Algebra 1 : Proportions

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : Proportions

The  probability of an event is 3/11. Find the chance the event will not occur.

Possible Answers:

11/3

3/8

8/3

3/11

8/11

Correct answer:

8/11

Explanation:

If the chance an event will happen is 3/11, that means there are 8 instances where the even would not occur out of every 11, giving us 8/11.

3 chances out of 11 = event

11 – 3 = 8

8 chances out of 11 = no event

Example Question #2 : Proportions

Solve for :

Possible Answers:

Correct answer:

Explanation:

Cross multiply:

Solve for :

Example Question #2 : Proportions

Solve for  in the following proportion statement:

Possible Answers:

Correct answer:

Explanation:

Use cross-multiplication to set up the following equation:

 

Rewrite with improper fractions and solve:

So the correct choice is .

Example Question #4 : Proportions

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Proportions

If Max drives 10 miles in 24 minutes, how many minutes will it take for him to drive 25 miles?

Possible Answers:

Correct answer:

Explanation:

Set up a proportion, with miles driven on top and the time (in minutes) on the bottom:

Then, cross multiply:

, or

Finally, dividing both sides by 10 gives:

 minutes.

 

Example Question #4 : Proportions

A recipe for making 24 cookies calls for 6 cups of sugar. How many cups of sugar would be needed to make 16 cookies?

Possible Answers:

Correct answer:

Explanation:

To solve the equation, you can set up a proportion with as the cups of sugar needed for making cookies. In this case, we know that it takes 6 cups of sugar to make 24 cookies, so we can set up the proportion as . Since we know that we need to make 16 cookies, we can substitute 16 for , . Cross multiply the fractions to get . Now, solve for  to get a solution of 4.

Example Question #5 : Proportions

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Proportions

To make 36 cookies, a recipe calls for 5 ounces of chocolate chips. How many ounces of chocolate chips would you need to make 900 cookies?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To figure out how many ounces of chocolate chips are needed to make 900 cookies, you simply need to set up a proportion. In this case, we know that 5 ounces of chocolate chips are needed to make 36 cookies, and we are trying to make a total of 900 cookies. Therefore, you can set up the proportion as

where is the ounces of chocolate chips needed to make 900 cookies.

For this proportion, solving for would give you a result of 125 ounces of chocolate chips.

Example Question #7 : Proportions

If , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Proportions are useful for solving many types of problems, but here our equation itself is a proportion.

To solve, we cross-multiply: the numerator of one side times the denominator of the other and vice versa. We are left with

  or

 

A simple FOIL gives us 

so our solutions are  and .

Example Question #8 : Proportions

If , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

To solve this equation, we need to set up a simple proportion. Since the variables  and  are already in use, let's call the quantity that we are solving for . From the given information, we know we can use the proportion . Cross-multiplication yields . Dividing by the common term of  and simplifying the right side gives us , so our solution must be .

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