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Math: Ratio and Rate - Tutorial
This section will cover the fundamentals of ratio and
rate.
How Ratios Are Used
Example 1:
15 out of every 20 children in the group prefer playing outdoors. This means that out of the total group of 20 children, 15 prefer playing outdoors while 5 do not.
Ratios can be written three ways.
Example 2:
4 out of 7 dogs in the group have had obedience training. This means that out of the total group of 7 dogs, 4 have had obedience training while 3 have not.
Remember to reduce to lowest terms.
How Rates Are Used
Rates show a relationship between two quantities that are often with different units.
amount and cost
amount and time
amount and speed
Example 1:
The apples are 6 for a dollar. This means that 6 apples can be bought for one
dollar.
You could go a step further to say that 12 apples can be bought for two dollars.
Example 2:
The makers of the new fuel efficient cars say that cars can drive 40 miles per every gallon of gas.
You could go a step further to say that a car can drive 80 miles on 2 gallons of gas.
Example 3:
Using a ratio can help a smart shopper find the better value.
Let's say that you're buying lunch at your favorite restaurant. You have a taste for a turkey club sandwich, chips, and an ice tea. Even though you have enough money to buy lunch, you wouldn't mind finding a good deal. You notice that there are three options.
Option 1: A single turkey club with cheese costs $2.99.
Option 2: A double turkey club with mushrooms costs $3.99.
Option 3: A triple-decker turkey club with mushrooms and extra cheese cost $4.99.
Which is the better value for your money?
The answer is based on the ratio of:
Option 1: $2.99
single
turkey club
(divide $2.99 by 1.)
Option 2: $3.99
double
turkey club
(divide $3.99 by 2.)
Option 3: $4.99
triple-decker
turkey club
(divide $4.99 by 3.)
Option 3 turns out to be the better value, giving you more turkey club sandwich for lesser cost per turkey slice.
cost
amount
$2.99
single turkey slice = $2.99 per turkey slice
$2.00
single turkey slice = $2.00 per turkey slice
$1.66
single turkey slice = $1.66 per turkey slice
How Ratios and Rates Are Written
Ratios that are written as fractions should be reduced to lowest terms.
Example:
Ratios that are written as improper fractions are acceptable.
Example:
Ratios written as fractions should not be written as a mixed number or changed from an improper fraction to a whole number.
Example:
The words per and out of tell you to set up a ratio.
Ratios are used everyday. Ratios usually include the words out of.
