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Splash Screen

Solve proportions. proportional proportion cross product Main Idea/Vocabulary

KC 1

Identify Proportional Relationships MATH Before dinner, Mohammed solved 8 math problems in 12 minutes. After dinner, he solved 2 problems in 3 minutes. Is the number of problems he solved proportional to the time? Method 1 Compare unit rates. Since the unit rates are equal, the number of math equations is proportional to the time in minutes. Example 1

Identify Proportional Relationships Method 2 Compare ratios by comparing cross products. ? 8 × 3 = 12 × 2 Find the cross products. ? 24 = 24 Multiply.  Answer: Since the cross products are equal, the number of math equations is proportional to the time in minutes. Example 1

Determine if the quantities $30 for 12 gallons of gasoline and $10 for 4 gallons of gasoline are proportional. ? 120 120 A. yes B. no 30 10 = 12 4 A B Example 1

5x = 8 ● 18 Find the cross products. 5x = 144 Multiply. Solve a Proportion Write the proportion. 5x = 8 ● 18 Find the cross products. 5x = 144 Multiply. Divide each side by 5. x = 28.8 Answer: x = 28.8 Example 2

9 * 18 = 15k 162 = 15k A. k = 9.4 B. k = 12 C. k = 10.8 D. k = 18.6 15 15 10.8 = k A B C D Example 2

3.5 ● n = 14 ● 6 Find the cross products. 3.5n = 84 Multiply. Solve a Proportion Write the proportion. 3.5 ● n = 14 ● 6 Find the cross products. 3.5n = 84 Multiply. Divide each side by 3.5. n = 24 Simplify. Answer: The solution is 24. Example 3

4.6 * 5 = 4w 23 = 4w A. w = 5.25 B. w = 5.5 C. w = 5.75 D. w = 6.25 4 4 5.75 = w A B C D Example 3

length Write a proportion. width FLAGS According to specifications, the ratio of the length of the U.S. flag to its width must be 1.9 to 1. How long must a U.S. flag be if it is designed to have a width of 2.5 feet? length Write a proportion. width Find the cross products. Multiply. Answer: The length of a U.S. flag having a width of 2.5 feet must be 4.75 feet. Example 4

SCHOOL The ratio of boys to girls at Blue Hills Middle School is 4 to 5. How many girls attend the school if there are 96 boys? A. 72 girls B. 108 girls C. 120 girls D. 148 girls A B C D Example 4

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