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Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard Copyright © by The Mc. Graw-Hill Mathematics: Applications and Concepts, Course 2 Interactive Chalkboard Copyright © by The Mc. Graw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/Mc. Graw-Hill 8787 Orion Place Columbus, Ohio 43240

Lesson 7 -1 Ratios Lesson 7 -2 Rates Lesson 7 -3 Solving Proportions Lesson Lesson 7 -1 Ratios Lesson 7 -2 Rates Lesson 7 -3 Solving Proportions Lesson 7 -4 Scale Drawings Lesson 7 -5 Fractions, Decimals, and Percents Lesson 7 -6 Percents Greater Than 100% and Percents Less than 1% Lesson 7 -7 Percent of a Number Lesson 7 -8 The Percent Proportion

Example 1 Write Ratios in Simplest Form Example 2 Write Ratios in Simplest Form Example 1 Write Ratios in Simplest Form Example 2 Write Ratios in Simplest Form Example 3 Write a Ratio by Converting Units Example 4 Compare Ratios Example 5 Compare Ratios

Write the ratio 30 to 9 as a fraction in simplest form. Write the Write the ratio 30 to 9 as a fraction in simplest form. Write the ratio as a fraction. Simplify. Answer: Written as a fraction in simplest form, the ratio 30 to 9 is

Write the ratio 35 to 20 as a fraction in simplest form. Answer: Write the ratio 35 to 20 as a fraction in simplest form. Answer:

Write the ratio 4: 24 as a fraction in simplest form. Write the ratio Write the ratio 4: 24 as a fraction in simplest form. Write the ratio as a fraction. Simplify. Answer: The ratio 4: 24 is in simplest form.

Write the ratio 9: 36 as a fraction in simplest form. Answer: Write the ratio 9: 36 as a fraction in simplest form. Answer:

Write the ratio 3 feet to 8 inches as a fraction in simplest form. Write the ratio 3 feet to 8 inches as a fraction in simplest form. Convert 3 feet to inches. 9 Divide by the GCF, 4 inches. 2 Simplify.

Answer: The ratio 3 feet to 8 inches can be written as Answer: The ratio 3 feet to 8 inches can be written as

Write the ratio 4 feet to 20 inches as a fraction in simplest form. Write the ratio 4 feet to 20 inches as a fraction in simplest form. Answer:

Determine whether 12: 15 and 32: 40 are equivalent. Write each ratio as a Determine whether 12: 15 and 32: 40 are equivalent. Write each ratio as a fraction in simplest form. The GCF of 12 and 15 is 3. The GCF of 32 and 40 is 8. Answer: The ratios in simplest form both equal So, 12: 15 and 32: 40 are equivalent ratios.

Determine whether 8: 24 and 14: 42 are equivalent. Answer: yes Determine whether 8: 24 and 14: 42 are equivalent. Answer: yes

POOLS It is recommended that no more than one person be allowed into the POOLS It is recommended that no more than one person be allowed into the shallow end of an outdoor public pool for every 15 square feet of surface area. If a local pool’s shallow end has a surface area of 1, 800 square feet, are the lifeguards correct to allow 120 people into that part of the pool? 1 to 15 or Recommended ratio 120 to 1, 800 or Actual ratio Answer: Since the ratios are equivalent, the lifeguards are correct to allow 120 people into the shallow end of the pool.

WALLPAPER The instructions on a particular brand of wallpaper suggest using 1 quart of WALLPAPER The instructions on a particular brand of wallpaper suggest using 1 quart of wallpaper paste for every 32 square feet of wallpaper hung. Bill purchases 8 quarts of wallpaper paste to complete a job that requires hanging 256 square feet of wallpaper. Is Bill using the proper amount of paste? Answer: yes

Example 1 Find a Unit Rate Example 2 Find Unit Rates Example 3 Find Example 1 Find a Unit Rate Example 2 Find Unit Rates Example 3 Find Unit Rates Example 4 Choose the Best Buy

READING Julia read 52 pages in 2 hours. What is the average number of READING Julia read 52 pages in 2 hours. What is the average number of pages she read per hour? Write the rate as a fraction. Then find an equivalent rate with a denominator of 1. Write the rate as a fraction. Divide the numerator and denominator by 2. Simplify.

