University:
Purdue University
Course:
MA 15300 | College Algebra
Academic year:

2024
Views:

394

Pages:

3
Author:

Delphinixxc3

Question 1 What fraction is equivalent to 3 8 8 3 ? Answer 1 Multiply 3 8 8 3 by a fraction that is equivalent to 1. For example: 3 8 × 2 2 = 6 16 8 3 × 2 2 = 16 6 This gives the equivalent fraction 6 16 16 6 . Answer 2 Another example: 3 8 = 18 48 8 3 = 48 18 Answer 3 There are infinite fractions equivalent to 3 8 8 3 , such as: 6 16 , 9 24 , 12 32 16 6 , 24 9 , 32 12 Question 2 Which fraction is equivalent to 2 6 6 2 ? Answer 1 Multiply both the numerator and denominator by the same number. For instance: 2 6 = 4 12 , 8 24 , 10 30 6 2 = 12 4 , 24 8 , 30 10 Question 3 Reduce each fraction to lowest terms: 12 16 16 12 . Answer 1 Step 1: Find the GCD of 12 and 16, which is 4. Step 2: Divide both the numerator and denominator by 4: 12 16 = 12 ÷ 4 16 ÷ 4 = 3 4 16 12 = 16÷4 12÷4 = 4 3 Question 4 Write out the form of the partial fraction decomposition of the function. Answer 1 For part a): 𝑥 4 + 6 𝑥 6 + 7 𝑥 3 = 𝐴 𝑥 + 𝐵 𝑥 2 + 𝐶 𝑥 3 + 𝐷 𝑥 + 𝐸 𝑥 2 + 7 x 6 +7x 3 x 4 +6 = x A + x 2 B + x 3 C + x 2 +7 Dx+E For part b): 2 ( 𝑥 2 − 9 ) 2 = 2 ( ( 𝑥 + 3 ) ( 𝑥 − 3 ) ) 2 = 𝐴 𝑥 + 3 + 𝐵 𝑥 − 3 (x 2 −9) 2 2 = ((x+3)(x−3)) 2 2 = x+3 A + x−3 B Question 5 What is the simplest form of 64% as a fraction? Answer 1 64 100 100 64 Divide by the GCD of 4: 64 100 = 16 25 100 64 = 25 16 Answer 2 The simplest form of 64% is 16 25 25 16 .