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Today’s subject is … Ratios and Percents

Mr. Whalen. Today’s subject is … Ratios and Percents. Key Vocabulary for this lesson. Ratio - a comparison of 2 quantities using division. Key Vocabulary for this lesson. Percent - is a ratio of a number to 100

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Today’s subject is … Ratios and Percents

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  1. Mr. Whalen Today’s subject is… Ratios and Percents

  2. Key Vocabulary for this lesson Ratio- a comparison of 2 quantities using division.

  3. Key Vocabulary for this lesson Percent- is a ratio of a number to 100 It means “out of 100.” For example the term “50 per cent” (or 50%) means 50 out of 100”

  4. Objectives for this lesson: • Describe any ratio using “For every _____,there are _____” • Identify, write and compare ratios and rates. • Simplify ratios • Write equivalent fractions, decimals and percents.

  5. Woodpeckers… There are many species of woodpeckers in North America. Here are two common species. Northern Flicker Red-bellied Woodpecker

  6. Quick review… The ratio of Red-bellied Woodpeckers to Northern Flickers can be written in 3 ways: Red-bellied Woodpeckers 2 to 3 2:3 Northern Flickers

  7. Quick review… The ratio of Northern Flickers to Red-bellied Woodpeckers is different: Red-bellied Woodpeckers 3 to 2 3:2 Northern Flickers

  8. Quick review… A football (soccer) team has 9 wins in 12 matches played. The team can compare the number of wins to the total number of matches played by using a ratio. 9 to 12 9:12

  9. Fractions vs. Ratios • Fractions represent “part to whole” relationship. • Ratios can often stand for a part to part relationship.

  10. Helpful website for Ratios. • http://www.mathsisfun.com/numbers/ratio.html

  11. Dr. Oz’ Green Drink 2 apples, cored 1/2 inch gingerroot (or 1 teaspoon) 1 bunch chopped parsley (approx. 1/2 cup chopped)4 ounces water (handful of ice cubes) 1 stalk celery 1 or 2 cucumbers2 cups spinach1 lime, juice of 1/2 lemon, juice of

  12. Writing Ratios Example 1 The recipe calls for the juice of 1 lime and the juice of half a lemon. To double the recipe, it would be the 2 limes and 1 lemon. The ratio stays the same. Write each ratio in all three forms. 2:1 2 to 1

  13. Ratios and Rates:“What’s the difference?” A rate is a ratio that compares two quantities measured in different units. In 21 minutes I run 3 miles, my “rate of travel” is .

  14. Rates and Unit Rates: If the measure of the second quantity is one unit, then the rate is a “unit rate.” To change a rate to a unit rate, divide both numerator and the denominator by the number in the denominator.

  15. Writing Rates and Unit Rates Find the Unit Rates and write them in both fraction and word form. “Leonard hiked 36 miles in 9 hours.” Rate in fraction form. Unit rate in fraction form. Unit rate in word form. “4 miles per hour”

  16. Writing Rates and Unit Rates A recipe for cookie icing says to mix 8 tablespoons of milk with 4 cups of sugar. Rate in fraction form. Unit rate in fraction form. Unit rate in word form. 4 tablespoons of milk per cup of sugar.

  17. To compare the actual cost of two similar items we can use “Unit price.” To compare which case is a better value, divide the actual price by the number of bottles in the package.

  18. A 24-pack costs $4.99 and a 30-pack costs $5.99. Which one is “cheaper”? By dividing, we find the 24-pack costs about $0.21 per bottle. The 30-pack costs around $0.20 per bottle. The difference is $0.02 per bottle.

  19. Writing Equivalent Ratios Equivalent ratios are ratios that name the same comparison. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by the same number. (The procedure is the same as finding equivalent fractions.)

  20. Writing Equivalent Ratios The ratio of Adelie Penguins to Emperor Penguins is: To find an equivalent ratio:

  21. Ratios and Percents A percent is a ratio of a number to 100. The symbol % is used to indicate that a number is a percent. For example, 40% is the ratio 40 to 100, or . Percents can be written as fractions or as decimals.

  22. Write Percents as Fractions Write 35% as a fraction in simplest form. 35% = = Write the percent as a fraction with a denominator of 100. Simplify.