Answer: The average number of pages Julia reads, or unit rate, is 26 pages Answer: The average number of pages Julia reads, or unit rate, is 26 pages per hour.

SKATING Kyle skated 16 laps around the ice rink in 4 minutes. What is SKATING Kyle skated 16 laps around the ice rink in 4 minutes. What is the average number of laps he skated per minute? Answer: 4 laps per minute

GRID-IN TEST ITEM Write 440 miles in 8 hours as a unit rate in GRID-IN TEST ITEM Write 440 miles in 8 hours as a unit rate in miles per hour. Read the Test Item Write the ratio as a fraction. Then divide to get a denominator of 1. Solve the Test Item 440 miles in 8 hours Write the rate as a fraction.

Divide the numerator and the denominator by 8. Simplify. The unit rate is 55 Divide the numerator and the denominator by 8. Simplify. The unit rate is 55 miles per hour.

Answer: Answer:

GRID-IN TEST ITEM Write 455 miles in 7 hours as a unit rate in GRID-IN TEST ITEM Write 455 miles in 7 hours as a unit rate in miles per hour. Answer:

Find the unit price per can if it costs $3 for 6 cans of Find the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest hundredth if necessary. Write the rate as a fraction. Divide the numerator and the denominator by 6. Simplify. Answer: The unit price is $0. 50 per can.

Find the unit price per cookie if it costs $3 for one dozen cookies. Find the unit price per cookie if it costs $3 for one dozen cookies. Round to the nearest hundredth if necessary. Answer: $0. 25 per cookie

The costs of different sizes of orange juice are shown in the table. Which The costs of different sizes of orange juice are shown in the table. Which container costs the least per ounce? Amount 16 oz 32 oz 64 oz Total Cost $1. 28 $1. 92 $2. 56 96 oz $3. 36

Find the unit price, or the cost per ounce, of each size of orange Find the unit price, or the cost per ounce, of each size of orange juice. Divide the price by the number of ounces. 16 -ounce container 32 -ounce container 64 -ounce container 96 -ounce container Answer: The 96 -ounce container of orange juice costs the least per ounce.

The costs of different sizes of bottles of laundry detergent are shown below. Which The costs of different sizes of bottles of laundry detergent are shown below. Which bottle costs the least per ounce? Amount 16 oz 32 oz 64 oz Total Cost $3. 12 $5. 04 $7. 04 96 oz $11. 52 Answer: 64 -ounce bottle

Example 1 Identify a Proportion Example 2 Identify a Proportion Example 3 Solve Proportions Example 1 Identify a Proportion Example 2 Identify a Proportion Example 3 Solve Proportions Example 4 Solve Proportions

Determine whether and form a proportion. Write a proportion. Find the cross products. Multiply. Determine whether and form a proportion. Write a proportion. Find the cross products. Multiply. Answer: The cross products are equal, so the ratios form a proportion.

Determine whether Answer: no and form a proportion. Determine whether Answer: no and form a proportion.

Determine whether and form a proportion. Write a proportion. Find the cross products. Multiply. Determine whether and form a proportion. Write a proportion. Find the cross products. Multiply. Answer: The cross products are not equal, so the ratios do not form a proportion.

Determine whether Answer: yes and form a proportion. Determine whether Answer: yes and form a proportion.

Solve Write the proportion. Find the cross products. Multiply. Divide each side by 3. Solve Write the proportion. Find the cross products. Multiply. Divide each side by 3. 5. Simplify. Answer: The solution is 24.

