Comparing and Scaling Ratios Percents Fractions Scaling and

Comparing and Scaling Ratios, Percents, Fractions, Scaling and Differences

Example The class has 12 girls and 15 boys. n

Ratios n Can be written 3 ways: n n 12: 15 12/15 Compare part-to-part: n n 12 to 15 Boys to girls is 15 to 12 (reduced = 5 to 4) Or part-to-whole n boys to class is 15 to 27 (reduced = 5 to 9)

Differences n n n Compare how much more or less one quantity is than another. Found by subtracting. Example: 15 boys – 12 girls = 3 n n n There are 3 more boys than girls. The boys outnumber the girls by 3. There is a difference of 3 between boys and girls.

Scaling n n n The number multiplied by one quantity to get another quantity. The scale factor is found by dividing. Example: Jane is 6 feet tall and Tom is 3 feet tall. How many times taller is Jane than Tom? n 6÷ 3=2 Jane is 2 times taller than Tom.

Fractions n n Compares part-to-whole. Example 1: What fraction of the class is boys? n n 15/27 (15 is the part of the class that is boys, 27 is the whole class). Example 2: What fraction of the class are girls? n 12/27 (12 is the part of the class that are girls, 27 is the whole class).

Percents n n n Means “out of 100. ” 30% = 30/100 72% = 72/100 To find a percent: n n 1. Write the fraction. 2. Divide the numerator by the denominator. 3. Multiply by 100. Example: What percent of the class are boys? n 15/27 = 15 ÷ 27 = 0. 5555 x 100 = 55. 6%

Examples n n n 25 chocolate cookies 20 vanilla cookies. 1. What is the ratio of chocolate cookies to vanilla cookies? n n 25 to 20 which reduces to 5 to 4 2. How many more cookies are chocolate than vanilla? n 25 - 20 = 5 more cookies are chocolate

Examples n 3. What fraction of the cookies are vanilla? n n 4. What percent of the cookies are chocolate? n n 20/45 which reduces to 4/9 25/45 = 25 ÷ 45 = 0. 5555 x 100 = 55. 6% 5. How many times more chocolate cookies are there than vanilla cookies? n 25 ÷ 20 = 1. 25 times

Practice Hamburger Hot Dog Pizza Boys 25 15 60 Girls 26 19 55 1. What is the ratio of boys who like pizza to girls who like pizza? 60 to 55 2. Girls who like hot dogs outnumber boys who like hot dogs by how many? 19 -15 = 4 3. What fraction of the students like hamburgers? 51/200 4. What percent of the students like pizza? 115/200 = 115 ÷ 200 = 0. 575 x 100 = 57. 5% 5. How many times more boys like pizza than girls? 60 ÷ 55 = 1. 09

Rates, and Unit Rates Course 3

Vocabulary rate unit price

A rate is a comparison of two quantities that have different units. Ratio: 90 3 Rate: 90 miles 3 hours Read as “ 90 miles per 3 hours. ”

Unit rates are rates in which the second quantity (or the denominator) is 1. The ratio 90 can be simplified by dividing: 3 90 = 30 3 1 unit rate: 30 miles, 1 hour or 30 mi/h

Additional Example 1: Finding Unit Rates Fred can type 30 words in half a minute. How many words can he type in 1 minute? 30 words 1 2 minute 30 words • 2 1 2 minute • 2 Write a rate. = 60 words 1 minute Multiply to find words per minute. Fred can type 60 words in one minute.

Example 1 Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? 90 words 2 minutes Write a rate. 90 words ÷ 2 2= 45 words 1 minutes ÷ 2 minute Divide to find words per minute. Penelope can type 45 words in one minute.

Unit price is a unit rate used to compare price per item.

Additional Example: Finding Unit Prices to Compare Costs Pens can be purchased in a 5 -pack for $1. 95 or a 15 pack for $6. 20. Which is the better buy? price for package = $1. 95 number of pens 5 $0. 39 price for package = $6. 20 number of pens 15 $0. 41 The better buy is the 5 -pack for $1. 95. Divide the price by the number of pens.

Additional Example: Finding Unit Prices to Compare Costs Jamie can buy a 15 -oz jar of peanut butter for $2. 19 or a 20 -oz jar for $2. 78. Which is the better buy? price for jar number of ounces = $2. 19 $0. 15 15 price for jar number of ounces = $2. 78 $0. 14 20 The better buy is the 20 -oz jar for $2. 78. Divide the price by the number of ounces.

Another Example Golf balls can be purchased in a 3 -pack for $4. 95 or a 12 -pack for $18. 95. Which is the better buy? price for package = $4. 95 number of balls 3 $1. 65 price for package = $18. 95 $1. 58 number of balls 12 The better buy is the 12 -pack for $18. 95. Divide the price by the number of balls.

One more Unit Rate Example… John can buy a 24 oz bottle of ketchup for $2. 19 or a 36 oz bottle for $3. 79. Which is the better buy? price for bottle number of ounces = $2. 19 $0. 09 24 price for bottles number of ounces = $3. 79 $0. 11 36 The better buy is the 24 -oz jar for $2. 19. Divide the price by the number of ounces.

Using Rate Tables to Find Values n Rate tables can be used to answer questions. Three sweaters cost $18. What is the cost of 7 sweaters? Number Cost 3 18

Ratio Tables Three sweaters cost $18. What is the cost of 7 sweaters? Number 1 Cost 6 3 18

Ratio Tables Three sweaters cost $18. What is the cost of 7 sweaters? Number 1 Cost 6 3 18 7 42

Try These! 1. Jacob can buy a 32 oz bottle of BBQ sauce for $2. 93 or a 36 oz bottle for $3. 19. Which is the better buy? 2. John can buy a 8 pencils for $1. 25 or a 12 pencils for $2. 00. Which is the better buy? 3. Mary made $25. 00 for working 7 hours at the mall. How much did Mary make per hour? 4. Lisa paid $158. 00 for 3 pair of jeans. What did Lisa pay for each pair of jeans? 5. Bob typed 593 words in 4 minutes. How many words did Bob type per minute?

ANSWERS 1. $2. 93 / 32 = $0. 09 $3. 19 / 36 = $0. 08 (better buy) 2. $1. 25 / 8 = $0. 16 (better buy) $2. 00 / 12 = $0. 17 3. $25. 00 / 7 hours = $3. 57 / Hr 4. $158. 00 / 3 pair of jeans = $52. 67 / jean 5. 593 / 4 minutes = 148. 3 words/minute

Homework Page Page 19, 20, 21, 24, 25, 26, 29, 31, #1 -3 #5 #8 #17, # 19, 22 #25 -27 #38 #60 Page 51, #1 Page 52, # 5, 7, 8 Page 53, #10 a/c (don’t do “b” and “d”) Page 55, #12 -14 Page 56, #24