  23. Writing Percents as Decimals Write 43% as a decimal. 43% = = 0.43 Write the percent as a fraction with a denominator of 100. Write the fraction as a decimal.

  24. Writing Decimals as Percents Write each decimal as a percent. 0.07 0.07 = = 7% Write the decimal as a fraction. Write the fraction as a percent.

  25. Writing Fractions as Percents Write each fraction as a percent. = Write an equivalent fraction with a denominator of 100. Write the fraction as a percent.

  26. -Using Division Use division to write the fraction as a decimal. Write the decimal as a percent. = 3 ÷ 8 = 0.375 = 37.5%

  27. GUIDED PRACTICE

  28. Guided Practice: There are 12 girls and 15 boys in a class. Write each ratio three different ways: • The ratio of the number of girls to the number of boys? • The number of girls to the total number of students? • The number of boys to the total number of students?

  29. Guided Practice: • Water rushes over Niagara Falls at the rate of 180 million cubic feet every 30 minutes. How much water goes over the falls in 1 minute?

  30. Guided Practice: • Kay rides her bike 4 miles in 20 minutes. Write her rate as miles per hour. • A merchant sells work gloves at $5 for a 3-pack or $15 for a 10-pack. Which is cheaper?

  31. Guided Practice: • About of the people in the United States have the last name Johnson. What percent of people in the United States have this last name?

  32. Guided Practice: • A baseball team won 85% of its games. Explain how to write 85% as a fraction in simplest form. Write the equivalent fraction.

  33. Guided Practice: • If 23 out of 50 voters students prefers Candidate A in an election, what percentage of voters prefer Candidate A? • Write the percentage of people that prefer Candidate A as a decimal.

  34. Guided Practice: Write the fractions as percents and round to the nearest tenth of a percent if necessary.. . . .

  35. GUIDED PRACTICEAnswers

  36. Guided Practice Answers: There are 12 girls and 15 boys in a class. Write each ratio three different ways: • The ratio of the number of girls to the number of boys? 12 to 15, 12:15 or • The number of girls to the total number of students? 12 to 27, 12:27 or • The number of boys to the total number of students? 15 to 27, 15:27 or

  37. Guided Practice Answers : • Water rushes over Niagara Falls at the rate of 180 million cubic feet every 30 minutes. How much water goes over the falls in 1 minute?

  38. Guided Practice Answers: • Kay rides her bike 4 miles in 20 minutes. Write her rate as miles per hour.

  39. Guided Practice Answers: • A merchant sells work gloves at $5 for a 3-pack or $15 for a 10-pack. Which is cheaper? Buying a 10-pack is a better value.

  40. Guided Practice Answers: • About of the people in the United States have the last name Johnson. What percent of people in the United States have this last name? Convert to a decimal, then to a percent.

  41. Guided Practice Answers: • A baseball team won 85% of its games. Explain how to write 85% as a fraction in simplest form. Write the equivalent fraction. First change to Then simplify:

  42. Guided Practice Answers: • If 23 out of 50 voters prefer Candidate A in an election, what percentage of voters prefers Candidate A? Write as a fraction. Find equivalent ratio with denominator of 100. Then change to a percent.

  43. Guided Practice Answers: • Write the percentage of people that prefer Candidate A as a decimal. That’s easy. Simply move the decimal point over two places to the left. (Divide by 100.) 46% 100= 0.46

  44. Guided Practice Answers: Write the fractions as percents and round to the nearest tenth of a percent if necessary.. . . .

  45. IndependentPRACTICE

  46. Independent Practice: Write each ratio in two other ways. • 3:7 • 2 to 5 • .

  47. Independent Practice: Write an equivalent ratio for each. 4- James has three pictures on his shelf. The pictures measure 4 in. long by 6 in. wide, 23mm long by 36mm wide, and 6cm long by 7cm wide. Which photos have a length-to-width ratio equivalent to 2:3?

  48. Independent Practice:Convert from a fraction to a percent. 5- 6- 7- 8- 9- 10-

  49. Independent Practice: 11- If a dog’s heart beats 25 times in 15 seconds, how many times will it beat per minute?

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