1. ALGEBRA READINESS LESSON 6-5 Warm Up Lesson 6-5 Warm-Up

2. ALGEBRA READINESS LESSON 6-5 Warm Up Lesson 6-5 Warm-Up

3. ALGEBRA READINESS “Proportions” (6-5) 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: Example: Work: = abab c d for b ≠ 0 and d ≠ 0 60 = 60 

4. ALGEBRA READINESS “Proportions” (6-5) 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

5. ALGEBRA READINESS Do and form a proportion? Explain. 4949 8 18 4949 8 18 gallons Write as a proportion. 4 18 = 9 8 Find out if the cross products are equal. Because the cross products are equal, = form a proportion. 4949 8 18 Proportions LESSON 6-5 Additional Examples 72 = 72  The cross products are equal

6. ALGEBRA READINESS Use cross products to solve the proportion -. w 4.5 6565 w 4.5 = - 6 5 w(5) = (4.5)(–6)Write cross products. 5w = –27 Simplify. 5w55w5 = –27 5 Divide each side by 5. w = –5.4 Simplify. Proportions LESSON 6-5 Additional Examples (-5.4) 4.5 = –6 5 Replace w with -5.4 and change both fractions into decimals by dividing bottoms into tops. Check: -1.2 = –1.2  True Statement (Both sides equal one another.)

7. ALGEBRA READINESS The fixed rate of conversion is 1 euro = 0.7876 Irish pounds. How many euros would you receive for 125 Irish pounds? You would receive 158.71 euros. Let x = the number of euros. = 1 0.7876 x 125 Write the proportion. 0.7876 x = 1 125 Write the cross products. = 0.7876 x 0.7876 125 0.7876 Isolate the variable. Use the Division Property of Equality. x ≈ 158.71 Simplify. Round to the nearest hundredth. Proportions LESSON 6-5 Additional Examples known ratiounknown ratio euro1 x Irish pounds0.7876 125

8. ALGEBRA READINESS Solve each proportion. 2. = 3. = 4.Suppose the exchange rate for dollars to Indian rupees is 0.02. How many rupees should you receive for $100? w 12 3434 20 r 4545 9 25 5,000 rupees 1. Is proportional to ? Explain. 5858 10 24 No; the fractions are not equal. Proportions LESSON 6-5 Lesson Quiz