LESSON Using Tables of Equivalent Ratios A table can be used to show the relationship between two quantities. You can use equivalent ratios to find a missing value in a table. EXAMPLE A The table shows the relationship between the number of green beads and the number of blue beads Mind uses when she makes bracelets. Green Beads Blue Beads How man blue beads does Mind use when she uses green beads Write the first two ratios as fractions. First ratio: green beads blue beads green beads Second ratio: blue beads Look for a pattern to see how the first ratio can be changed to the second, third, and fourth ratios. The ratios are equivalent. Etend the pattern to find the fifth ratio. Multipl each term in the first ratio b. green beads blue beads Mind uses blue beads when she uses green beads. DISCUSS Eplain how to find the number of green beads Mind uses when she uses blue beads. Domain : Ratios and Proportional Relationships
EXAMPLE B The table shows the relationship between the number of dog collars Travis can make and the number of hours he takes to make the collars. Number of Hours Number of Dog Collars Use ratios to complete the table. Decide what ratio the table shows. The table shows the ratio of hours to dog collars, or hours dog collars. Write equivalent ratios for the first ratio and the other ratios in the table. Compare the numerators of the equivalent ratios to decide how the terms are changing in each ratio. Think: So Think: So Think: So Use the equivalent ratios to complete the table. Number of Hours Number of Dog Collars CHECK How man dog collars can Travis make in hours Lesson : Using Tables of Equivalent Ratios
EXAMPLE C The table shows the relationship between the total number of games and the total number of weeks the games were plaed. Number of Games Number of Weeks Complete the table. Then list the ratios as ordered pairs. Decide what ratio the table shows and which ratio is known. Use the known ratio to find the first ratio in the table. The table shows the ratio of games to weeks, or games weeks. From the table, games were plaed in week. The ratio is. As one term in a ratio changes due to multiplication or division, the other unit changes in the same wa. Think:, so divide the denominator b. Use the first ratio to find the remaining ratios. Think:, so multipl the denominator b. Think:, so multipl the denominator b. Think:, so multipl the denominator b. TRY Use the equivalent ratios to complete the table. Number of Games Number of Weeks Write the ordered pair for the number of weeks needed to pla games. List the ratios as ordered pairs. An ordered pair is shown as (, ). The first coordinate, or the -coordinate, is the number of games. The second coordinate, or the -coordinate, is the number of weeks. The ordered pairs are (, ), (, ), (, ), (, ), and (, ). Domain : Ratios and Proportional Relationships
EXAMPLE D Use the ordered pairs from Eample C. Plot the ordered pairs on a coordinate plane. Decide what each ais represents on the coordinate plane. The horizontal ais is called the -ais. It shows the location of the -coordinate. In these ordered pairs, the -coordinate represents the number of games. The vertical ais is called the -ais. It shows the location of the -coordinate. In these ordered pairs, the -coordinate is the number of weeks. List the ordered pairs. (, ), (, ), (, ), (, ), (, ) Label the aes. Plot the first ordered pair. DISCUSS The first ordered pair is (, ). Start at the origin. Move units to the right. Then move up unit. Plot the point. Number of Weeks Number of Games Eplain how ou plotted the remaining ordered pairs. Plot the remaining ordered pairs. Number of Weeks Number of Games Lesson : Using Tables of Equivalent Ratios
Practice For questions, use equivalent ratios to complete each table.. Number of Hours Number of Miles.. Number of Teachers Number of Students Number of Words Number of Minutes HINT As one unit in a ratio changes, the other unit changes in the same wa. For questions and, use equivalent ratios to complete each table. List the ratios in each table as ordered pairs. Then plot the ordered pairs on the coordinate plane... Number of Das Inches of Snow REMEMBER To plot an ordered pair (, ), start at the origin. Move horizontall units and then verticall units. Inches of Snow Das Domain : Ratios and Proportional Relationships
For questions and, use the information given to complete the tables.. A recipe uses cups of cooked rice and cups of milk. Create a table of equivalent ratios that shows the relationship between the number of cups of rice and the number of cups of milk used for the recipe. Cups of Rice Cups of Milk. For ever sit-ups Ran does, he does push-ups. Create a table of equivalent ratios that shows the relationship between the number of sit-ups and the number of push-ups Ran does. Number of Sit-ups Number of Push-ups Complete the table and graph.. Ever das, students in a fitness class run miles. Use equivalent ratios to complete the table. Plot the corresponding ordered pairs on the coordinate plane. Number of Das Number of Miles Miles Das Solve.. REASON Which of the following ratios is not equivalent to the ratio Eplain.,,,. STRUCTURE Eplain how ou completed the table of equivalent ratios in question. Lesson : Using Tables of Equivalent Ratios