Math 7 (Period 4)

Ratios & Rates 7.1

Ratios = fractions with meaning (it is ALL about the labels!)
A ratio is a comparison of a number a and a nonzero number b using division. The ratio a to b can be written in three ways—and you read them all the same!

You can write it as a  (1) fraction    a/b  (2)    a:b  or (3) “a to b”
and all three (including your fraction) are read “a to b” 

Anything you can do with a fraction – you can do with a ratio… but a ratio needs two numbers!

Rates = ratios with 2 different labels
miles per gallon and miles per hour are the two most known rates.

A rate of “a per b” is a type of ratio that compares two different quantities, a and b that have different units of measure.

Unit Rates = rates with a denominator of 1 (it still needs to have different labels)
I drive 150 miles in 3 hours  that’s a rate  changing it to a unit rate, simply divide the numerator by the denominator
150 miles/3 hours = 50 mph    now that that’s a unit rate

People focus on MPG these days when they buy cars.
A Honda civic =40mpg while a Hummer = 8mpg

A special unit rate is called the unit price

We talked about how people decide whether to go to CostCo or Pavilions to purchase items, such as “goldfish”

$7.99 at Pavilions for 33.5oz and
$10.99 at CostCo for 48oz

If you divide $/oz you get a unit rate known as the UNIT PRICE

MONEY must be in the numerator