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 top Second thing on bottom Blank Proportion Follow the KEY
Key KeyKeyKeyKeyKeyKeyKeyKey Every problem must have a key and a proportion… No Key No Credit No Proportion No Credit No Options!!!!!!!!!!!!!!!!!!!!!!!!!!!
Steps for Solving a Proportion Cross Multiply You want your variable to end up on the left You now have a one step equation You know what to do from here!!!
Example • 1 2 • 5 x • 1x =5*2 • X = 10
Word Problems Make your Key Set up empty proportion The first sentence is OLD business it is your first ratio 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 Rate Unit 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 Key Is 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 size • Similar: 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 Proportions Three Keys Part / Average Part/ Total Difference/Original
Which Key Do you see the word Average: Key 1 Does the problem talk about part: Key 2 Do you see a change in price: Key 3
Setting up Percent Problems Part Percent Average 100 Decide which key to use Set up empty proportion Fill in the 100 If you have % put it on top right if not use variable Fill in other numbers Fill in the missing numbers with a variable 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.
Before Last 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 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? 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? 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? 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?