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.

Rate = quantity 1 / quantity 2

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.

Unit rate = quantity 1 / one unit of quantity 2Ex: $2 per slice, 5.3 ounces per dollar, 49 miles per gallon, $18/hour

A scale balancing between a pizza slice and coins

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?

Call Me Shut Up GIF by goodboy noah

1/6 acre per 1/4 hour = 2/3 acre 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.

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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?

An equation. Candy is the numerator, a dollar is the denominator.👉 4 candies per dollar

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

An equation. A pile of dollars is the numerator, and a piece of candy is the denominator.👉 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 differentper 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?

4 pound bag of apples for $5.99 versus individual apples at $1.69 per pound

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

CK

Chitra Krishnan

Lifelong Learner