Mathematics Applications and Concepts Course 3 Interactive Chalkboard

Mathematics: Applications and Concepts, Course 3 Interactive Chalkboard Copyright © by The Mc. Graw-Hill Companies, Inc. Developed by FSCreations, Inc. , Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/Mc. Graw-Hill 8787 Orion Place Columbus, Ohio 43240

Lesson 5 -1 Ratios and Percents Lesson 5 -2 Fractions, Decimals, and Percents Lesson 5 -3 The Percent Proportion Lesson 5 -4 Finding Percents Mentally Lesson 5 -5 Percent and Estimation Lesson 5 -6 The Percent Equation Lesson 5 -7 Percent of Change Lesson 5 -8 Simple Interest

Example 1 Write Ratios as Percents Example 2 Write Ratios as Percents Example 3 Write Ratios and Fractions as Percents Example 4 Write Ratios and Fractions as Percents Example 5 Write Percents as Fractions

POPULATION According to the 2000 U. S. Census Bureau, 13 out of every 100 people living in Delaware were 65 or older. Write this ratio as a percent. Answer: 13 out of every 100 = 13%

LIBRARY At the Booktown Library, 59 out of every 100 users is 12 or under. Write this ratio as a percent. Answer: 59%

BASEBALL In 2001, Manny Ramirez got on base 40. 5 times for every 100 times he was at bat. Write this ratio as a percent. Answer: 40. 5 out of 100 = 40. 5%

BASKETBALL Last season, Janelle made 68 baskets for every 100 tries. Write this ratio as a percent. Answer: 68%

TRANSPORTATION About 4 out of 5 commuters in the United States drive or carpool to work. Write this ratio as a percent. Answer: So, 4 out of 5 equals 80%.

TRANSPORTATION About 3 of 5 students at Wilder Elementary ride the bus to school. Write this ratio as a percent. Answer: 60%

INTERNET In 2000, about of the population in Peru used the Internet. Write this fraction as a percent. Answer: So, 3 out of 200 equals 1. 5%.

$INTERNET In 2001, teens used the Internet to visit music sites. Write this fraction$

INTERNET In 2001, teens used the Internet to visit music sites. Write this fraction as a percent. Answer: 61%

SCHEDULE The circle graph shows an estimate of the percent of his day that Peter spends on each activity. Write the percents for eating and sleeping as fractions in simplest from. Eating: Sleeping: Answer: eating: , sleeping:

SCHEDULE The circle graph shows an estimate of the percent of his day that Leon spends on each activity. Write the percents for school and television as fractions in simplest form. Answer: school: ; television:

Example 1 Percents as Decimals Example 2 Percents as Decimals Example 3 Decimals as Percents Example 4 Decimals as Percents Example 5 Fractions as Percents Example 6 Fractions as Percents Example 7 Compare Numbers

Write 52% as a decimal. Divide by 100 and remove the percent symbol. Answer: 0. 52

Write 28% as a decimal. Answer: 0. 28

Write 245% as a decimal. Divide by 100 and remove the percent symbol. Answer: 2. 45

Write 135% as a decimal. Answer: 1. 35

Write 0. 3 as a percent. Multiply by 100 and add the percent symbol. Answer: 30%

Write 0. 91 as a percent. Answer: 91%

Write 0. 71 as a percent. Multiply by 100 and add the percent symbol. Answer: 71%

Write 1. 65 as a percent. Answer: 165%

Write as a percent. Method 1 Use a proportion.

Method 2 Write as a decimal. 0. 75 Answer: So, can be written as 75%.

Write as a percent. Answer: 25%

Write as a percent. Method 1 Use a proportion.

Method 2 Write as a decimal. 0. 166… Answer: So, can be written as

Write as a percent. Answer:

POLITICS In Sun City, of voters are Democrats. In Moon Town, 48% of voters are Democrats. In which town is there a greater proportion of Democrats? Write as a percent. Multiply by 100 and add the percent symbol. Answer: Since 45% is less than 48%, there are more Democrats in Moon Town.

POLITICS In Star City, of voters are Republicans. In Meteorville, 13% of voters are Republicans. In which town is there a greater proportion of Republicans? Answer: Star City

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

34 is what percent of 136? Since 34 is being compared to 136, 34 is the part and 136 is the base. You need to find the percent. Replace a with 34 and b with 136. Find the cross products. Multiply. Divide each side by 136. Simplify. Answer: 34 is 25% of 136.

63 is what percent of 210? Answer: 30%

What number is 70% of 600? The percent is 70, and the base is 600. You need to find the part. Replace b with 600 and p with 70. Find the cross products. Multiply. Divide each side by 100. Simplify. Answer: 420 is 70% of 600.

