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Chapter 5 Ratios, Rates, Proportions

Chapter 5 Ratios, Rates, Proportions. Ratios. A ratio is a comparison of two quantities by division There are three ways to write a ratio: Using the word “ to ” 5 to 24 Using a colon “ : ” 5 : 24 Using a fraction 5 24 Two ratios that name the same number are equal ratios.

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Chapter 5 Ratios, Rates, Proportions

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  1. Chapter 5 Ratios, Rates, Proportions

  2. Ratios • A ratio is a comparison of two quantities by division • There are three ways to write a ratio: Using the word “to” 5 to 24 Using a colon “:” 5 : 24 Using a fraction 5 24 • Two ratios that name the same number are equal ratios

  3. Warm-Up • Write each fraction in simplest form. • 1. 3/9 2. 15/25 3. 45/54 • 4. 14/26 5. 26/42 6. 34/204

  4. Ratios cont’d • Ex. Two students report the ratio of the number of girls in a class to the total number of students. One student says the ratio is 18/30. The other says the ratio is 9/15. The two ratios are equal. • Ex. Find two ratios equal to 12 15 12 x 2 = 2412 ÷ 3 = 4 15 x 2 30 15 ÷ 3 5

  5. Ratios cont’d • To write a ratio as a decimal, divide Ex. 5 to 12, 5 : 12, 5 12 = 0.416… • To write a ratio in simplest form, divide the numerator and the denominator by the GCF Ex. 12 ÷ 3 = 4 15 ÷ 3 5

  6. Unit Rates • A unit rate is the rate for one given quantity • *unit price is the same as unit rate(just deals with money) • Ex. Determine the unit rate if a car travels 120 miles in 2 hours. ***Hint***-you want to know how many miles the car travels in “1” hour • *** the unit rate is 60 miles/1 hour or 60 miles/hour

  7. Example(s) of Unit Rates/Prices • 1.) 40miles/gal 4.) $1.59/lb • 2.) 5yds/min 5.) $24.99/dozen • 3.0 65 miles/hour 6.) $3.19/gal

  8. Proportions • A proportion is an equation stating that two ratios are equal • For two ratios, the cross products are found by multiplying the denominator of each ratio by the numerator of the other ratio • ***Hint***-to solve proportions “cross multiply” or “orbit” • ***after you “orbit” you have a one-step equation

  9. Scale Drawings(Models) & Maps • A scale drawing(***scale model is similar to the actual object it represents) is an enlarged or reduced drawing of an object that is similar to the actual object • A scale is the ratio that compares a length in a drawing to the corresponding length in the actual object Example: If a 30-mile road is 1 inch long on a map, you can write the scale of the map in these three ways 1 inch : 30 miles1 inch / 30 miles1 inch = 30 miles

  10. Scale Drawings(Models) & Maps • To find either the actual or drawing size(s), use the following proportion to solve. Drawing = Drawing Actual Actual

  11. Example(s): • The scale of a model building is 1 in : 40 ft. Suppose the height of the model is 3 in. What is the actual height of the building?

  12. Example(s): • The scale of a map is 1 in. : 15 mi. How many actual miles does each of the following measurements represents? • 1.) 3 ¼ 2.) 2 ½

  13. Example(s): • Suppose you want to make a map with a scale 1 in. : 4 mi. How many inches does each of the following actual distances represent? • 1.) 22 mi. 2.) 39 mi.

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