1. 4-4 Solving Proportions Vocabulary cross product

2. 4-4 Solving Proportions For two ratios, the product of the first term in one ratio and the second term in the other is a cross product. If the cross products of the ratios are equal, then the ratios form a proportion. 5 · 6 = 30 2 · 15 = 30 = 2525 6 15

3. 4-4 Solving Proportions You can use cross products to solve proportions with variables.

4. 4-4 Solving Proportions Use cross products to solve the proportion. Additional Example 1: Solving Proportions Using Cross Products 15 · m = 9 · 5 15m = 45 15m 15 = 45 15 m = 3 The cross products are equal. Multiply. Divide each side by 15 to isolate the variable. = m5m5 9 15

5. 4-4 Solving Proportions Check It Out: Example 1 Use cross products to solve the proportion. 6·14 = 7m;m = 12 = 6767 = m 14 84 7 A. B. 9·7 = 6r;r = 10.5 = 9696 = r7r7 63 6

6. 4-4 Solving Proportions It is important to set up proportions correctly. Each ratio must compare corresponding quantities in the same order. Suppose a boat travels 16 miles in 4 hours and 8 miles in x hours at the same speed. Either of these proportions could represent this situation. 16 mi 4 hr = 8 mi x hr 16 mi 8 mi = 4 hr x hr

7. 4-4 Solving Proportions Additional Example 2: Problem Solving Application If 3 binders of the same size take up 4 inches of space on a shelf, how much space will be needed for all 26 of these binders? 1 Understand the Problem Rewrite the question as a statement. Find the space needed for 26 binders. List the important information: 3 binders take up 4 inches of space.

8. 4-4 Solving Proportions 2 Make a Plan Set up a proportion using the given information. Let x represent the inches of space needed. 3 binders 4 inches = 26 binders x binders inches Additional Example 2 Continued

9. 4-4 Solving Proportions Solve 3 3434 = 26 x 3 · x = 4 · 26 3x = 104 3x 3 = 104 3 x = 34 2323 She needs 34 2323 inches for all 26 binders. Write the proportion. The cross products are equal. Multiply. Divide each side by 3 to isolate the variable. Additional Example 2 Continued

10. 4-4 Solving Proportions Look Back 4 3434 = 26 34 2323 4 · 26 = 104 3 · 34 2323 = 104 The cross products are equal, so 34 2323 is the answer Additional Example 2 Continued

11. 4-4 Solving Proportions Check It Out: Example 2A A stack of 33 CDs is 1.5 inches high. How many CDs would be in a stack that is 3.5 inches high? 1.5 33 = 3.5 x 1·5x = 33 x 3.5 x 77 CDs = 115.5 1.5 = x

12. 4-4 Solving Proportions Check It Out: Example 2B Maria drives at a constant speed for 3 hours and travels 175 miles. How far would she drive in 4.5 hours at the same speed? = 4.5 x 3x = 175. 4.5 x 262.5 miles = 787.5 3 = x 175

13. 4-4 Solving Proportions Lesson Quiz: Part I Use cross products to solve the proportion. 1. 25 20 = 45 t 2. x9x9 = 19 57 3. 2323 = r 36 4. n 10 = 28 8 t = 36 x = 3 r = 24 n = 35

14. 4-4 Solving Proportions Lesson Quiz: Part II 5.Carmen bought 3 pounds of bananas for $1.08. June paid $1.80 for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy? 5 pounds