Enrichment. Which rectangle in Exercise 1 is most nearly a golden rectangle?

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1 8- Ratios and Rectangles. Use a centimeter ruler to measure the width and the length of each rectangle. Then express the ratio of the width to the length as a fraction in simplest form. A B C A: width 2 cm length 4 cm ratio 2 D E 2. Similar figures have the same shape, but not necessarily the same size. Two rectangles are similar if the ratio of the width to the length is the same for each. Which rectangles in Exercise are similar? C and D 3. For centuries artists and architects have used a shape called the golden rectangle because people seem to find it most pleasant to look at. In a golden rectangle, the ratio of the width to the length is a little less than 5. 8 Which rectangle in Exercise is most nearly a golden rectangle? Glencoe/McGraw-Hill 57 and Connections, Course

2 8-2 Using Proportions to Change Units of Measure When you need to change units of measure gallons to quarts, ounces to pounds, and so on do you sometimes forget whether to multiply or divide? Almost everyone gets confused at one time or another, and so it is a good idea to learn an alternative method. Whether you are changing from smaller to larger units or from larger to smaller, you can start by writing a proportion. Here s how. 4 gal? qt Use the fact that gal 4 qt. gallons 4 q 4 gallons quarts quarts q 4 4 q 56 So, 4 gal 56 qt. 4 qt? gal gallons quarts 4 g g 4 4g 3 2 g So, 4 qt 3 2 gal. gallons quarts Write a proportion that can be used to change each measurement.. 24 ft? in i oz? lb 6 p cm? m 00 m in.? ft 2 f c? fl oz 8 f L? ml, m Complete yd ft 8. 9 pt qt 9. 2 oz lb qt pt. 49 km m L ml mg g mm cm Glencoe/McGraw-Hill 58 and Connections, Course

3 8-3 Planning a Room Before moving furniture into a room, many people plan an arrangement by making a scale drawing. This makes it possible to find the best arrangement for the room without actually moving heavy furniture. For each piece of furniture, actual measurements are given. Compute scale measurements using the scale 2 inch foot.. bed: 6 feet long, 3 feet wide 3 4 inches long, 2 2 inches wide 2. bedside table: 2 feet long, 2 feet wide 3 4 inch long, 3 4 inch wide 3. bookcase: 3 2 feet long, foot wide 3 4 inches long, 2 inch wide 4. desk: 42 inches long, 8 inches wide 3 4 inches long, 3 4 inch wide 5. chest of drawers: 39 inches long, 8 inches wide 5 8 in. long, 3 4 in. wide 6. Use your answers from Exercises -5. Show how the furniture might be arranged in the bedroom shown below. WINDOW Scale: 2 inch = foot DOOR Glencoe/McGraw-Hill 59 and Connections, Course

4 8-4 Percent and the Hundred Chart The chart at the right shows all the whole numbers from through 00. This page challenges you to connect percents to what you know about number theory factors, multiples, divisibility, and so on. Whenever you can, use a pattern in the chart to make your work easier. For example, the multiples of 5 make up two columns of the chart the fifth column and the tenth. So, 20 out of 00 numbers, or 20% of the numbers, are multiples of Use the hundred chart above. Find the percent of the numbers that:. are even numbers. 50% 2. are odd numbers. 50% 3. are multiples of are divisible by are divisible by 2 and divisible by are multiples of. 6. are divisible by are divisible by 2 and divisible by contain only even digits.. have digits whose sum is contain the digit are factors of are prime. 0. contain only odd digits. 2. have digits whose sum is contain the digit are factors of are composite. Glencoe/McGraw-Hill 60 and Connections, Course

5 8-5 Percent and Per Mill A percent is a ratio that compares a number to percent 83% 0.83 A ratio that compares a number to,000 is called a per mill. Just like percent, the ratio per mill has a special symbol,. 83, per mill Throughout the world, the ratio that is used most commonly is percent. However, in some countries, you will find both ratios in use. Express per mill as a decimal Express each per mill as a fraction in simplest form , Express each fraction as a per mill , CHALLENGE In the United States, you will sometimes find the mill used as a monetary unit. What amount of money do you think is represented by mill? Glencoe/McGraw-Hill 6 and Connections, Course

6 8-6 Estimating Sales Tax Many states charge a on purchases. To be sure that you have enough money, you should be able to estimate the amount of and the total cost of an item. For example, this is how you can estimate the total cost of the purchase shown at the right. $0.95 rate: 6.75% First, round the Multiply the rounded numbers. price and the rate. dollars $0.95 $ 7 per dollar 7% means 7 per 00, 6.75% 7% or 7 per dollar. So, the total cost is close to $ 80, or $.80. Estimate the total cost of each purchase.. 2. $6.98 $ $ rate: 5% $ rate: 5.75% $ rate: 4.255% $ rate: 6 2 % $ rate: 8 4 % Will $50 be enough money to make each purchase? $ rate: 6.25% $46.99 rate: 3% rate: 4.75% rate: 8 4 % 0. CHALLENGE The price marked on a cassette tape is $8.99. With the, the total cost of the tape is $9.37. Estimate the rate. Glencoe/McGraw-Hill 62 and Connections, Course

7 8-7 Using 00%, 0%, and % Many people think of 00%, 0%, and % as key percents. 00% is the whole. 0% is one tenth of the whole. % is one hundredth of the whole. 00% of 24 24, or 24. 0% of , or 2.4. % of , or Find the percent of each number.. 00% of 8,000 8, % of 8, % of 8, % of % of % of % of % of % of % of 2. % of % of 7 This is how you can use the key percents to make some computations easier. 3% of 60 =?. 5% of 24 =?. % of 60 = 6., 0% of 24 = 2.4, so 3% of 60 = 3 6., or 8.3. so 5% of 24 = 2 of 2.4, or.2. Find the percent of each number. 3. 2% of % of 2, % of % of % of % of 4,0 9. 5% of % of % of % of % of % of 28 Glencoe/McGraw-Hill 63 and Connections, Course