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Example 2-3c Objective Solve proportions by using cross products

Example 2-3c Vocabulary Proportion An equation that shows that two ratios are equivalent

Example 2-3c Vocabulary Cross products The products of the terms on the diagonals when two ratios are compared. If the cross products are equal, then the ratios form a proportion

Lesson 2 Contents Example 1Solve a Proportion Example 2Solve a Proportion Example 3Use a Proportion to Solve a Problem

Example 2-1a Cross multiply and write equation horizontal Solve x = Write proportion 4x=5(28) 4x = Ask “what is being done to the variable?” The variable is being multiplied by 4 Do the inverse on both sides of the equal sign 1/3 Bring down 4x = Combine “like” terms 140

Example 2-1a Solve x = Bring down 4x = 140 4x=5(28) 4x = 1/ x = 140 Using the fraction bar, divide both sides by Combine “like” terms 1  x = 35 Use the Identity Property to multiply 1  x x = 35Answer:

Example 2-1b Answer: x = 24 Solve 1/3

Example 2-2a Solve 1.0 y = 1.2y=1.0(0.6) 1.2y = Write proportion 2/3 Cross multiply and write equation horizontal Bring down 1.2y = Combine “like” terms 0.6 Ask “what is being done to the variable?” The variable is being multiplied by 1.2 Do the inverse on both sides of the equal sign

Example 2-2a Solve 1.0 y = 1.2y=1.0(0.6) 1.2y = 2/3 0.6 Bring down 1.2y = y = 0.6 Using the fraction bar, divide both sides by Combine “like” terms 1  y = 0.5 Use the Identity Property to multiply 1  y y = 0.5Answer:

Example 2-2b Answer: m = 3 Solve 2/3

Example 2-3a SPORTS Out of the 40 students in a gym class, 12 rate soccer as their favorite sport. Based on this result, how many of the 4,200 students in the community will rate soccer as their favorite sport? 3/3 First, make a ratio with the students in gym class Set up ratio Favorite sport as soccer is the part which will be the numerator soccer Total will be the denominator total

Example 2-3a SPORTS Out of the 40 students in a gym class, 12 rate soccer as their favorite sport. Based on this result, how many of the 4,200 students in the community will rate soccer as their favorite sport? 3/3 soccer total 12 will be the numerator will be the total 40

Example 2-3a SPORTS Out of the 40 students in a gym class, 12 rate soccer as their favorite sport. Based on this result, how many of the 4,200 students in the community will rate soccer as their favorite sport? 3/3 soccer total The second ratio will be used with the students in the community Define the variable with how many will rate soccer x k The total will be the 4,200 students in the community 4,200 Place an = sign between the ratios to make a proportion =

Example 2-3a 3/3 soccer total x k 4,200 = Cross multiply and write equation horizontal 40x =12(4,200) Bring down 40x = Combine “like” terms 40x =50,400 Ask “what is being done to the variable?” The variable is being multiplied by 40 Do the inverse on both sides of the equal sign

Example 2-3a 3/3 soccer total x k 4,200 = 40x =12(4,200) 40x =50,400 Bring down 40x = 50,400 40x = 50,400 Using the fraction bar, divide both sides by Combine “like” terms 1  x = 1,260 Use the Identity Property to multiply 1  x x = 1,260 Add dimensional analysis How many of the 4,200 students in the community will rate soccer as their favorite sport? rate soccer as favorite Answer:

Example 2-3c BUSINESS Out of 50 people in one department of a large corporation, 35 stated that they enjoy their job. Based on this result, how many of the 2,400 employees of this corporation can be expected to say that they enjoy their job? Answer: x = 1,680 employees enjoy their job * 3/3

End of Lesson 2 Assignment Lesson 10:2Algebra: Solving Proportions All