Express in simplest form:

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Presentation transcript:

Express in simplest form: Warm up: Express as a unit rate: 19 yards in 2.5 minutes 25 feet in 3.2 hours Express in simplest form: 18 cups to 45 cups 9 pounds to 16 tons 11 gallons to 11 quarts

Discuss your answers with your team: Express as a unit rate: 19 yards in 2.5 minutes = 7.6yd/min 25 feet in 3.2 hours = 7.8 ft/h Express in simplest form: 18 cups to 45 cups = 2/5 9 pounds to 16 tons= 9/32,000 (there are 2,000 lb in 1 ton) 5. 11 gallons to 11 quarts = 4/1 (1 gal = 4 quarts)

Do you know what a proportion is? Think Write Share

A proportion is….. When two ratios are equal Like equivalent fractions

So, how do we know if two ratios form a proportion? We can use the cross products. If when cross multiplying- you get the same product, then the two ratios form a proportion.

Let’s look at some examples: Do the following form a proportion? 1 3 3 and 9 Cross multiply to determine: 1 3 3 9 1 x 9 = 9 3 x 3 = 9 9 = 9 , therefore, these rations DO from a proportion.

Try the following on your dry board: ¼ and 4/16 Yes, because 16 = 16 2.1/3.5 and 3/7 No, because 14.7 = 10.5

Try on your dry board: 18/2.4 and 15/2 Yes, because 36= 36

What if we know two ratios form a proportion , but we have an unknown? How would we solve for an unknown? a = 52 25 100 Think Write Share

Find the cross products: a = 52 25 100 a (100) = 25 (52) 100a = 1300 Now we have a one-step equation, we know how to solve for the unknown: Divide each side by 100 to get “a” alone.

Solve the equation: 100a = 1300 100 100 a = 13 Check: 13/25 = 52/100 100 100 a = 13 Check: 13/25 = 52/100 1300 = 1300

Try some on your dry boards: p/6 = 24/36 P=4 w/11 = 14/22 W=7

Try on your dry boards: 4/10 = 8/a a= 20 a/2.8 = 4/1.4 a= 0.8

Showdown: You need one sheet of paper per team Dry materials per person All solve the SAME problem at the SAME time Compare, coach or praise answers Record team answer on paper.