Solve Answer: 25 Solve Answer: 25

FLAGS According to specifications, the ratio of the length of the U. S. flag FLAGS According to specifications, the ratio of the length of the U. S. flag to its width must be 1. 9 to 1. How long must a U. S. flag be if it is designed to have a width of 2. 5 feet? length → width → Write a proportion. Find the cross products. Multiply. Answer: The length of a U. S. flag having a width of 2. 5 feet must be 4. 75 feet.

SCHOOL The ratio of boys to girls at Blue Hills Middle School is 4 SCHOOL The ratio of boys to girls at Blue Hills Middle School is 4 to 5. How many girls attend the school if there are 96 boys? Answer: 120 girls

Example 1 Use a Scale Drawing Example 2 Read a Scale Drawing Example 3 Example 1 Use a Scale Drawing Example 2 Read a Scale Drawing Example 3 Find the Scale Factor Example 4 Make a Scale Model

MAPS On the map below, the distance between Portland Olympia is about What is MAPS On the map below, the distance between Portland Olympia is about What is the actual distance? Let d the actual distance between the cities. Write and solve a proportion. Use the scale written as a fraction. inches.

Scale Portland to Olympia map → ← map actual → ← actual Cross products Scale Portland to Olympia map → ← map actual → ← actual Cross products Multiply both sides by Simplify.

Answer: The distance between Portland Olympia is about 125 miles. Answer: The distance between Portland Olympia is about 125 miles.

MAPS On a map, the scale is given as 2 inches 100 miles. If MAPS On a map, the scale is given as 2 inches 100 miles. If the distance on the map between two cities is 15 inches, what is the actual distance between the two cities? Answer: 750 miles

ARCHITECTURE On the blueprint of a new house, onequarter inch represents bedroom on the ARCHITECTURE On the blueprint of a new house, onequarter inch represents bedroom on the blueprint is actual length of the room? feet. If the length of a inches, what is the

Scale blueprint → actual → Length of Room ← blueprint ← actual Cross products Scale blueprint → actual → Length of Room ← blueprint ← actual Cross products Multiply. Simplify. Multiply each side by 4.

Answer: The length of the room is 15 feet. Answer: The length of the room is 15 feet.

ARCHITECTURE On a blueprint of a new house, onequarter inch represents 3 feet. If ARCHITECTURE On a blueprint of a new house, onequarter inch represents 3 feet. If the width of the kitchen on the blueprint is 2 inches, what is the actual width of the room? Answer: 24 feet

Find the scale factor of a blueprint if the scale is Write the ratio Find the scale factor of a blueprint if the scale is Write the ratio of in simplest form. Convert 3 feet to inches. Multiply by to eliminate the fraction in the numerator. Cancel the units.

Answer: The scale factor is the blueprint is That is, each measure on the Answer: The scale factor is the blueprint is That is, each measure on the actual measure.

Find the scale factor of a blueprint if the scale is 1 inch 4 Find the scale factor of a blueprint if the scale is 1 inch 4 feet. Answer:

PHOTOGRAPHY A model is being created from a picture frame which has a length PHOTOGRAPHY A model is being created from a picture frame which has a length of inches. If the scale to be used is 8 inches 1 inch, what is the length of the model? Write a proportion using the scale. Scale Length of Model model → ← model actual → ← actual

Find the cross products. Multiply. Answer: The scale model is 38 inches long. Find the cross products. Multiply. Answer: The scale model is 38 inches long.

FURNITURE A model is being created from a childsized rocking chair which has a FURNITURE A model is being created from a childsized rocking chair which has a height of 8 inches. If the scale to be used is 12 inches 1 inch, what is the height of the model? Answer: 96 in.

Example 1 Percents as Fractions Example 2 Percents as Fractions Example 3 Fractions as Example 1 Percents as Fractions Example 2 Percents as Fractions Example 3 Fractions as Percents Example 4 Fractions as Percents Example 5 Fractions as Percents Example 6 Fractions as Percents

NUTRITION In a recent consumer poll, 41. 8% of the people surveyed said they NUTRITION In a recent consumer poll, 41. 8% of the people surveyed said they gained nutrition knowledge from family and friends. What fraction is this? Write in simplest form. Write a fraction with a denominator of 100. Multiply by to eliminate the decimal in the numerator. Simplify.

