Percent Proportion and Converting Percentages - Chapter 3.1 Examples
Learn about percent proportion and how to convert percentages to decimals and vice versa. Explore examples and practice writing fractions as percents in this detailed chapter 3.1 guide.
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Chapter 3.1 Percent Proportion
Parallel Example 1 Understanding Percent a. If 52 out of 100 chickens are hens, then 52 per 100 or , or 52% of the chickens are hens. 100 52 b. If a person pays a tax of $9 on every $100 of purchases, then the tax rate is $9 per $100. The ratio is and the percent of tax is 9%. 100 9 3
Parallel Example 2 Writing Percents as Decimals Write each percent as a decimal. a. 32% p% = p 100 32% = 32 100 = 0.32 b. 78% 78% = 78 100 = 0.78 c. 93.4% 93.4% = 93.4 100 = 0.934 d. 200% 200% = 200 100 = 2.00 4
Parallel Example 3 Writing Percents as Decimals by Moving the Decimal Point Write each percent as a decimal by moving the decimal point two places to the left. a. 23% 23.% 0.23 23% = 0.23 b. 180% 180.% = 180.% = 1.80 or 1.8 Decimal point starts at far right side Percent sign is dropped (Step 1) Decimal point is moved two places to the left. (Step 2) 5
Parallel Example 3 Writing Percents as Decimals by Moving the Decimal Point Write each percent as a decimal by moving the decimal point two places to the left. c. 3.2% .032 0 is attached so the decimal point can be moved two places to the left. d. 0.7% 0.7% = Two zeros are attached so the decimal point can be moved two places to the left. 0.007 6
Parallel Example 4 Writing Decimals as Percents by Moving the Decimal Point Write each decimal as a percent by moving the decimal point two places to the right. a. 0.26 0.26 Decimal point is moved two places to the right. 0.26 = 26% Percent sign is attached and decimal point is not written with whole number percents. = 37.6% b. 0.376 7
Parallel Example 4 Writing Decimals as Percents by Moving the Decimal Point Write each decimal as a percent by moving the decimal point two places to the right. c. 1.83 = 183% 0 is attached so the decimal point can be moved two places to the right. = 3.40 d. 3.4 3.4 = 340% Attach % sign. e. 5 Two zeros are attached so the decimal point can be moved two places to the right. 5. = 5.00 so 5 = 500% Attach % sign. 8
Parallel Example 3 continued Writing Fractions as Percents Write each fraction as a percent. Round to the nearest tenth if necessary. 5 8 5 8 100 Find cross products and show that they are equivalent. 8 5 100 p = 8 500 p = 8 500 8 8 1 62.5 p = b. Write as a percent by solving a proportion. p = So, 5 1 p 8= 62.5%. = 9
Parallel Example 3 continued Writing Fractions as Percents Write each fraction as a percent. Round to the nearest tenth if necessary. 5 12 5 12 100 12 5 100 p = 12 500 p = 12 500 12 12 1 41.6 p = 41.7 p c. Start with a proportion. p = Find cross products and show that they are equivalent. 1 p So, 5 = 41.7% 12= 41.6 10
The percent proportion can be used to solve problems. 11
Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. a. part = 20, percent = 80; find the whole. part percent whole 100 20 80 100 x whole = part percent 100 = Find the cross products. x 80 20 x 80 100 = 20 100 Show that the cross products are equivalent. = 20 100 80 x = 80 x 2000 x = 25 12
Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. b. part = 12, whole = 40; find the percent. part percent whole 100 12 40 100 whole = part percent 100 x = 3 x Write the fraction in lowest terms. = 10 10 10 100 3 100 = 300 = 30 x = x x Find the cross products. Divide both sides by 10. The percent is written as 30%. 13
Parallel Example 1 Using the Percent Proportion Use the percent proportion and solve for the unknown value. Let x represent the unknown. c. whole = 120, percent = 90; find the part. part percent whole 100 90 120 100 whole = part percent 100 x = x 9 = Write the fraction in lowest terms. 120 10 10 10 9 120 = 1080 = 108 x = Find the cross products. x x Divide both sides by 10. The part is 108. 14
CLASSROOM EXAMPLE 8 Solving Percent Equations Solve each problem. What is 6% of 80? Solution: x = 4.8 16% of what number is 12? x = 75 What percent of 75 is 90? x = 1.2 or 120% Slide 2.6-19
CLASSROOM EXAMPLE 9 Solving Applied Percent Problems Mark scored 34 points on a test, which was 85% of the possible points. How many possible points were on the test? Solution: Let x = the number of possible points on the test. 34 x 8 00 1 5 = 34 0 0 85 8 40 x = 85 5 x = There were 40 possible points on the test. Slide 2.6-20
Parallel Example 1Solving for Sales Tax Sam s Sporting Goods sells a tent for $189. If the sales tax is 5%, how much tax is paid? What is the total cost of the tent? ? 189= 100 ?=945 100 ?=$9.45 5 This is the tax amount. 9.45 + 189 = $198.45 The total amount for the tent is $198.45 Slide 6.6- 17
Parallel Example 2Finding the Sales Tax Rate The sales tax on a $580 recliner is $46.40. Find the rate of the sales tax. 46.4 580= ? 100 ? = 8% Slide 6.6- 18
Parallel Example 3Determining the Amount of Commission Caleb Martinez had exercise equipment sales of $12,700 while working part-time last month. If his commission rate is 9%, find the amount of his commission. ? 12700= ? = 1143 9 100 Caleb earned $1143. Slide 6.6- 19
Parallel Example 5Finding a Sale Price Art Designs has a painting with an original price of $620 on sale for 15% off. Find the sale price of the painting. ? 620= 100 ? = 93 15 $93 was slashed from the original amount. 620-93=527 The final sale price is $527 Slide 6.6- 20
We are often interested in looking at increases or decreases in sales, production, population, and many other items. Use the following steps to find the percent of increase. Finding the Percent of Increase Step 1 Step 2 Use subtraction to find the amount of increase. Use the percent proportion to find the percent of increase. amount of increase (part) original value (whole) percent 100 = = Slide 6.6- 21
Parallel Example 6Finding the Percent of Increase A budget had an increase from $19,600 last year to $40,060 this year. Find the percent of increase. 20460 19600= ? = 104.38% ? 100 The percent of increase is 104.4%. Slide 6.6- 22
Finding the Percent of Decrease Step 1 Step 2 Use subtraction to find the amount of decrease. Use the percent proportion to find the percent of decrease. amount of decrease (part) original value (whole) percent 100 = = Slide 6.6- 23
Parallel Example 7Finding the Percent of Decrease The number of minutes Rita used on her cell phone dropped this month to 798 from 840 last month. Find the percent of decease. 42 840= 100 4200 840= ? ? = 5 ? The percent of decrease is 5%. Slide 6.6- 24
HW 3.1 1-26 Slide 1- 25