What number is 40% of 400? Answer: 160

BASEBALL From 1999 to 2001, Derek Jeter had 11 hits with bases loaded. This was about 30% of his at bats with bases loaded. How many times was he at bat with bases loaded? The percent is 30, and the part is 11. You need to find the base.

Replace a with 11 and p with 30. Find the cross products. Multiply. Divide each side by 30. Simplify. Answer: Derek Jeter was at bat 37 times with bases loaded.

BASEBALL In the 2002 season, Barry Bonds had 149 hits. This was about 37% of his at bats. How many times was he at bat? Answer: 403

Example 1 Use Fractions to Compute Mentally Example 2 Use Fractions to Compute Mentally Example 3 Use Decimals to Compute Mentally Example 4 Use Decimals to Compute Mentally Example 5 Use Mental Math to Solve a Problem

$Compute 40% of 80 mentally. 40% of of 80 or 32 Use the fraction$

Compute 40% of 80 mentally. 40% of of 80 or 32 Use the fraction form of 40%, which is Answer: 32

Compute 20% of 60 mentally. Answer: 12

$Compute of 75 mentally. of 75 or 50 Use the fraction form of which$

Compute of 75 mentally. of 75 or 50 Use the fraction form of which is Answer: 50

Compute Answer: 200 of 300 mentally.

Compute 10% of 65 mentally. of 65 or 6. 5 Answer: 6. 5

Compute 10% of 13 mentally. Answer: 1. 3

Compute 1% of 304 mentally. of 304 or 3. 04 Answer: 3. 04

Compute 1% of 244 mentally. Answer: 2. 44

TECHNOLOGY A company produces 2, 500 of a particular printer. They later discover that 25% of the printers have defects. How many printers from this group have defects? Method 1 Use a fraction. of 2, 500 THINK of 2, 000 is 500 and of 500 is 125. 25% of 2, 500 is 625. So, of 2, 500 is 500 + 125 or 625.

Method 2 Use a decimal. 25% of 2, 500 = 0. 25 of 2, 500 THINK 0. 5 of 2, 500 is 1, 250. 25% of 2, 500 is 625. So, 0. 25 of 2, 500 is or 625. Answer: There were 625 printers that had defects.

TECHNOLOGY A company produces 1, 400 of a particular monitor. They later discover that 20% of the monitors have defects. How many monitors from this group have defects? Answer: 280

Example 1 Estimate Percents of Numbers Example 2 Estimate Percents of Numbers Example 3 Estimate Percents of Numbers Example 4 Estimate Percents Example 5 Estimate Percents Example 6 Estimate Percents Example 7 Estimate Percent of an Area

Estimate 48% of 70. 48% is about 50% or and 70 are compatible numbers. of 70 is 35. Answer: So, 48% of 70 is about 35.

Estimate 51% of 60. Answer: 30

Estimate 75% of 98. 75% is and 98 is about 100. and 100 are compatible numbers. of 100 is 75. Answer: So, 75% of 98 is about 75.

Estimate 25% of 33. Answer: 8

Estimate 12% of 81. 12% is about 12. 5% or and 81 is about 80. of 80 is 10. Answer: So, 12% of 81 is about 10. and 80 are compatible numbers.

Estimate 37% of 17. Answer: 8

Estimate the percent 12 out of 47. or 47 is about 48. Answer: So, 12 out of 47 is about 25%.

Estimate the percent 15 out of 76. Answer: 20%

Estimate the percent 19 out of 31. 19 is about 20, and 31 is about 30. Answer: So, 19 out of 31 is about

Estimate the percent 14 out of 47. Answer:

Estimate the percent 41 out of 200. 41 is about 40. Answer: So, 41 out of 200 is about 20%.

Estimate the percent 11 out of 100. Answer: 10%

ART An artist creates a design on a grid. Estimate the percent of the grid that has been painted so far. About 6 squares out of 20 squares are covered with paint.

Answer: So, about 30% of the grid has been painted.

ART An artist creates a design on a grid. Estimate the percent of the grid that has been painted so far. Answer: about 35%

Example 1 Find the Part Example 2 Find the Percent Example 3 Find the Base Example 4 Solve a Real-Life Problem

Find 30% of 450. Estimate 10% of 450 is 45. So, 30% of 450 is or 135. The percent is 30%, and the base is 450. Let n represent the part. Write 30% as the decimal 0. 30. Simplify. Answer: So, 30% of 450 is 135. Compare to the estimate.

Find 20% of 315. Answer: 63

102 is what percent of 150? Estimate The part is 102, and the base is 150. Let n represent the percent. Write the equation. Divide each side by 150. Simplify.

Answer: In the percent equation, the percent is written as a decimal. Since 102 is 68% of 150.

135 is what percent of 250? Answer: 54%

144 is 45% of what number? Estimate 144 is 50% of 288. The part is 144, and the percent is 45%. Let n represent the base. Write 45% as the decimal 0. 45. Divide each side by 0. 45. Simplify.

