When you're shopping, do you know how to find a good deal?

Can you figure out how long it'll take you to finish your chores?

### Math can help you solve real problems!

If you know what **ratios and rates** are, you can figure out the answers to these tricky questions and more by **calculating and comparing rates**.

## What Is A Ratio?

A ratio compares two or more **quantities**, or amounts,that are **measured with the same units.**

If you **compare a and b**,you can explain the ratio in different ways:

**a : b**—the symbol**:**means "to", as in "a to b"**a / b**—the**/**represents a**fraction**, with "a" as the numerator (the top or left side of the ratio) and "b" as the denominator (the bottom or right side of the ratio)

## Rate Versus Unit Rate

## Rate:

A **rate** is a ratio that compares **two quantities of different units of measurement**.

Use the word **per** or the symbol** /** to explain a rate.

**Ex**: $52 **per** 64 ounces, 120 miles**/**2 hours, 150 words in 5 minutes

## Unit Rate:

A **unit rate** is a ratio that compares **the first quantity to one unit of the other quantity.**

A unit rate has a **denominator of 1**.

**Ex**: $2 **per** **slice**, 5.3 ounces **per** **dollar**, 49 miles **per** **gallon**, $18**/hour**

## Calculating Unit Rate

## To calculate unit rate:

Reduce the fraction ratio so it has a 1 as the denominator

OR

Divide the first term (or part) of the ratio by the second term

### Example:

Percy mows 1/6 acre in 1/4 hour. How many** acres** can Percy mow **per hour**?

## You can also use a ratio table:

Compare acres to hours.

**Answer**: Percy can mow 2/3 acre in 1 hour.

## Scenario:

It takes Ben 15 minutes to run 1.5 miles.

#### Quiz

What is Ben's unit rate in miles/hour?

4 mph

5 mph

6 mph

7 mph

## Different Ways To Explain Unit Rate

### When comparing two measures, there's more than one way to write a unit rate.

Consider the examples below.

### How many pieces of candy can you buy for $1?

👉 4 candies** per dollar**

### How many dollars does it cost to buy 1 piece of candy?

👉 25 cents (1/4 of a dollar)** per candy**

Here, the 2** measures** considered are the **same **— the **number of pieces of candy **& the **price in dollars.**

Both involve a quantity of 1 in the denominator.

In each case, the **unit rate to be calculated is different** — **per dollar **versus **per candy**.

## How To Comparison Shop?

To compare the prices of **different sized packages**, find the **unit price**. It's the **unit rate for one item**.

## Scenario:

Store A is selling 3 boxes of cereal for $6. Each box has 13.75 ounces (oz) of cereal.

Store B is selling 3 boxes of cereal for $7. Each box has 15 oz.

### 👉 Store A has the better deal because it costs less per 1 oz of cereal.

Store A's costs 14.5 cents per oz vs. Store B's at 15.5 cents per oz.

## It's your turn now!

Should you buy apples by the bag? Or is it a better deal to get individual apples?

#### Quiz

Which is the better deal?

The bag of apples

The individual apples

Unit price for both is the same

## Take Action

### Become more confident in your purchasing decisions and more efficient with your chores!

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## This Byte has been authored by

### Chitra Krishnan

Lifelong Learner