Warm-Up If 5 pencils cost $4.00, write 8 other statements that must be true.

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Presentation transcript:

Warm-Up If 5 pencils cost $4.00, write 8 other statements that must be true.

Some ratios can be written as fractions There are 6 red toys and 8 blue toys. 6:8 Whole: Total number of toys (14) 6/14 of the toys are red.

Some ratios or rates can’t be written as fractions I rode my skateboard 5 miles per hour. There are 3 teachers for every 22 students. There is no “whole”, and so a fraction does not really make sense.

Reciprocal Unit Ratios Suppose I tell you that 4 doodads can be exchanged for 3 thingies. How much is one thingie worth? 4 doodads/3 thingies means 1 1/3 doodads per thingie. How much is one doodad worth? 3 thingies/4 doodads means 3/4 thingie per doodad.

To solve a proportion… If a/b = c/d, then ad = bc. This can be shown by using equivalent fractions. Let a/b = c/d. Then the LCD is bd. Write equivalent fractions: a/b = ad/bd and c/d = cb/db = bc/bd So, if a/b = c/d, then ad/bd = bc/bd.

To set up a proportion… I was driving behind a slow truck at 25 mph for 90 minutes. How far did I travel? Set up equal rates: miles/minute 25 miles/60 minutes = x miles/90 minutes. Solve: = 60 x; x = 37.5 miles.

Strange looking problems I see that 1/4 of the balloons are blue, and there are 6 more red balloons than blue. Let x = number of blue balloons, and so x + 6 = number of red balloons. Also, the ratio of blue to red balloons is 1 : 3 Proportion: x/(x + 6) = 1/3 Alternate way to think about it. x + 6 = 3x x x + 6

Exploration 6.3 Do the questions for #1.