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

2024
Views:

49

Pages:

2
Author:

Delphinixxc3

Question 1 Write the reciprocal of each of the following: a. 1 8 8 1 b. 12 5 5 12 c. 1 2 2 1 d. 1 1 2 1 2 1 e. 2 3 4 2 4 3 f. 6 6 Answer 1 a) Reciprocal of 1 8 8 1 is 8. b) Reciprocal of 12 5 5 12 is 5 12 12 5 . c) Reciprocal of 1 2 2 1 is 2. d) Convert 1 1 2 1 2 1 to an improper fraction: 1 1 2 = 3 2 1 2 1 = 2 3 , so the reciprocal is 2 3 3 2 . e) Convert 2 3 4 2 4 3 to an improper fraction: 2 3 4 = 11 4 2 4 3 = 4 11 , so the reciprocal is 4 11 11 4 . f) Reciprocal of 6 6 (which is 6 1 1 6 ) is 1 6 6 1 . Question 2 What is the improper fraction for 9 6 6 9 ? Answer 1 9 6 6 9 is an improper fraction, but it can be simplified: Find the common factor of 3: 9 6 = 3 × 3 2 × 3 = 3 2 6 9 = 2×3 3×3 = 2 3 So, the simplified improper fraction is 3 2 2 3 . Question 3 Evaluate − 8 + ( − ( 1 8 ) ) −8+(−( 8 1 )). Answer 1 Rewrite − 8 −8 as − 64 8 8 −64 : − 8 = − 64 8 −8= 8 −64 Then add − 1 8 8 −1 : − 8 + ( − 1 8 ) = − 64 − 1 8 = − 65 8 −8+(− 8 1 )= 8 −64−1 = 8 −65 So, the answer is − 65 8 8 −65 . Question 4 One cake recipe calls for 2 3 3 2 cup of sugar. Another recipe calls for 1 4 4 1 cup of sugar. How many cups of sugar are needed to make both cakes? Answer 1 Add the two amounts of sugar: 2 3 + 1 4 3 2 + 4 1 . Find the Least Common Denominator (LCD), which is 12. 2 3 = 8 12 and 1 4 = 3 12 3 2 = 12 8 and 4 1 = 12 3 Add the fractions: 8 12 + 3 12 = 11 12 12 8 + 12 3 = 12 11 So, the total amount of sugar needed is 11 12 12 11 cups.