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Ratio and Proportion

Ratio and Proportion. A ratio is a comparison of numbers. The ratio of squares to stars can be expressed in three different ways:  ★★★★ Using the word “to ” - 3 to 4 As a fraction (note that ratios should never be written as mixed numbers ) - 3/4 Using a colon - 3:4

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Ratio and Proportion

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  1. Ratio and Proportion A ratio is a comparison of numbers. The ratio of squares to stars can be expressed in three different ways: ★★★★ Using the word “to”- 3 to 4 As a fraction (note that ratios should never be written as mixed numbers) - 3/4 Using a colon - 3:4 *Note that the ratio of stars to squares would be different – it would be 4 to 3.

  2. Ratio and Proportion • A proportion is simply a statement that two ratios are equal. They’re proportionate. Remember how to get equal fractions? Multiply or divide the numerator and denominator by the same number. Proportions will always be equal fractions.

  3. Ratio and Proportion • One way to test if a set of ratios is a true proportion is to use cross products. If you multiply a true proportion across the diagonal, you will always get the same number. For example: 5 x 160 = 800 8 x 100 = 800 Because the cross products are equal, we know that this is a true proportion.

  4. Ratio and Proportion • if you’re making a drink that’s 1 cup seltzer to 2 cups juice and you want to make a bowl full, you can use 4 cups of seltzer and 8 cups of juice – your drink will taste the same because it’s using the same proportion of ingredients. You multiplied each of the ingredients (represented by the numerator and denominator) by 4.

  5. Ratio and Proportion • If you have a photograph that is 3hx5w inches and you wish to double its size, you would enlarge it to 6hx10w inches – it would still have the same proportions; it wouldn’t looked stretched or squished.

  6. Solving Proportions • To find a missing number in a proportion: • First: Set up your equal ratios • Say you have that same photo, but you want to make it into a poster 75 inches wide. The parts that have to stay proportional are the height and the width:

  7. Solving Proportions • Now you follow two steps that should look familiar. First, cross-multiply Then, divide by the remaining number 3x75 = 225 225/5 = 45 Your poster would be 45hx75w

  8. Solving Proportions • Try: • If a chain link fence costs $180 for 20 feet installed, how much would it cost to install 300 feet?

  9. Solving Proportions • If a chain link fence costs $180 for 20 feet installed, how much would it cost to install 300 feet? 180 x 300 = 54000 54000 ÷ 20 = 2700 300 feet of fencing would cost $2700

  10. Solving Proportions • The scale on a map is 1 inch equals 5 feet. What is the distance between two points on the map that are 8 1/2 inches apart on the map?

  11. Solving Proportions • The scale on a map is 1 inch equals 5 feet. What is the distance between two points on the map that are 8 1/2 inches apart on the map? 5 x 8.5 = 42.5 42.5 ÷ 1 = 42.5 In real life, the points would be 42.5 feet away from one another.

  12. Solving Proportions • A store makes a profit of $15,000 for every 300 coats that they sell. If they make a profit of $25,000, how many coats did they sell?

  13. Solving Proportions • A store makes a profit of $15,000 for every 300 coats that they sell. If they make a profit of $25,000, how many coats did they sell? 300 x 25000 = 7500000 7500000 ÷ 15000 = 500 To make a profit of $25,000, they must have sold 500 coats.

  14. Rates • Aunitrate is a special kind of proportion. Usually, the denominator in your second fraction will be 1 (this is called a unit rate). • Say your car goes 216 miles on 12 gallons. How do you figure out how many miles per gallon your car gets?

  15. Rates • Say your car goes 216 miles on 12 gallons. How do you figure out how many miles per gallon your car gets? 216x1=216 216/12 = 18 Your car gets 18mpg

  16. Rates • Say Jennifer reads can read 30 pages in an hour. How many pages does she read per minute? *Notice that the question uses two different units of measurement – make sure you convert! 30x1 = 30 30/60 = .5 She reads .5 pages per minute.

  17. Rates • Solving for unit rate shortcut: The simplest way to solve a problem that gives you a ratio and asks for the unit rate is to write the ratio and then divide the numerator by the denominator. You can skip the cross-multiplication, since a number times 1 will always stay the same. You have to make sure that the “per” thing you’re solving for is on the bottom of the fraction, though.

  18. Rates • Find the unit rate: • $50 in 5 hours, how much per hour? • $440 for 8 visits, how much per visit? • 99 feet in 9 seconds, how many feet per second? • 2500 words on 10 pages, how many words per page.

  19. Rates • $50 in 5 hours, how much per hour? • 50/5 = 10 • 8 visits for $440, how much per visit? • 440/8 = 55 • 99 feet in 9 seconds, how many feet per second? • 99/9 = 11 • 2500 words on 10 pages, how many words per page. • 2500/10 = 250

  20. Ratios and Proportions • You should now be able to do the problems on pages 134-138 in the book. • Do pages 22 – 23 in the GED Practice packet and submit your answers using the Ratios and Proportions answer sheet.

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