents

Convert  to a percent.

Possible Answers:

Correct answer:

Explanation:

Set up a proportion such that some number out of 100 parts is equal to one-eighth.

Multiply by 100 on both sides and reduce the fraction.

Divide 25 by 2 and add a percent sign.

The answer is:  

Example Question #27 : Percents

In a high school basketball game, the combined final score of both teams was  points. If the winning team scored  of those points, how many points did the losing team score?

Possible Answers:

Correct answer:

Explanation:

First, use the percentage information given to solve for the total points scored by the winning team. Convert the percentage into a decimal by dividing by one-hundred:

Multiply this by the combined final score from the game:

   The winning team scored  points.

Subtract this from the combined final score to find the losing teams final score:

The losing team scored  points. 

Example Question #1111 : Algebra 1

What is  of  ?

Possible Answers:

Correct answer:

Explanation:

Remember, percentages are always out of one-hundred even if they exceed one-hundred. Using this rule, we can set up an algebraic equation representing what we need to find:

      Cross multiply to remove the fractions

     Divide both sides by one-hundred to isolate the variable

Example Question #22 : Percents

A new TV costs  in November, but for the Christmas season in December the price drops to . What is the percent change in the price of the TV from November to December?

Possible Answers:

 decrease

 decrease

 decrease

 decrease

 decrease

Correct answer:

 decrease

Explanation:

The formula for solving percent change problems is as follows:

First, find the difference between the original and the new values.

Second, divide the difference between the values by the original value.

Finally, multiply the found value by one-hundred to convert it into a percent.

  

Since the price went down, we know the percent change was an  decrease in price. 

Example Question #22 : Percents

What is  as a ?

Possible Answers:

Correct answer:

Explanation:

A percent is a number out of , or 

Suppose if we have , we will have:

The percentage, , is equivalent to one.

If the number is , this means that we would have .

The answer is .

Example Question #31 : Percents

Convert  to a percent.

Possible Answers:

Correct answer:

Explanation:

A percent is a number out of 100 parts.  Suppose we have 100 percent.  This number would be out of 100 parts.

This would indicate that we will need to move the decimal place two positions to the right, and then add a percent sign to the end.

Therefore:   

The answer is:  

Example Question #1111 : Algebra 1

Determine the decimal value of .

Possible Answers:

Correct answer:

Explanation:

In order to determine the decimal of a percent, simply remove the percent sign and move the decimal place back two spaces.  

This method is similar to dividing this number by 100.

The answer is:  

Example Question #1112 : Algebra 1

Convert  to a decimal.

Possible Answers:

Correct answer:

Explanation:

A percent is a number over 100 parts.

Remove the percentage sign and divide the number by 100.

When dividing a number by 100, we can shift the decimal place back two spaces.

The answer is:  

Example Question #1113 : Linear Equations

Which of the following percents is closest to ?

Possible Answers:

Correct answer:

Explanation:

In order to determine which percentages are closest to the integer given, we should convert this integer to a percentage.  

A percent is a number out of 100 parts.

Some number out of 100 parts is equal to 50.

Set up this equation.

Multiply by 100 on both sides.

Simplify both sides.

We are looking at a number closest to five thousand percent.

The answer is:  

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