7th Grade Math with Mrs. Davidson STANDARDS: -CCSS.Math.7RP.A3 -CCSS.Math.7RP.A2.C Try and solve the POD! (Problem of the Day) Brandi walked ½ mile in ¼ of an hour. Becky walked 1/3 of a mile in ½ of an hour. Who had the faster rate? What was their rate? OBJECTIVES: -We can write proportions with matching labels. -We can solve proportions using cross multiplication. Previous Lessons: -Determine the unit rate. -Compare rates. 7th Grade Math with Mrs. Davidson Topic: Writing and Solving Real World Proportions Lesson 13

Review of Rates Rates are a comparison of two quantities with different units. EX: ½ mile ¼ hour In this example we are comparing miles to hours. We can use rates and ratios to help find an unknown amount of units. If I know Brandi’s walking rate, I can use this to determine how long it would take for her to walk 3 miles. Take a moment and think how you would solve this problem! Share your ideas in the chat.

Proportions ½ mile ¼ hour If I know Brandi’s walking rate, I can use this to determine how long it would take for her to walk 3 miles. Some of you may have used prior knowledge to form equivalent ratios or fractions, found a pattern, or used the unit rate to scale the answer up. Today we are going to solve this problem through the use of a proportion. Proportion: Equation stating that two rates are equivalent. ½ mile = 3 miles ¼ hour X hours

Proportions A proportion is an equation stating two rates are equivalent. A rate is a comparison of two quantities with different units. In order to compare rates and units, we must include our unit labels! When writing a proportion it is important to include your unit labels. EX: ½ mile = 3 miles ¼ hour 1 ½ hours To check our work and see if the two rates are equivalent: Put them in simplest form (unit rate or decimal) OR Cross multiply to see that the cross products are equivalent

Proportion Format When you are given a rate and asked to find an unknown unit with one other piece of information, set up a proportion! Draw two fraction bars and insert your matching unit labels first! Then fill in your numbers and use a variable to represent the unknown quantity. The purple boxes represent one of the matching unit labels (miles) __________________ = _____________________ The green boxes represent the other matching unit label (hours)

Example 1 If 8 ounces of medicine must be mixed with 20 ounces of water, how many ounces of this medicine must be mixed with 50 ounces of water? Lets use our proportion format to set up the problem! To solve the problem, we will cross multiply and divide.

Example 2 Nicole can assemble 12 car parts in 60 minutes.  How many minutes does she need to assemble 15 car parts?

Example 3 Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 330 miles on 20 gallons of gas. How far could you drive on 55 gallons of gas?

Example 4 A jet travels 400 miles in 5 hours. At this rate, how far could the jet fly in 14 hours?

Example 5 A Ferris wheel can accommodate 45 people in 30 minutes. How many people could ride the Ferris wheel in 2 hours? Be careful in determining your unit labels. There are people, minutes, and hours. Minuets and hours are time, so we must convert them to match!

Practice Set Solve the following 3 problems. If you have a question please ask in the chat. Once you have completed these, please privately send the answers to me in the chat. Take about 5 minutes then we will review the answers. A boat can travel 369 miles on 41 gallons of gasoline. How much gasoline will it need to go 144 miles? 40 lbs of scrap metal cost $464. How much would 4 lbs cost? In a shipment of 400 parts, 14 are found defective. How many defective parts should we expect in a shipment of 1,000 parts.

Video https://www.youtube.com/watch?v=ifoEgWtn6_o At a festival I bought 4 tickets for $40. The festival wants to raise $3,200. How many tickets do they need to sell to reach their goal?