Ratios (pages )

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1 A Ratios (pages 80 8) You can compare two quantities by using a ratio. A common way to express a ratio is as a fraction in simplest form. If the two quantities you are comparing have different units of measure, this kind of ratio is called a rate. A rate is in the form of a unit rate when the denominator is. Writing a Rate and a Unit Rate A rate is a ratio of two measurements that have different units. To write a ratio as a unit rate, divide the numerator and denominator by the same number to rewrite the ratio as a fraction with a denominator of. A Write the ratio sixth-graders out of students in three different ways. Express this ratio as a fraction in simplest form. As a fraction As a ratio : In words to Another way is in the problem: out of. in simplest form is. Express the ratio pencils for $ as a unit rate. How many pencils can you buy for $? pencils Write the ratio as a fraction. $ To rewrite the fraction with a denominator of, divide numerator and denominator by. pencils pencils $ $ or pencils for $. Write the ratio 7 sodas out of 0 are. Express the ratio $0 for rides as a sugar free in three different ways. rate. What is the cost for one ride? HINT: Write the numbers in the same order as HINT: Divide numerator and denominator by. they appear in the problem. Write each ratio as a fraction in simplest form.. 4 out of 6 papers are typed out of 0 horses are white. 7 blue bicycles out of bicycles 6. 4 watermelons out of 0 melons Write each ratio as a unit rate. $.0 for bottles of juice bracelets for $ Standardized Test Practice If milk costs $.0 for gallons, how much does it cost per gallon? A $.00 $0.0 C $.7 D $.0 7 $0 Answers:. 7:0, 7 to 0;. or $.90 per ride rides 4 $0.0 per bottle of juice $.00 per bracelet 9. C 69 Mathematics: Applications and Concepts, Course

2 A Solving Proportions (pages 86 89) A proportion is an equation that shows that two ratios are equivalent. The general form of a proportion is, where neither b nor d is equal to zero. The cross products of a proportion are ad and bc. Property of The cross products of a proportion are equal. a c Proportions If, then ad bc. b d a b c d A Use cross products to find out whether this pair of ratios forms a proportion., 9 9 Does? Are the cross products equal? Does 9? Yes, because is a proportion because the cross products are equal.. Use cross products to determine whether this pair of ratios forms a 0. proportion., Solve the proportion for y. Write the cross products. 7 y 4 7y 4 7 7y 7 6 y The solution is 6. 7 y Divide each side of the equation by 4 p 0 HINT: Set the cross products equal to each other and solve for p.. Solve the proportion. Determine whether each pair of ratios forms a proportion..,,., 6., Solve each proportion. 6 0 x 4 4 w z 8 d 0.. Standardized Test Practice The home economics class is making a casserole. They need eggs for casserole. How many eggs do they need for 4 casseroles? A 9 C D 0 Answers:. yes.. yes yes. no 6. no Mathematics: Applications and Concepts, Course

3 A Scale Drawings and Models (pages 9 9) A scale drawing is exactly the same shape as an object, but the drawing may be larger or smaller than the real object. Reading a Scale Drawing The scale written on the drawing or model gives the ratio that compares the measurements on the drawing to the actual measurements of the object. Use the scale of the drawing for one of the ratios and the known and unknown measurements for the other ratio. Write a proportion and solve it for the unknown measurement. A A model car has a scale of :6. A window on the model measures of a meter. What will this same window measure on the real car? 6 meter Write a proportion. 6 meter Find cross products. The doorway of an actual house measures ft wide. How wide will the doorway in a model house be if the scale is ft in.? ft ft in. w so x w 6 or w 6. The model doorway will be 6 inches wide. meter Solve. The actual window measures meter.. The scale of a map is inch miles.. A line on a scale drawing of a building The distance on the map between two measures inches. The same length on cities is 7 inches. How many miles apart the actual building is yards. What is are they? the scale of the drawing in simplest form? x inches HINT: Write a proportion using as one ratio. HINT: One ratio is and the other is yard.. Transportation The oldest monorail system in the world is in Wuppertal, Germany. Its track is miles long. If you wanted to build a model of the track that has a scale of inch 0. miles, how long would the model track be?. Standardized Test Practice Mavis and Reese want to rearrange the furniture in their living room. efore they move the furniture, they make a model. The scale for the model is inch feet. If their sofa is actually 6 feet long, how long is the model of the sofa? A inches 4 inches C feet D 4 feet Answers:. 7 miles. inches to yard. 7 inches A 7 Mathematics: Applications and Concepts, Course

4 A Modeling Percents (pages 9 97) A percent is a ratio that compares a number to 00. Since percent means out of one hundred, you can use a 0 0 grid to model percents. A Model 0% Model 6% 0% 0% means 0 out of 00. So, shade 0 of the 00 squares. 6% 6% means 6 out of 00. So, shade 6 of the 00 squares. Model each percent.. 8%. 4%. 7% 6%. % 6. 90% Identify each percent modeled At the school cafeteria, 6% of the students drink soda. Make a model to show 6%. Use a model to show which is smaller, 8% or 77%... Standardized Test Practice In the eighth grade class, 6% exercise to 4 hours per week, % exercise to hours per week, % exercise to hours per week, 6% exercise 0 to hours per week. What amount of time spent exercising has the least percentage of students? A to 4 hours to hours C to hours D 0 to hours Answers: 6 See Answer Key % 8% 9. % 0. 7%. 6%. 8% See Answer Key. 77% is smaller.. A 7 Mathematics: Applications and Concepts, Course

