Mark B. answered • 11/21/17

Tutor

New to Wyzant
PhD Candidate and Algebra I Tutor with 20 Years of Experience

Hello,

If I understand your question there are two parts to it:

First, what is a unit rate, correct?

A unit rate is much like a ratio, with a numerator and denominator describing two things. Let me illustrate, okay?

Let's say you have the following problem:

It takes Suzie 3 minutes to walk 189 meters. How many meters per minute does she walk?

In this problem you place the 3 over the 189 and express as a fraction.

Next, since it is a ratio, you can flip that fraction to 189 over 3

Therefore, we have the following:

189/3

Now, if you look at the fraction above, you see you can easily divide 3 into 189 precisely 63 times, right? Because that is what you are doing with a fraction. You are dividing the denominator into the numerator.

Now, when you divide that denominator into the numerator as I have shown you are left with this:

63/1 In other words, we have simplified the fraction, correct? That fraction is turned into 63, because any number over a one is what? That number.

So, we now know Suzie walks 63 meters per minute.

Now, let's say your teacher asks for your answer in yards versus meters, okay? This is obviously a possibility, isn't it?

So, what do we know in order to solve this part of the possible problem?

We know for example, one meter equals 1.09 meters.

So, let's express that as a fraction.

1/1.09 and we know that Suzie walked 63 meters correct? What we do not know is how many yards she walked.

Look again at our fraction: The 1 is for meter and the 1.09 is for yards. This is setting up a proportion problem and it is not hard at all.

meters/yards = meters/yards. Note: To do the proportion you want the same units of measure on numerators and denominators.

Now we plug in what we know:

1 (meter)/1.09 (yard) = 63 (meters)/ x (yards)

Therefore:

1/1.09 = 63/x and now since we have the same units of measure on numerators and denominators and an equal sign in between, we can cross-multiply.

Cross multiplying means we take the numerator from the left fraction or ratio and multiply it by the denominator of the right. And, when we do that we come out with

1x or simply x

Then we cross multiply the denominator from the left fraction with the numerator of the right. So,

x = 63 (1.09)

Now multiply the 63 and 1.09 to arrive at the yards Suzie travels per minute.

When we do this we arrive at 68.67 yards per minute.

Now, if you can be a bit more specific as to what kind of percentage problem you need assistance with, I will be glad to assist.

Please let me know through a follow up response either here, or in my inbox as to whether this made sense and helped you.

Have a Happy Thanksgiving.