1. PRE-ALGEBRA

2. Lesson 6-2 Warm-Up

3. PRE-ALGEBRA “Proportions” (6-2) What is a “proportion”? What is the “extremes of the proportion”? What is the “means of the proportion”? What are “cross products”? Why do “cross products” work? proportion: equal ratios (in other words, equal fractions) Example: extremes of the proportion: the first cross product of a proportion. In the above proportion, the “extremes of the proportion” are a and d. means of the proportion: the second cross product of a proportion. In the above proportion, the “extremes of the proportion” are b and c. cross products: the product of the means equals the product of the extremes (in the above example, ad = bc). Rule: ad = bc Example: Show that =. = abab c d for b ≠ 0 and d ≠ 0 60 = 60  4545 12 15

4. PRE-ALGEBRA Solve =. 2727 y 14 Method 1: Multiplication Property of Equality = 2727 y 14 14= 14 2727 y 14 = y 28 7 4= y Proportions LESSON 6-2 Additional Examples

5. PRE-ALGEBRA (continued) Method 2: Cross products = 2727 y 14 2 14= 7 y 28= 7y 4= y = 28 7 7y77y7 Proportions LESSON 6-2 Additional Examples

6. PRE-ALGEBRA “Proportions” (6-2) How can you determine whether two ratios (fractions) are equal (form a proportion)? To determine whether two ratios form a proportion (in other words, are equal), test the cross products. If the cross products are equal, then the ratios form a proportion. If the cross products aren’t equal, the two fractions aren’t equal. Example:Do and form a proportion? : The cross products are equal, so =. 4545 12 15 4545 12 15

7. PRE-ALGEBRA Do the ratios and form a proportion? Explain. 105= 105 Simplify. Yes; the ratios do form a proportion. The cross products are equal. 3535 21 35 Test by writing as a proportion. 3535 21 35 3 35 5 21 Write cross products. Proportions LESSON 6-2 Additional Examples

8. PRE-ALGEBRA How do you solve a word problem using a proportion? You can always solve a words problem using a proportion if the problem involves four numbers (one of them is a variable) and two labels. To set up the proportion correctly, use a proportion table in which the two labels in the problem are on top and “known” and “unknown” are on side. Example: One hundred nautical miles (used by sailors and pilots) equal about 115 standard, or statute, miles (used by us). About how many statute miles equal 381 nautical miles. ? Method 1: Proportion Nautical MilesStatute Miles Known100 115 Unknown381 x = Proportion. 100 381 115 x 100 x = 381 115 Cross products are equal. 100x = 381 (115) Simplify. = Divide both sides by 100.. 100x 100 381 (115) 100 x = 438 Simplify. 381 nautical miles equals 438 statute miles. 1 23 20 1 Proportions (6-2) 1

9. PRE-ALGEBRA One hundred rods is about 275 fathoms. About how many fathoms is 25 rods? Let d = distance in fathoms. 100d = 275(25) Write cross products. d = 68.75A calculator may be useful. d = Divide each side by 100. 275(25) 100 25 rods is about 68.75 fathoms. Proportions LESSON 6-2 Additional Examples 1 4 RodsFathoms Known100 275 Unknown25 d

10. PRE-ALGEBRA Solve each proportion. 1.2. Does each pair of ratios form a proportion? Explain. 3.4. 5.100 nautical miles equals about 115 statute miles. About how far in nautical miles is 50 statute miles? Round to the nearest whole number. a 12 5656 = 6x6x = 3838 0.4 1.8 = 2929 21 50 = 14 25 1016 Yes; the cross products are equal. No; the cross products are not equal. about 43 nautical miles Lesson Quiz Proportions LESSON 6-2