5 A Percents and Fractions (pages ) A percent is a ratio that compares a number to 00. Writing To write a percent as a fraction, follow these steps. a Percent as Write the percent as a fraction with a denominator of 00. a Fraction Simplify the fraction. Writing a Fraction as a Percent To write a fraction as a percent, follow these steps. Set up a proportion with the fraction as one ratio and x 00 as the other. Find the cross products and divide to solve for x. The fraction is equal to x percent. A Write 7% as a fraction in simplest form. 7 7% is 00. 7% 7% 7 00 Divide numerator and denominator by the common factor of. Write 4 4 x 00 as a percent. Write a proportion.,400 x Find the cross products.,400 x Divide to solve for x. 4 6 x, so 6% 0. Write as a percent.. Write 0% as a fraction in simplest form. Write each percent as a fraction in simplest form.. % 0%. 0% 6. 4% 60% 9% 9. 6% 0. 8% Write each fraction as a percent Standardized Test Practice Write 4% as a fraction in simplest form. 8 A C D Answers:. 6% %. 60 %. 7% 44%. 60% 6. 90% 0% 40% 9. D 7 Mathematics: Applications and Concepts, Course

6 A Percents and Decimals (pages ) You have seen that percents can be written as fractions. Percents can also be written as decimals, and decimals can be written as percents. Writing a To write a percent as a decimal, follow these steps. Percent as Rewrite the percent as a fraction with a denominator of 00. a Decimal Write the fraction as a decimal. Writing a To write a decimal as a percent, follow these steps. Decimal as Rewrite the decimal as a fraction with a denominator of 00. a Percent Write the fraction as a percent. A Write 6% as a decimal. Write 0.84 as a percent % which is which is 84% C Write 0.% as a decimal. D Write 0.0 as a percent % Multiply by to get rid of ,000 Divide numerator and denominator by 0. the decimal in the numerator. 0. which is 0.% which is ,000. Write 0.4% as a decimal.. Write 0.09 as a percent. Write each percent as a decimal.. 7% 8%. 46% 6. % 7% 9% 9. % 0. % Write each decimal as a percent Standardized Test Practice In a taste test at a grocery store, people were given a chip with salsa on it and asked if they would buy the salsa. Of those who answered, 67% said yes. Express this percent as a decimal. A C 0.4 D 0.0 Answers: % %. 87%. % 6%. 9% 6. % 7% 6.% Mathematics: Applications and Concepts, Course

7 A Percent of a Number (pages 409 4) To find the percent of a number, you can change the percent to a fraction or to a decimal, and then multiply by the number. You can also use a calculator. Finding the Percent Method : Change the percent to a fraction and multiply. of a Number Method : Change the percent to a decimal and multiply. A Find % of 6. Find 0% of % 0% 00 which is % of 60 is 6. % of 6 is Notice that when you take a percent greater than 00 of a number, the answer is greater than the number.. Find 0.% of 0.. Find 7% of HINT: Rewrite the percent as and HINT: Rewrite 7% as or 0.0 then as,000 or Then multiply. Find the percent of each number.. % of 0 40% of 6. % of % of 80% of 0 7% of % of % of 4. % of 00. 0% of 0. 0% of 64 90% of 60. What is 90% of 70? 6. Find 80% of 80. Games 7% of the games sold at a game store are board games. If the game store sold 6 games in one day, how many of those games were board games? anking Catalina s mother went to the bank to take out $ She asked for 0% of the $40.00 in dollar bills. How much money did she receive in dollar bills?. 9. Standardized Test Practice What is 0% of 90? A 7 0 C D 4 Answers: $ A 7 Mathematics: Applications and Concepts, Course

8 A Estimating with Percents (pages 4 47) When a problem asks for about how many, the word about tells you that an exact answer is not needed. You can estimate the answer. Common Equivalents Memorizing these common equivalents will help you estimate. for Percents and Often you can think of money to help you remember these. Fractions For example: A quarter is $0. which is of a dollar. 0% % % 6 % 40% 0% 7 % % 60% 7% 6 % 66 % 4 80% 00% 87 % % A Estimate 6% of. Estimate 9% of 4. The table shows that 60% is. Multiply to estimate. 0% is 0. Multiply to estimate.. So 6% of is about. 0. So 9% of 4 is about. Estimate 88% of 6. Estimate 7% of 7 HINT: Multiply to find of 6 HINT: Multiply to find 6 of Estimate each percent.. 6% of 40 8% of 0. 48% of % of 7% of 04 80% of 9. 0% of % of 9. About how much is 48% of?. School There are students in Donovan s class. About % of his classmates are older than him. Estimate how many of Donovan s classmates are older than him... Standardized Test Practice Tyler s family gets a busy signal % of the time they try to log on to the Internet. If they tried to log on 0 times in one day, about how many times would they get a busy signal? A C 4 D Answers: Sample answers are given A 76 Mathematics: Applications and Concepts, Course

9 Chapter 0 Review Ratio Treasure Use the treasure map to answer the following questions. Treasure cm Windmill N cm 4 cm cm = m You are here.. You re using the map to find a hidden treasure. If you walk directly to the treasure, how far will you walk?. To make sure you find the treasure, you decide to use a compass to walk north to the windmill first, then east to the treasure. How far are you from the windmill? How far is the windmill from the treasure?. Suppose instead that you are 60 meters south of a boulder, and the boulder is 80 meters west of a buried treasure. Draw a treasure map with a scale of cm 0 m. e sure to label distances on your map according to the scale. Answers are located on p Mathematics: Applications and Concepts, Course