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Splash Screen. Five-Minute Check (over Lesson 6–5) Main Idea and Vocabulary Key Concept: Proportion Example 1: Identify Proportional Relationships Example 2: Solve a Proportion Example 3: Solve a Proportion Example 4: Real-World Example. Lesson Menu. Solve proportions.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 6–5) Main Idea and Vocabulary Key Concept: Proportion Example 1: Identify Proportional Relationships Example 2: Solve a Proportion Example 3: Solve a Proportion Example 4: Real-World Example Lesson Menu

  3. Solve proportions. • Cross Product: is the product of the numerator of one ratio and the denominator of the other ratio. • Proportion: an equation stating that two ratios are equivalent. Since rate are types of ratios, they can also form proportions. • Proportional: Two quantities are proportional, if they have a constant rate or ratio. Main Idea/Vocabulary

  4. KC 1

  5. Identify Proportional Relationships MATHBefore 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

  6. ? ? 8 × 3 = 12 × 2 Find the cross products. Identify Proportional Relationships Method 2 Compare ratios by comparing 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

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

  8. Steps to solve proportions with variables: You can use cross products to solve a proportion that contains a variable. Example: n = 10 9 15 Step 1: n = 10Make sure your proportion issetup 9 15 and ready to solve forthe variable. Step 2: 15 x n = 9 x 10 Use cross multiplication to (15n = 90) setup a one-step equation. Step 3: 15n = 90 is now setup into a one-step division equation to solve for n. Remember to balance the equation by dividing both sides of the equal sign by the value that is attached to the variable. Step 4: n = 6 Solve by showing what the variable equals and plugging the value back into the original proportion to check your answer.

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

  10. A B C D A.k = 9.4 B.k = 12 C.k = 10.8 D.k = 18.6 Example 2

  11. 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

  12. A B C D A.w = 5.25 B.w = 5.5 C.w = 5.75 D.w = 6.25 Example 3

  13. length Write a proportion.width FLAGSAccording 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? 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

  14. A B C D 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 Example 4

  15. End of the Lesson End of the Lesson

  16. Five-Minute Check (over Lesson 6–5) Image Bank Math Tools Scale Drawings Using Proportions Resources

  17. A B C D (over Lesson 6-5) Complete 640 cm = ■ m. Complete 0.05 m = ■ mm. Complete 894 mg = ■ g. Complete 124.5 kL = ■ L. Complete 65,000 mL = ■ L. The longest suspension bridge in the United States is the Verrazano–Narrows in the Lower New York Bay. It spans 1,298 meters. How many kilometers long is this bridge? Five Minute Check 1

  18. A B C D (over Lesson 6-5) Complete 640 cm = ■ m. A. 6,400 B. 64 C. 6.4 D. 0.64 Five Minute Check 1

  19. A B C D (over Lesson 6-5) Complete 0.05 m = ■ mm. A. 0.0005 B. 0.05 C. 5 D. 50 Five Minute Check 2

  20. A B C D (over Lesson 6-5) Complete 894 mg = ■ g. A. 0.894 B. 8.94 C. 89.4 D. 8,940 Five Minute Check 3

  21. A B C D (over Lesson 6-5) Complete 124.5 kL = ■ L. A. 1.245 B. 12.45 C. 12,450 D. 124,500 Five Minute Check 4

  22. A B C D (over Lesson 6-5) Complete 65,000 mL = ■ L. A. 6,500 B. 650 C. 65 D. 6.5 Five Minute Check 5

  23. A B C D (over Lesson 6-5) The longest suspension bridge in the United States is the Verrazano–Narrows in the Lower New York Bay. It spans 1,298 meters. How many kilometers long is this bridge? A. 1,298,000 km B. 129.8 km C. 12.98 km D. 1.298 km Five Minute Check 6

  24. End of Custom Shows

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