Pre Algebra (Period 2 & 4)

RATIOS AND RATES: 6-1



Ratios = fractions with meaning (it's all about the labels!)
3 ways to write a ratio:


EXAMPLE: 16 girls and 14 boys at a party


16 girls to 14 boys or

16 girls: 14 boys or
16 girls/14 boys


You can simplify this just like a fraction:
8 girls to 7 boys


In fact, anything you can do with a fraction, you can do with a ratio!



Rates = ratios with 2 DIFFERENT LABELS

Miles per gallon, miles per hour

10 out of 16 girls went to my party is not a rate.
Not 2 different labels! (but it is a ratio)



Unit rates = rates with a denominator of 1
(SO MUST HAVE 2 DIFFERENT LABELS)


I drive 150 miles in 3 hours is a rate

To change it to a UNIT RATE, simply DIVIDE the numerator by the denominator
150 miles/3 hours = 50 miles per hour

NOW IT'S A UNIT RATE


People focus on MPGs these days when they buy cars!

A Honda Civic = 40 mpg while a Hummer = 8 mpg




A special unit rate called the UNIT PRICE:
I USE UNIT RATES ALL THE TIME WHEN I TRY TO DECIDE WHETHER IT'S WORTH GOING TO COSTCO INSTEAD OF PAVILIONS
Goldfish = $7.99 at Pavilions for 33.5 oz and $10.99 at Costco for 48 oz.



If you divide $/oz you get a unit rate know as UNIT PRICE
MONEY MUST BE THE NUMERATOR!!!!






IN CLASS: Chapter 6-2: Proportions
A proportion = 2 equal ratios (2 equivalent fractions)

Solve using equivalent fractions or


Cross multiplication and then a one-step equation
(see if you can simplify the fractions before multiplying)

Example: Solve the proportion for y:


4/3 = y
/21

EQUIVALENT FRACTION APPROACH:


Multiply both top and bottom by 7, y = 28



CROSS PRODUCTS APPROACH:
You'll get 3y = (21)(4)
Now divide each side by 3.

Do this before multiplying on the right side!

Why? Because a lot of the time you'll be able to simplify and keep the numbers smaller!


3y/3 = (21)(4) /3

See how the 3 cross cancels into the 21?
so y = 28


ALWAYS SIMPLIFY THE FRACTIONS FIRST!