PRE-ALGEBRA

Lesson 6-2 Warm-Up

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 

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

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

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 =

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 Test by writing as a proportion Write cross products. Proportions LESSON 6-2 Additional Examples

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 Known Unknown381 x = Proportion x 100 x = Cross products are equal. 100x = 381 (115) Simplify. = Divide both sides by x (115) 100 x = 438 Simplify. 381 nautical miles equals 438 statute miles Proportions (6-2) 1

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 (25) rods is about fathoms. Proportions LESSON 6-2 Additional Examples 1 4 RodsFathoms Known Unknown25 d

PRE-ALGEBRA Solve each proportion Does each pair of ratios form a proportion? Explain nautical miles equals about 115 statute miles. About how far in nautical miles is 50 statute miles? Round to the nearest whole number. a = 6x6x = = = Yes; the cross products are equal. No; the cross products are not equal. about 43 nautical miles Lesson Quiz Proportions LESSON 6-2