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## Proportions

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**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?