Answer: So, 144 is 45% of 320. Compare to the estimate.

186 is 30% of what number? Answer: 620

SALES TAX The price of a sweater is $75. The sales tax is percent. What is the total price of the sweater? Find the amount of the tax t. Words Symbols Equation What amount is of $75?

Write the equation. Simplify. Answer: The amount of tax is $4. 31. The total cost of the sweater is $75 + $4. 31 or $79. 31.

SALES TAX The price of a pair of tennis shoes is $60. The sales tax is 5 percent. What is the total price of the shoes? Answer: $63

Example 1 Find the Percent of Increase Example 2 Find the Percent of Change Example 3 Find the Selling Price Example 4 Find the Sale Price

HOMES The Nietos bought a house several years ago for $120, 000. This year, they sold it for $150, 000. Find the percent of increase. Step 1 Subtract to find the amount of change. Step 2 Write a ratio that compares the amount of change to the original amount they paid for the house. Express the ratio as a percent.

Definition of percent of change The amount of change is 30, 000. The original amount is 120, 000. Divide. Write as a percent. Answer: The percent of increase is 25%.

CLUBS Last year Cedar Park Swim Club had 340 members. This year they have 391 members. Find the percent of increase. Answer: 15%

SCHOOLS Johnson Middle School had 240 students last year. This year, there are 192 students. Find the percent of change. State whether the percent of change is an increase or a decrease. Step 1 Subtract to find the amount of change. Step 2 Write a ratio that compares the amount of change to the number of students last year. Express the ratio as a percent.

Definition of percent of change The amount of change is 48. The original amount is 240. Divide. Write as a percent. Answer: The percent of change is 20%. Since the new amount is less than the original, it is a percent of decrease.

CARS Meagan bought a new car several years ago for $14, 000. This year she sold the car for $9, 100. Find the percent of change. State whether the percent of change is an increase or a decrease. Answer: 35%; decrease

MARKUP Shirts bought by a sporting goods store cost them $20 per shirt. They want to mark them up 40 percent. What will be the selling price? Method 1 Find the amount of the markup. Find 40% of $20. Let m represent the markup. Write 20% as a decimal. Multiply. Add the markup to the price they paid for the shirts.

Method 2 Find the total percent. The customer will pay 100% of the price the sporting goods store paid plus an extra 40% of the price. Find 100% + 40% or 140% of the price the sporting goods store paid for the shirts. Let p represent the price. Write 140% as a decimal. Multiply. Answer: The selling price of the shirts for the customer is $28.

MARKUP Silk flowers bought by a craft store cost them $10 per yard. They want to mark them up 35 percent. What will be the selling price? Answer: $13. 50

SHOPPING A computer usually sells for $1, 200. This week it is on sale for 30% off. What is the sale price? Method 1 Find the amount of the discount. Find 30% of $1, 200. Let d represent the discount. Subtract the amount of the discount from the original price.

Method 2 Find the total percent. If the amount of the discount is 30%, the percent paid is 100% – 30% or 70%. Find 70% of $1, 200. Let s represent the sale price. Answer: The sale price of the computer is $840.

SHOPPING A DVD sells for $28. This week it is on sale for 20% off. What is the sale price? Answer: $22. 40

Example 1 Find Simple Interest Example 2 Find the Total Amount Example 3 Find the Interest Rate

Find the simple interest for $2, 000 invested at 5. 5% for 4 years. Write the simple interest formula. Replace p with 2, 000, r with 0. 055, and t with 4. The simple interest is $440. Answer: $440

Find the simple interest for $1, 500 invested at 5% for 3 years. Answer: $225

GRID-IN TEST ITEM Find the total amount of money in an account where $80 is invested at 6% for 6 months. Read the Test Item You need to find the total amount in an account. Notice that the time is given in months. Six months is year.

Solve the Test Item The amount in the account is $80 + $2. 40 or $82. 40.

Answer:

GRID-IN TEST ITEM Find the total amount of money in an account where $60 is invested at 8% for 3 months. Answer:

LOANS Gerardo borrowed $4, 500 from his bank for home improvements. He will repay the loan by paying $120 a month for the next four years. Find the simple interest rate of the loan. First find the total amount of money Gerardo will pay a total of $5, 760. He will pay $5, 760 – $4, 500 or $1, 260 in interest. The loan will be for 48 months or 4 years.

Use the simple interest formula to find the interest rate. Words Variables Equation Interest equals principal times rate times time.

Write the equation. Simplify. Divide each side by 18, 000. Simplify. Answer: The simple interest rate is 7%.

LOANS Jocelyn borrowed $3, 600 from her bank for home improvements. She will repay the loan by paying $90 a month for the next five years. Find the simple interest rate of the loan. Answer: 10%

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