University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2021
Views:

155

Pages:

26
Author:

Tobsuchtbvow

8.1 Exploring Ratio and Proportion Ratio – a comparison of 2 numbers measured in the same units  The ratio of x to y can be written: ◼ x to y ◼ x:y x y   Because a ratio is a quotient, its denominator cannot be zero. Ratios are expressed in simplified form. ◼ 6:8 is simplified to 3:4. Ex. 1: Simplifying Ratios  a. Simplify the ratios: 12 cm 4m b. 6 ft 18 in Ex. 1: Simplifying Ratios  a. Simplify the ratios: 12 cm 4m 12 cm 12 cm 4m 4∙100cm 12 400 3 100 Ex. 1: Simplifying Ratios  Simplify the ratios: b. 6 ft 18 in 6 ft 6∙12 in 18 in 18 in. 72 in. 18 in. 4 1 Ex. 2: Using Ratios  The perimeter of rectangle ABCD is 60 centimeters. The ratio of AB: BC is 3:2. Find the length and the width of the rectangle B C w A l D Ex. 2: Using Ratios  SOLUTION: Because the ratio of AB:BC is 3:2, you can represent the length of AB as 3x and the width of BC as 2x. B C w A l D Solution: Statement 2l + 2w = P 2(3x) + 2(2x) = 60 6x + 4x = 60 10x = 60 x=6 Reason Formula for perimeter of a rectangle Substitute l, w and P Multiply Combine like terms Divide each side by 10 So, ABCD has a length of 18 centimeters and a width of 12 cm. Ex. 3: Using Ratios  The measures of the angles in ∆JKL are in the ratio 1:2:3. Find the measures of the angles. Solution: Statement x°+ 2x°+ 3x° = 180° 6x = 180 x = 30 Reason Triangle Sum Theorem Combine like terms Divide each side by 6 So, the angle measures are 30°, 2(30°) = 60°, and 3(30°) = 90°. Ex. 4: Using Ratios  The ratios of the side lengths of ∆DEF to the corresponding side lengths of ∆ABC are 2:1. Find the unknown lengths. F C 3 in. A D 8 in. E B Ex. 4: Using Ratios  SOLUTION: ◼ ◼ ◼ ◼ DE is twice AB and DE = 8, so AB = ½(8) = 4 Use the Pythagorean Theorem to determine what side BC is. DF is twice AC and AC = 3, so DF = 2(3) = 6 EF is twice BC and BC = 5, so EF = 2(5) or 10 F C 3 in. A 4 in a2 + b2 = c2 D 8 in. E 32 + 42 = c2 9 + 16 = c2 25 = c2 5=c B Using Proportions    Proportion - An equation that sets two ratios equal to one another If using an extended proportion – a:b:c = d:e:f Means Extremes = The numbers a and d are the extremes of the proportions. The numbers b and c are the means of the proportion. Properties of proportions 1. If CROSS PRODUCT PROPERTY. The product of the extremes equals the product of the means.  = , then ad = bc Properties of proportions 2. RECIPROCAL PROPERTY. If two ratios are equal, then their reciprocals are also equal. If  = , then b a = Ex. 5: Solving Proportions 4 x x = = 5 7 28 5 Ex. 5: Solving Proportions 3 2 = y+2 y y = 4 8.2 – Problem Solving With Proportions Ex: Determine values of x and y: