Proportions

Ratios

Comparison of two items/objects

Written one of 3 ways•As a fraction•With : (colon)• using word “to”

When writing a ratio

First thing you talk about is the numerator

Second thing you talk about is the denominator

THE KEY IS THE KEY TO SETTING UP ALL RATIOS!!!!!!!!!!!!!!!!!!

Read carefully,,,, first thing on top, second thing on bottom

Keep to your key!!!

Checking for Equivalent Ratios

Cross Multiply

2/3 = 5/6

2* 6 = 3 * 5

Setting up a Key/Proportion

First thing on topSecond thing on bottom

Blank ProportionFollow the KEY

Key Key Key Key Key Key Key Key Key

Every problem must have a key and a proportion…

No Key No CreditNo Proportion No Credit

No Options!!!!!!!!!!!!!!!!!!!!!!!!!!!

Steps for Solving a Proportion

1) Cross Multiply2) You want your variable to end up

on the left3) You now have a one step equation4) You know what to do from here!!!

Example

1 1 22 5 x

3 1x =5*24 X = 10

Word Problems

1) Make your Key2) Set up empty proportion3) The first sentence is OLD business it

is your first ratio4) The second sentence is NEW

business it is your second ratio

Math games are on sale at 8 for $10.00. How much would 15 math games cost.

Joel can do 20 math problems in 90 seconds. How fast can he do 32?

Albertson’s sells 3 cans of green beans for $.89. How much would 12 cans of green beans cost?

It takes 6 Oscar Mayer hotdogs to weigh .5kg. How many hotdogs does it take to weigh 2.5 kg?

Unit RateUnit Rate: Unit, Each, Per all say: How much for 1!

$11.49 for 3 packages

2,550 gallons in 20 days

175 Calories in 12 ounces

13 apples for 2 pies

$299 for 4 tires

A machinist can produce 114 parts in 6 minutes. At this rate, how many parts can the machinist produce in 15 minutes?

A recipe that makes 8 jumbo blueberry muffins calls for 1 ½ teaspoons of baking powder. How much baking powder is needed to make 3 dozen jumbo muffins?

Scale Drawings

A scale drawing is an enlarged or reduced drawing of an object that is similar to the actual object.

Similar: same shape different size.

A scale is the ratio that compares a length in a drawing to the corresponding length in the actual object.

Your KeyIs

Your Scale

Your Key is Your Scale… So your scale is actually your first ratio. (fraction)

You have a scale drawing of a boat. The length of the boat on the drawing is 3 cm. What is the actual length of the boat?

Key: 1 cm = 1.5 m

Similar Figures

Congruent: same shape and same sizeSimilar: same shape, different size

Best way to solve similar figure proportions is to let one figure be “old” news and the other be “new” news, or figures A and B

All similar figure proportions must have:

•Picture•Key•Proportion•Equation•Solution with units of measure

If they give you to much information: Ignore what you don’t need.

Pick the parts that you want to use, make sure and pick the sides that match,

Always pick the side with a variable

Percent ProportionsThree Keys

Part / Average

Part/ Total

Difference/Original

Which Key

Do you see the word Average: Key 1Does the problem talk about part: Key 2Do you see a change in price: Key 3

Setting up Percent Problems

Part PercentAverage 100

1. Decide which key to use2. Set up empty proportion3. Fill in the 1004. If you have % put it on top right if not

use variable5. Fill in other numbers6. Fill in the missing numbers with a

variable7. Go on from there, you know what to

do!!!

Difference/Original

When there is a change in the amount you use Difference/Original.

Sometimes you do the math before……..

Sometimes after.

BeforeLast year a ticket to a movie cost $8.00. This year, the price increased to $10.00 By what percent did the price increase?

WHAT’S THE DIFFERENCE

After

A grocery store special gave a 20% discount on meat. If the original price was $4.50 a pound, what is the discount price?

Find the DIFFERENCE, then SUBTRACT or ADD

Practice

1. At Brewer Middle School, 75 boys and 55 girls belong to the school band. Of the 75 boys, 15 play drums. Only 5 girls play the drums. What percent of the boys play the drums?

2. A grocery store special offered customers a 10% discount on hamburger meat. If the original price of the meat was $2.50 pound, what was the discount price?

3. Last year, a ticket to a movie cost $7.50. This year the price increased to $9.00 By what percent did the price increase?

4. The average yearly rainfall in Wyatt County is 25 inches. This year the county only received 80% of the average amount of rain. How much rain did the country receive?