Answer: So, of the people gained nutrition knowledge from family and friends. Answer: So, of the people gained nutrition knowledge from family and friends.

ELECTION In a recent election, 64. 8% of registered voters actually voted. What fraction ELECTION In a recent election, 64. 8% of registered voters actually voted. What fraction is this? Write in simplest form. Answer:

Write as a fraction in simplest form. Write a fraction. Divide. Write as an Write as a fraction in simplest form. Write a fraction. Divide. Write as an improper fraction.

Multiply by the reciprocal of 100, which is Simplify. Answer: Multiply by the reciprocal of 100, which is Simplify. Answer:

Write Answer: as a fraction in simplest form. Write Answer: as a fraction in simplest form.

PRODUCE In one shipment of fruit to a grocery store, 5 out of 8 PRODUCE In one shipment of fruit to a grocery store, 5 out of 8 bananas were still green. Find this amount as a percent. To find the percent of green bananas, write Estimate is greater than as a percent. or greater than 50%. Write a proportion using Find the cross products.

Divide each side by 8. Simplify. Answer: So, This is greater than 50%, which Divide each side by 8. Simplify. Answer: So, This is greater than 50%, which was the estimate.

HOCKEY During a hockey game, the forward on one of the teams scored 3 HOCKEY During a hockey game, the forward on one of the teams scored 3 goals out of 8 shots taken. Find this amount as a percent. Answer: 37. 5%

Write as a percent. Round to the nearest hundredth. Estimate is about which equals Write as a percent. Round to the nearest hundredth. Estimate is about which equals or 50%. Write a proportion using Find the cross products. ENTER Answer: So, 41. 66666667 Use a calculator to simplify. is about 41. 67%. This result is close to the estimate.

Write as a percent. Round to the nearest hundredth. Answer: 73. 33% Write as a percent. Round to the nearest hundredth. Answer: 73. 33%

Write as a percent. Write as a decimal. Multiply by 100 and add the Write as a percent. Write as a decimal. Multiply by 100 and add the %. Answer: 45%

Write as a percent. Answer: 52% Write as a percent. Answer: 52%

Write as a percent. Round to the nearest hundredth. Write as a decimal. Multiply Write as a percent. Round to the nearest hundredth. Write as a decimal. Multiply by 100 and add the %. Answer: 42. 86%

Write as a percent. Round to the nearest hundredth. Answer: 81. 82% Write as a percent. Round to the nearest hundredth. Answer: 81. 82%

Example 1 Percents as Decimals or Fractions Example 2 Percents as Decimals or Fractions Example 1 Percents as Decimals or Fractions Example 2 Percents as Decimals or Fractions Example 3 Real-Life Percents as Decimals Example 4 Decimals as Percents

Write 220% as a decimal and as a mixed number or fraction in simplest Write 220% as a decimal and as a mixed number or fraction in simplest form. Definition of percent Simplify. Answer:

Write 375% as a decimal and as a mixed number or fraction in simplest Write 375% as a decimal and as a mixed number or fraction in simplest form. Answer:

Write 0. 6% as a decimal and as a mixed number or fraction in Write 0. 6% as a decimal and as a mixed number or fraction in simplest form. Definition of percent Simplify. Answer:

Write 0. 4% as a decimal and as a mixed number or fraction in Write 0. 4% as a decimal and as a mixed number or fraction in simplest form. Answer:

STOCKS During a stock market rally, a company’s stock increased in value by 200%. STOCKS During a stock market rally, a company’s stock increased in value by 200%. Write 200% as a decimal. Divide by 100. Answer: 2

Write 420% as a decimal. Answer: 4. 2 Write 420% as a decimal. Answer: 4. 2

Write 5. 12 as a percent. Multiply by 100. Answer: 512% Write 5. 12 as a percent. Multiply by 100. Answer: 512%

