Chapter 6. Percents and their Applications

Transcription

1 Chapter 6 Percents and their Applications

2 What is a percent? A percent is 1 one hundredth of a number. For instance, a penny is 1/100 of a dollar. Each one hundredth is 1% A nickel is 5/100 of a dollar or 5% A dime is 10/100 of a dollar or 10%

3 No. of fraction % of decimal currency pennies of dollar a dollar number (cents) 50 50/100 50%.50 $ /100 25%.25 $ /100 10%.10 $ /100 5%.05 $ /100 1%.01 $.01 Notice the difference between these two sets of numbers.

4 Visualize the alphabet to determine which way to move the decimal point when converting from decimals to percent and from percent to decimals a b c D e f g h i j k l m n o P q r s t u v w x y z D for Decimal Left Toward D Right Toward P P for Percent.xx xx. Decimal to Percent (from D toward P) move the decimal point two places to the right Percent to Decimal (from P toward D) move the decimal point two places to the left

5 Converting Decimals to Percents Move decimal point 2 places to the right, and add zeros if necessary. Add a percent symbol at the end of the number..01 1%.75 75% % a b c D e f g h i j k l m n o P q r s t u v w x y z

6 Converting a fraction to a decimal number, to a percent, and then rounding to the hundredth place 5 13 = % = 38.46%

7 Converting Percents to Decimals, example 1 Drop the percent symbol. Move decimal point 2 places to the left, add zeros if necessary 8%.08 35% % 2.50 a b c D e f g h i j k l m n o P q r s t u v w x y z

8 Converting Percents to Decimals-- Example 2 Drop the percent symbol Move the decimal point 2 places to left..8% A B C D In this case we had to add zeros to fill in the empty places to the left of the 8. a b c D e f g h i j k l m n o P q r s t u v w x y z

9 Converting Fractional Percents to Decimals A fractional percent is a part (fraction) of a percent. Start by dividing the denominator into the numerator %.5 2 At this point, the number is still a percent and has to be converted to a decimal..005

10 Converting Proper Fractions to Percents % Remember, converting from a decimal number to a percent means moving the decimal point two places to the right. (D to P) Then add the percent sign (%). Fraction Decimal Percent

11 Converting a Whole Percent to a Fraction 76% 76 x Divide 4 into the numerator and the denominator to reduce this fraction to lowest terms.

12 Converting a Mixed Percent (also called a Decimal Percent) to a Fraction 12½ % 25 2 Drop % symbol, and change the mixed percent to an improper fraction. 25 x 1 = Reduce to lowest terms. Multiply improper fraction by 1/

13 Application of Percents - Portion Formula Portion (P) = Base (B) x Rate (R) Base: 100% - whole. Usually given after the word of but not always $100 Bonus check Rate: Usually expressed as a percent but could also be a decimal or fraction. 20% taxes Portion: A number not a percent and not the whole $20 taxes Portion is Base of Rate % X Center line stands for division.

14 To find the portion, multiply the rate x base To find the rate, divide portion by base To find base, divide portion by rate Very Useful

15 McDonalds has two major categories of sales drive-through and eat-in. Both are portions of total McDonalds sales. The following business math problems have to do with these portions of the total sales.

16 Solving for Portion rate Sales to McDonalds drive-thru customers are 60% of total sales. Total sales are $1,600,000. What are the drive-thru sales? base portion 960,000 portion.60 1,600,000 Portion = Base x Rate P = $1,600,000 x.60 P = $960,000 rate base

17 Solving for Rate Sales to McDonalds drive-thru customers are $960,000. Total sales are $1,600,000. What Percent of customers eat in the restaurant? portion rate base? 640,000 1,600,000 Rate = Portion Base R = $640,000 $1,600,000 R = 40% Eat in $1,600, , ,000 total drive-thru

18 Solving for Base Sales to McDonalds drive-thru customers are 60% of total sales. Sales to eat-in customers are $640,000. What are total sales? Percent of customers that eat-in ( ) Base = Portion Rate B = $640, B = $1,600,000 eat in sales

19 Rate of Decrease (rates are percent) Original New The actual decrease in size (portion) is 15 oz. 3 oz. = 12 oz. What percent is 12 (the decrease) of 15 (the original size)? 15 oz. bunch 3 oz. bunch Rate = Portion Base Rate = or 80% decrease Amount of Decrease (Portion) Original Weight (Base)

20 Rate of Percent Increase Original New The actual increase (portion) is 2,500 1,000 = 1,500 What percent is 1,500 (the increase) of 1,000 (the original size)? You are seeking the rate. $1,000 $2,500 Percent of Increase (Rate) Rate = Portion Base Amount of Increase (Portion) Rate = $1,500 $1,000 Original sales (Base) 1.5 or 150% Increase