Part To Whole Ratio Definition

Part-to-Function and Part-to-Whole Ratios

Last Updated on November thirty, 2021

Ratios are a common topic for the word problems that y'all can expect to run into on the GRE. This article will talk over some of the bones backdrop of ratios and help you lot recognize and solve both part-to-function and part-to-whole ratio questions.

To starting time, permit'south discuss what a ratio is.

What is a Ratio?
What Information Tin can We Gather from a Ratio?
Solving Ratio Questions

What Is a Ratio?

In its simplest grade, a ratio compares two quantities. For example, if in that location are 5 cats and 6 dogs in a room, we can say that the ratio of the number of cats to the number of dogs is 5 to 6. Equivalently, we can say that for every v cats in the room, in that location are vi dogs.

At present suppose instead that the room contains 10 cats and 12 dogs. By dividing the cats and dogs each into two equal groups, nosotros can nevertheless say that for every 5 cats in the room, there are 6 dogs. So, the ratio of the number of cats to the number of dogs is notwithstanding 5 to half-dozen.

KEY FACT:

A ratio compares 2 quantities.

We can express ratios in 3 equivalent ways. Using the previous example, we can express the ratio of cats to dogs as any of the post-obit:

cats to dogs = 5 to 6
cats : dogs = v : half dozen
cats/dogs = 5/6

While the GRE might use whatsoever of these three notations, we will use the partial ratio when solving ratio questions in the problems that follow.

What Information Tin We Gather from a Ratio?

To successfully solve ratio questions on the GRE, nosotros need to understand the information a ratio provides. A ratio allows us to determine both of the following relationships:

How one part of a ratio relates to the other role
How one role of a ratio relates to the whole or full

Going dorsum to the cat and domestic dog example, nosotros express the function-to-part ratio of cats to dogs as 5 to six, or 5/half dozen, considering there are 5 cats for every six dogs in the room.

We tin also apply this information to determine a part-to-whole ratio. Because we have 5 cats and 6 dogs, nosotros know that the total number of animals in the room is half dozen + 5 = 11. And so, the part-to-whole ratio of cats to full is 5 to 11, or 5/11, and the function-to-whole ratio of dogs to total is 6 to 11, or half-dozen/eleven.

Cardinal FACT:

A function-to-part ratio shows how one role relates to another office, and a role-to-whole ratio shows how one part relates to the whole.

The major takeaway is that if nosotros have a ratio that compares a function to a part, we can use that information to determine the ratio that compares a role to a whole.

Let's practice with another example:

If the ratio of girls to boys in a class is four to 3, and all students in the class are either boys or girls, then what is the role-to-part ratio of girls to boys, and what is the office-to-whole ratio of girls to the total number of students in the class?

The part-to-part ratio of girls to boys is Girls/Boys = iv/3.

The total number of students in the form is iv + three = seven. Thus, the part-to-whole ratio of girls to the full number of students is Girls/Total = 4/vii.

So, in full general, if we have a function-to-role ratio of A to B, nosotros can say that the corresponding part-to-whole ratios are equally follows:

A/(A + B)
B/(A + B)

Now, permit's discuss solving ratio questions.

Solving Ratio Questions

In our cat-and-dog example, we calculated that the ratio of cats to dogs was v to 6 when in that location were 11 animals in the room. However, what if we were in a new room with 18 dogs, and nosotros were told that the ratio of cats to dogs was still five to 6? Could we determine the number of cats in the new room?

The answer is yep. Since the trouble gives us a new number of dogs, nosotros need only to extend the cats/dogs = 5/half dozen ratio to the new situation by letting the new number of cats exist C and proverb the following:

cats/dogs = 5/6 = C/18

We tin can cross-multiply in this equation, and solve for C:

(5)(18) = (6)(C)

90 = 6C

fifteen = C

In this role-to-part ratio question, we were given the part-to-part ratio of cats to dogs and a new number of dogs, and nosotros were able to utilise that information to determine the new number of cats.

All the same, what if instead of existence given a new number of dogs, we were given a new total number of animals? Suppose in a new room, the ratio of cats to dogs is still v/6, while the full number of animals is 33. Can we all the same summate the number of cats?

To do this calculation, we must re-express our office-to-part ratio of v/6 as the part-to-whole ratio of cats/total = 5/xi, which we volition use to solve the trouble by letting C over again equal the new number of cats.

cats/total = 5/xi = C/33

(5)(33) = (xi)(C)

165 = 11C

15 = C

Thus, in that location are fifteen cats in this new room.

Now, let's look at some more examples of ratio issues.

Example 1

In a particular refrigerator, the ratio of bottles of soda to bottles of water is 2 to iii. If there are 24 bottles of water in the refrigerator, how many bottles of soda are there?

Solution:

Nosotros are given a part-to-part ratio of bottles of soda to bottles of h2o, and we are given the number of bottles of h2o. Thus, we can solve this trouble with only part-to-part information, letting S = the number of bottles of soda in the refrigerator and setting up the post-obit ratio:

soda/water = 2/3

Since there are 24 bottles of water, we accept:

South/24 = 2/three

Nosotros can cantankerous-multiply to obtain:

(S)(3) = (ii)(24)

3S = 48

South = xvi

Thus, at that place are 16 bottles of soda.

Let'south try i more.

Example 2

If the ratio of boys to girls in a sure class is four to 3, and if there are 35 total students in the class, all of whom are either girls or boys, how many boys are in the grade?

Solution:

In the problem stem, we should detect that we are given the part-to-office ratio of boys to girls, but we are provided with the total number of students in the class. Thus, we need to catechumen the part-to-office ratio to a part-to-whole ratio, and and then nosotros will be able to determine the number of boys in the class.

Boys/Total = 4/(4 + 3) = 4/7

Since in that location are 35 students in the class, nosotros can let B = the number of boys and fix up the following equation:

B/35 = 4/7

Cross–multiplying gives u.s.a. the following:

(B)(7) = (4)(35)

7B = 140

B = twenty

Thus, there are xx boys in the class.

In this commodity, nosotros have reviewed just a small portion of the topic of ratios and how they tin can exist tested on the GRE. If you would like to learn more than about GRE Ratio questions, you lot tin can check out the top-rated Target Test Prep GRE Prep Course.

About The Author

Jeff Miller

Jeffrey Miller is the caput GRE instructor for Target Exam Prep. Jeff has more than fourteen years of feel in the business organization of helping students with low GRE scores hurdle the seemingly impossible and reach the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GRE educational activity, and will exist a pivotal resource for many more to follow.