Write 9. 35 as a percent. Answer: 935% Write 9. 35 as a percent. Answer: 935%

Write 0. 0015 as a percent. Multiply by 100. Answer: 0. 15% Write 0. 0015 as a percent. Multiply by 100. Answer: 0. 15%

Write 0. 0096 as a percent. Answer: 0. 96% Write 0. 0096 as a percent. Answer: 0. 96%

Example 1 Use a Proportion to Find a Percent Example 2 Use Multiplication to Example 1 Use a Proportion to Find a Percent Example 2 Use Multiplication to Find a Percent Example 3 Use Multiplication to Find a Percent

SURVEYS Out of 1, 423 adults surveyed, 30% said they knew the name of SURVEYS Out of 1, 423 adults surveyed, 30% said they knew the name of their mail carrier. How many of the people surveyed knew their mail carrier’s name? 30% means that 30 out of 100 people knew their mail carrier’s name. Find an equivalent ratio x out of 1, 423 and write a proportion. number that knew name → total number in survey → percent of people that knew name

Now solve the proportion. Write the proportion. Find the cross products. Multiply. Divide each Now solve the proportion. Write the proportion. Find the cross products. Multiply. Divide each side by 100. Simplify. Answer: About 427 of the 1, 423 adults surveyed knew their mail carrier’s name.

SURVEYS Out of 765 students surveyed, 42% said that they watch some television after SURVEYS Out of 765 students surveyed, 42% said that they watch some television after school before doing their homework. How many of the students surveyed watch some television after school before doing their homework? Answer: about 321

What number is 120% of 24? Write a multiplication expression. Write 120% as a What number is 120% of 24? Write a multiplication expression. Write 120% as a decimal. Multiply. Answer: 120% of 24 is 28. 8.

What number is 160% of 44? Answer: 70. 4 What number is 160% of 44? Answer: 70. 4

Find 25% of $600. Write a multiplication expression. Write 25% as a decimal. Multiply. Find 25% of $600. Write a multiplication expression. Write 25% as a decimal. Multiply. Answer: 25% of $600 is $150.

Find 80% of $450. Answer: $360 Find 80% of $450. Answer: $360

Example 1 Find the Percent Example 2 Find the Part Example 3 Find the Example 1 Find the Percent Example 2 Find the Part Example 3 Find the Base

What percent of 24 is 18? 18 is the part, and 24 is the What percent of 24 is 18? 18 is the part, and 24 is the base. You need to find the percent p.

Percent proportion Replace a with 18 and b with 24. Find the cross products. Percent proportion Replace a with 18 and b with 24. Find the cross products. Simplify. Divide each side by 24. Simplify. Answer: 75% of 24 is 18. Compare the answer to the model.

What percent of 80 is 28? Answer: 35% What percent of 80 is 28? Answer: 35%

What number is 30% of 150? 30 is the percent and 150 is the What number is 30% of 150? 30 is the percent and 150 is the base. You need to find the part.

Percent proportion Replace b with 150 and p with 30. Find the cross products. Percent proportion Replace b with 150 and p with 30. Find the cross products. Simplify. Divide each side by 100. Simplify. Answer: 30% of 150 is 45. Compare the answer to the model.

What number is 65% of 180? Answer: 117 What number is 65% of 180? Answer: 117

12 is 80% of what number? 12 is the part and 80 is the 12 is 80% of what number? 12 is the part and 80 is the percent. You need to find the base, or the whole quantity.

Percent proportion 12 Replace a with 12 and p with 80. Find the cross Percent proportion 12 Replace a with 12 and p with 80. Find the cross products. Simplify. Divide each side by 80. Simplify.

Check In the model, the whole quantity is 12 3 or 15. 15 Answer: Check In the model, the whole quantity is 12 3 or 15. 15 Answer: 12 is 80% of 15.

36 is 40% of what number? Answer: 90 36 is 40% of what number? Answer: 90

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