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Warm-Up

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.

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Warm-Up

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

  2. 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.

  3. 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.

  4. 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 means3/4 thingie per doodad.

  5. 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.

  6. 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: 25 • 90 = 60 • x; x = 37.5 miles.

  7. x x + 6 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

  8. Exploration 6.3 • Do the questions for #1.

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