5.1 Introduction to Ratios

Transcription

1 5.1 Introduction to Ratios A ratio is a comparison of two quantities that uses division. Ratios can be represented in words, with a colon, as a fraction, or with a model. There are two types of ratios: Part-To-Part Ratio Part-To-Whole Ratio A department store sells multi-packs of dress socks. Each pack includes 3 pairs of grey socks, 2 pairs of striped socks, and 1 pair of polka dot socks. There are different ways to think about this relationship and make comparisons. The relationship between the number of pairs of striped socks and the number of pairs of grey socks can be represented in a model as follows. The relationship between the number pairs of polka dot socks and the number of pairs of striped socks can be written in words as follows. These ratios are examples of part-to-part ratios. 1 polka dot pair to 2 striped pairs 2 striped pairs to 1 polka dot pair The relationship between the number of black pairs of socks and the total number of pairs of socks can be written with a colon as follows. These ratios are examples of part-to-whole ratios. 3 grey pairs : 6 total pairs 6 total pairs : 3 grey pairs The relationship between the number of grey pairs of socks and the number of polka dot pairs of socks can be written in fractional form as follows. Information:

2 5.2 Comparing Ratios To compare two ratios: Write each ratio in fractional form Write each ratio in simplest form A survey of middle school students shows that 175 out 250 seventh grade students prefer sports drinks to water. For eight grade students, the survey shows 160 out of 200 prefer sports drinks to water. Seventh Grade Students: Eighth Grade Students: Because water., the eighth grade has a higher ratio of students who prefer sports drinks to 5.3 Writing Rates A rate is a ratio that compares two quantities that are measured in different units. Shen is taking a timed math quiz. During the 10-minute quiz he answers 24 problems. The rate at which Shen took the quiz is the number of problems answered per amount of time. Shen s rate is 24 problems per 10 minutes, or. 5.3 Scaling Up and Scaling Down When you change a ratio to an equal ratio with larger numbers, you are scaling up the ratio. When you change a ratio to an equivalent ratio with smaller numbers, you are scaling down the ratio. Scaling up means you multiply the numerator and the denominator by the same factor. Scaling down means you divide the numerator and the denominator by the same factor.

3 5.3 Scaling Up and Scaling Down (cont.) A variety box of fruit snacks contains 6 packs of orange snacks, 3 packs of cherry snacks, and 3 packs of grape snacks. The ratio of packs of orange snacks to the total number of packs in a box is. You can scale up the ratio to determine the number of packs of orange snacks if there are 36 total packs. You can scale down the ratio to determine the number of packs of orange snacks if there are 6 total packs. 5.4 Drawing Models to Solve Problems Involving Ratios You can use any symbols to represent objects in a ratio. You can compare parts to parts to parts, or parts to the whole. Represent simple fractions with parts of a circle or other shape. One container of soup feeds four adults. To determine how many containers of soup will feed 15 people, you can perform the following steps: Draw groups of four people per container until you draw 15 people. Because three people form three-fourths of a group, draw only three-fourths of the symbol representing the container. Count the number of containers. A total of containers of soup are needed for 15 people.

4 5.4 Drawing Double Number Lines to Solve Problems Involving Ratios A double number line is a model that is made up of two number lines used to represent the equivalence of two related numbers. Each interval on the number line has two sets of numbers and maintains the same ratio. Kelly used 7 balls of yarn to knit 3 sweaters of the same size. You can complete a double number line to determine equivalent ratios and determine how many balls of yarn are needed for 12 sweaters. Kelly would need 28 balls of yarn to make 12 sweaters. 5.5 Completing Ratio Tables A ratio table shows how two quantities are related. Nina is mixing red paint and yellow paint to make orange paint. The shade of orange Nina wants to make is made by mixing 2 parts red paint to 5 parts yellow paint. You can complete a ratio table to determine the amount of paint Nina needs to make 28 pints of orange paint. Amount of Orange Paint 7 pints 14 pints 21 pints 28 pints Red Paint 2 pints 4 pints 6 pints 8 pints Yellow Paint 5 pints 10 pints 15 pints 20 pints

5 5.6 Graphing Equivalent Ratios Equivalent ratios can be represented on a coordinate plane. Carmen is driving to the beach for a summer vacation. She is traveling at a steady rate of 60 miles per hour. The table shows the ratio time : distance. Time (hours) Distance (miles) The coordinate plane also shows the ratio time : distance. The graph can be used to determine other equivalent ratios. From the graph you can see that Carmen traveled 120 miles after 2 hours.

6 5.7 Reading and Interpreting Ratios from Graphs Equivalent ratios can be represented on a coordinate plane. The graph shows the cost of bananas on sale at a local grocery store. Write each point on the graph as the ratio of cost : pound. $0.50 : 1 pound of bananas $1.00 : 2 pounds of bananas $2.00 : 4 pounds of bananas Eight pounds of bananas would cost $4.00.

7 5.8 Unit Rates A unit rate is a comparison of two measurements in which the denominator has a value of one unit. Pedro is comparing brands of cereal at the grocery store. Brand A: 20 oz box for $3.49 Brand B: 18 oz box for $2.89 Brand C: 22 oz box for $3.15 The unit rate for Brand A is The unit rate for Brand B is The unit rate for Brand C is, or approximately $0.17 per ounce., or approximately $0.16 per ounce., or approximately $0.14 per ounce. Brand C has the lowest unit rate price per ounce and is the best buy.