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What is a ratio?

What is a ratio?. What is the difference between a ratio and a fraction?. What is a proportion?. Additive vs Multiplicative relationships. What is the meaning of?. “proportional to”. Proportions. A comparison of equal fractions A comparison of equal rates A comparison of equal ratios.

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What is a ratio?

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  1. What is a ratio?

  2. What is the difference between a ratio and a fraction?

  3. What is a proportion?

  4. Additive vs Multiplicative relationships

  5. What is the meaning of? “proportional to”

  6. Proportions • A comparison of equal fractions • A comparison of equal rates • A comparison of equal ratios

  7. Ratios and Rates • If a : b = c : d, then a/b = c/d. • If a/b = c/d, then a : b = c : d. • Example: • 35 boys : 50 girls = 7 boys : 10 girls • 5 miles per gallon = 15 miles using 3 gallons

  8. To determine proportional situations… • Start easy: • I can buy 3 candy bars for $2.00. • So, at this rate, 6 candy bars should cost… • 9 candy bars should cost… • 30 candy bars should cost… • 1 candy bar should cost… this is called a unit rate.

  9. To determine proportional situations • Here’s another. • 7 small drinks cost as much as 5 large drinks. At this rate… • How much should 14 small drinks cost? • How much should 21 small drinks cost? • How much should 15 large drinks cost?

  10. Ratios are not the same as fractions • The ratio of males to females is 3 : 2. • That means 3/5 of the people are male, and 2/5 of the people are female. • The mixture is 3 parts water and 1 part green dye. • That means that 3/4 of the mixture is water and 1/4 of the mixture is green dye.

  11. We can add fractions, but not ratios • On the first test, I scored 85 out of 100 points. • On the second test, I scored 90 out of 100 points. • Do I add 85/100 + 90/100 as • 175/200 or 175/100?

  12. Exploration 6.3 • Do the questions in part 1.

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

  14. 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.

  15. 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.

  16. 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.

  17. 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. 2x + 6 = 4x

  18. Let’s look again at proportions • Explain how you know which of the following rates are proportional? • 6/10 mph • 1/0.6 mph • 2.1/3.5 mph • 31.5/52.5 mph • 240/400 mph • 18.42/30.7 mph • 60/100 mph

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