percentages

percentages - Fifth Grade Fifth Math Course I Math Ratio,...

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Unformatted text preview: Fifth Grade Fifth Math Course I Math Ratio, Proportion, and Percent 1 Ratios Ratios A ratio is a comparison of numbers ratio that can be expressed as a fraction. that If there were 18 boys and 12 girls in If a class, you could compare the number of boys to girls by saying there is a ratio of 18 boys to 12 girls. You could represent that comparison in three different ways: in 18 to 12 18 : 12 18 12 2 Ratios The ratio of 18 to 12 is another The 18 way to represent the fraction 12 way All three representations are All equal. equal. 18 18 18 to 12 = 18:12 = 12 The first operation to perform on The a ratio is to reduce it to lowest terms terms ÷6 18 = 12 18:12 = 3 2 18:12 = ÷6 = 3:2 3 2 3 Ratios A basketball team wins 16 games basketball and loses 14 games. Find the reduced ratio of: reduced Wins to losses – 16:14 = 16 = 8 Wins 16:14 14 7 14 7 Losses to wins – 14:16 = = Losses 14:16 16 8 Wins to total games played – Wins 16:30 = 16 = 8 16:30 30 15 The order of the numbers is critical 4 Ratios A jjar contains 12 white, 10 red ar and 18 blue balls. What is the reduced ratio of the following? reduced White balls to blue balls? Red balls to the total number of Red balls? balls? Blue balls to balls that are not blue? 5 Proportions A proportion is a statement that proportion one ratio is equal to another ratio. ratio. Ex: a ratio of 4:8 = a ratio of 3:6 3 1 4:8 = 4 = 1 and 3:6 = =2 6 2 8 4:8 = 3:6 4= 3 8 These These 6 ratios form a proportion proportion 6 since they are equal to other. since Proportions In a proportion, you will notice In that if you cross multiply the cross terms of a proportion, those cross-products are equal. cross-products 4 8 = 3 6 3 2 = 18 18 7 12 3 x 12 = 2 x 18 (both equal 36) 12 4 x 6 = 8 x 3 (both equal 24) Proportions Determine if ratios form a Determine proportion proportion 12 12 21 21 and 8 14 14 10 10 17 17 and 20 20 27 27 3 8 and 9 24 24 8 Proportions The fundamental principle of The proportions enables you to solve problems in which one number of the proportion is not known. of For example, if N represents the For number that is unknown in a proportion, we can find its value. 9 Proportions N= 12 12 3 4 4 x N = 12 x 3 12 Cross multiply the proportion 4 x N = 36 36 4xN 4 36 = 4 Divide the terms on both sides Divide of the equal sign by the number next to the unknown letter. (4) next 1xN=9 N=9 That will leave the N on the left That side and the answer (9) on the right side right 10 Proportions Solve for N 2=N 5 35 35 5 x N = 2 x 35 35 Solve for N 15 15 N =3 4 5 x N = 70 70 6 7 102 = 102 N 5xN 5 4 N =6 27 27 = 70 5 1 x N = 14 N = 14 11 Proportions At 2 p.m. on a sunny day, a 5 ft At woman had a 2 ft shadow, while a church steeple had a 27 ft shadow. Use this information to find the height of the steeple. find 5 2 =H 27 27 height height shadow = height height shadow 2 x H = 5 x 27 You must be careful to place You 2 x H = 135 tche same quantities in in the orresponding positions proportion proportion H = 67.5 ft. 12 Proportions If you drive 165 miles in 3 hours, how many If miles can you expect to drive in 5 hours traveling at the same average speed? traveling A brass alloy contains only copper and zinc brass in the ratio of 4 parts of copper to 3 parts zinc. If a total of 140 grams of brass is made, how much copper is used? made, If a man who is 6 feet tall has a shadow If that is 5 feet long, how tall is a pine tree that has a shadow of 35 feet? that 13 Percents Percent means out of a hundred An 85% test score means that out of 100 An points, you got 85 points. points, 25% means 25 out of 100 25 = 0.25 25% = 25 100 137% means 137 out of 100 137% = 137 = 1.37 137% 1.37 100 6.5% means 6.5 out of 100 6.5% = 6.5 = 0.065 100 14 Converting Percents to Converting Fractions Fractions To convert a percent to a fraction, To drop the % sign, put the number over 100 and reduce if possible over Express 30% as a fraction 30% = 30% 30 30 100 = 3 10 10 (a reduced fraction) (a Express 125% as a fraction 125% = 125 = 100 5 4 =11 4 (a reduced mixed number) 15 Converting Percents to Converting Decimals Decimals To convert a percent to a To decimal, drop the % sign and move the decimal point two places to the left places Express the percents as a Express decimal decimal 30% 125 = .30 % = 1.25 16 Converting Decimals to Converting Fractions and Percents Fractions Convert each percent to a Convert reduced fraction or mixed number and a decimal number 17% 5% 23% 236% 8% 17 Converting Decimals to Converting Percents Percents To convert a decimal to a To percent, move the decimal point percent move two places to the right and attach a % sign. attach Ex: 0.34 = 34% Ex: 0.01 = 1% 18 Converting Fractions to Percents Percents To convert a fraction to a percent, To divide the denominator of the fraction into the numerator to get a decimal number, then convert that decimal to a percent (move the decimal point percent move two places to the right) two 3 4 = .75 4 3.00 = 75% 19 Converting Decimals and Converting Fractions to Percents Fractions Convert the Decimal to a percent .08 =? 3.26 = ? .75 = ? Convert the Fraction to a percent 1 5 7 10 10 20 Percent of a Number Percents are often used to find a part Percents of a number or quantity of Ex: “60% of those surveyed” Ex: “35% discount” Ex: 8.25% sales tax” 60% of 5690 means 60% x 5690 35% of $236 means 35% x $236 8.25% of $180 means 8.25% x $180 Change the percent into either a fraction Change or a decimal before you use it in 21 multiplication multiplication Percent of a Number Find 25% of 76 (as a decimal) (as 25% = .25 25% of 76 = .25 x 76 = 1 OR OR Find 25% of 76 (as a fraction) (as 25% = 1 25% 4 1 25% of 76 = x 76 = 19 4 Find 60% of 3420 Find 30% of 50 Find 5% of 18.7 22 Percentage Problems On a test you got 63 out of 75 On possible points. What percent did you get correct? you 63 75 75 Since “percent” means “out of a Since hundred”, 63 out of 75 is what number out of 100 out = P (P is used to represent the percent or part 100 out of 100) 100 75 x P = 6300 75 75 75 75 P = 84 84 Percent Proportion A B = P 100 A is the amount B is the base (follows the word “of”) P is the percent (written with the 23 word “percent” or the % sign) Percentage Problems 15 is what percent of 50? 16 is 22% of what number? 91 is what percent of 364? What is 9.5% What of 75,000? Percent Proportion A B = P 100 A is the amount B is the base (follows the word “of”) P is the percent (written with the word “percent” or 24 % sign) the ...
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