# Unit Rate Calculator

Welcome to Omni's **unit rate calculator**, where we'll explain **how to find the unit rate for a given fraction**. "*But what is a unit rate?*" Don't you worry, we'll get to the unit rate definition soon enough. For now, let's just say that it's connected to the ratio of two numbers, although **ratios and rates are something slightly different**. Still, we'll explain in detail how to find the unit rate and give a few numerical unit rate examples.

Ready? Fasten your seatbelt, and **let's get going**!

## Ratios and rates. Unit rate definition

You know how, when you get a good grade, your parents say, "*But your friend Jack got a better one. Why didn't you?*" And when you get an average grade, but it's **one of the best ones in class**, you hear, "*You shouldn't look at other kids!*" Funny how people can choose to compare two values only **when it suits their purposes**.

Mathematically speaking, this comparison is called **the ratio**. We often present it as a fraction, although not always. For instance, say that **you got** `75%`

**on the test**, and the class average was `62%`

. Then the ratio `75 / 62`

describes your score in terms of the mean. If it's larger than `1`

(i.e., the first number is larger than the second), then **you're above the average**. If not, then perhaps it's best to spend some more time studying?

**The rate**, on the other hand, tells you **how much of the first number corresponds to how much of the second**. This vague definition is better explained with an example.

Say that you have a dog and **you give him treats every now and then**. If, in a week, it eats twenty-one treats, then the corresponding rate is `21`

treats per `7`

days. Note how colloquially, we'd react to that with something like, "*At this rate, I'll have to buy more in a couple of days.*" The word "*rate*" **is no coincidence** here.

## What is a unit rate?

**So what is a unit rate?** It is the same thing but with the second number equal to `1`

. Or, if you prefer a more scientific unit rate definition, it is a way to **translate the rate as we have it into the equivalent fraction with the denominator** `1`

. After all, it might be useful to know that the `21`

dog treats per week translate to **three treats a day**.

As we've seen, ratios and rates are connected, but **it's quite impossible to say that one is better than the other**. They're just different. To convince yourself of that, recall how a map scale is always given in form `1 : 30,000,000`

, which is a ratio, while we measure the density of objects in ounces (or grams) per cubic inch (or centimeter), which is a rate. **The latter is a unit rate example**, and, in fact, most of physics is.

Now that we have the unit rate definition out in the open, it's time to see **how to find this unit rate**. The doggy example above should have got the idea through to you, but, nevertheless, why don't we commit a whole section to describe it in detail?

## How to find the unit rate?

Suppose that you have two numbers, `a`

and `b`

. Then their rate is `a / b`

, but **what is the unit rate**?

From the unit rate definition, we know that it is the equivalent fraction with denominator `1`

. In other words, **we want to find the** `c`

**which satisfies the equation**

`a / b = c / 1`

,

which is simply

`a / b = c`

.

This already suggests what we must do: we divide `a`

by `b`

, and **the result is our answer**. Simple as that. **A piece of cake, wouldn't you say?**

A piece of cake it might be, but let's still see **how to find the unit rate when we actually have numbers instead of symbols**. The theory is fine and all, but if it's unit rate examples that you're looking for, then the next section is the one for you!

## Unit rate examples: using the unit rate calculator

You're finally able to make your dream come true - **you're going on a road trip**! The plan is to get there by plane, and, once you've landed, find a car to rent and **visit a few places in one week**.

All in all, **you want to visit four cities**, call them `A`

, `B`

, `C`

, and `D`

, so **you have three trips to make** between them: `A -> B`

, `B -> C`

, and `C -> D`

. From what you found on the net, the distances are `80 mi`

, `140 mi`

, and `110 mi`

respectively. Also, your GPS tells you that the drives should respectively take `1.5 hr`

, `3 hrs`

, and `2.5 hrs`

. Well, it's quite a lot of driving, but even the gas costs **can't spoil your enthusiasm**!

But what speed will you travel at? It's one thing to know how far and how long it will take, but it might also be useful to know **what kind of road you can expect**.

For the first trip, **the rate at which you'll be driving** is simply the fraction `80 mi / 1.5 hr`

. However, to get the actual velocity, we should divide the two numbers and **find** (surprise, surprise) **the unit rate**.

Take a look at the unit rate calculator and the formula at the top. Accordingly, in order to find the unit rate, **we need to input the values of** `a`

**and** `b`

. In our case, this means that for the `A -> B`

trip, we have to input

`a = 80`

, `b = 1.5`

.

Similarly, for the other two trips, we input

`a = 140`

, `b = 3`

,

and

`a = 110`

, `b = 2.5`

.

From the previous section, we know quite well how to find the unit rate: **we divide the two numbers**. So why don't we grab a piece of paper, and **check if we agree with the unit rate calculator**?

Denote the consecutive velocities by `v₁`

, `v₂`

, and `v₃`

. Then, we have

`v₁ = 80 mi / 1.5 hr ≈ 53.33 mph`

,

`v₂ = 140 mi / 3 hr ≈ 46.67 mph`

,

`v₃ = 110 mi / 2.5 hr ≈ 44 mph`

.

Well, it looks like **the road is going to get tougher and tougher**. Perhaps the terrain becomes more hilly?

Still, **it's going to be worth it**! You have your beach body ready, so, without further ado... sandy beaches, **here we come**!