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

2024
Views:

262

Pages:

3
Author:

Delphinixxc3

Question 1 In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. − 4 𝑥 32 𝑦 32y −4x Answer 1 Concept used: A fraction is considered simplified if there are no common factors in the numerator and denominator. The process of simplifying a fraction is called reducing the fraction. a) For reducing the fraction, we use the equivalent fractions property in reverse. We know that the equivalent fractions property is, 𝑎 𝑏 = 𝑎 ⋅ 𝑐 𝑏 ⋅ 𝑐 , b a = b⋅c a⋅c , where 𝑏 ≠ 0 b  =0, 𝑐 ≠ 0 c  =0, and 𝑎 , 𝑏 , 𝑐 a,b,c are numbers. Now, the reverse form of equivalent fractions property is, 𝑎 ⋅ 𝑐 𝑏 ⋅ 𝑐 = 𝑎 𝑏 , b⋅c a⋅c = b a , where 𝑐 c is the common factor in the numerator and denominator. Calculation: We are given the fraction − 4 𝑥 32 𝑦 32y −4x . From the above concept: Notice that 4 is a factor of both 4x and 32y. − 4 𝑥 32 𝑦 = − 𝑥 8 𝑦 32y −4x = 8y −x Factor the numerator and denominator: − 4 𝑥 32 𝑦 = − 𝑥 ⋅ 4 𝑦 ⋅ 4 ⋅ 8 32y −4x = y⋅4⋅8 −x⋅4 Remove the common factors. Hence the simplified form of the given fraction − 4 𝑥 32 𝑦 32y −4x is, as follows: − 𝑥 8 𝑦 8y −x . Question 2 List two equivalent fractions. 1 2 2 1 a) 3 6 6 3 b) 4 6 6 4 c) 5 8 8 5 d) 6 12 12 6 Answer 1 Step 1 Fraction is equivalent to 1 2 2 1 . Step 2 Option A: 3 6 = 1 2 6 3 = 2 1 Option D: 6 12 = 1 2 12 6 = 2 1 So, options A and D are correct. Question 3 What is the value of 1 − 4 + 9 − 16 + 25 − 36 + 49 − 64 + 81 − 100 1−4+9−16+25−36+49−64+81−100? Answer 1 Step 1 Given, 1 − 4 + 9 − 16 + 25 − 36 + 49 − 64 + 81 − 100 1−4+9−16+25−36+49−64+81−100 Step 2 Now, 1 − 4 + 9 − 16 + 25 − 36 + 49 − 64 + 81 − 100 1−4+9−16+25−36+49−64+81−100 = 1 + 9 + 25 + 49 + 81 − 4 − 16 − 36 − 64 − 100 =1+9+25+49+81−4−16−36−64−100 = ( 1 + 9 + 25 + 49 + 81 ) − ( 4 + 16 + 36 + 64 + 100 ) =(1+9+25+49+81)−(4+16+36+64+100) = 165 − 220 =165−220 = − 55 =−55 ∴ The value of 1 − 4 + 9 − 16 + 25 − 36 + 49 − 64 + 81 − 100 = − 55 1−4+9−16+25−36+49−64+81−100=−55 Question 4 Simplify: − 4 8 ÷ 16 64 8 −4 ÷ 64 16 Answer 1 Step 1 To simplify the given fraction. Step 2 Given information: − 4 8 ÷ 16 64 8 −4 ÷ 64 16 Step 3 Division rule: Compound fractions can be simplified by using the rule, division is same as multiplication by the reciprocal. 𝑎 𝑏 ÷ 𝑐 𝑑 = 𝑎 𝑏 × 𝑑 𝑐 b a ÷ d c = b a × c d Step 4 Explanation: Apply division rule. − 4 8 ÷ 16 64 = − 4 × 64 8 × 16 8 −4 ÷ 64 16 = 8×16 −4×64 ⇒ − 256 128 = − 2 ⇒ 128 −256 =−2 Question 5 Put these numbers in order from least to greatest. 6 16 , 17 40 , 15 24 , − 3 , 1 8 16 6 , 40 17 , 24 15 ,−3, 8 1 Answer 1 Step 1 Given numbers 6 16 , 17 40 , 15 24 , − 3 , 1 8 16 6 , 40 17 , 24 15 ,−3, 8 1 Least common denominator of all fractions: - LCD of 16, 40, 24, 1, 8 is 240. Step 2 Given function are equivalent to, 90 240 , 102 240 , 150 240 , − 720 , 30 240 240 90 , 240 102 , 240 150 ,−720, 240 30 Ordering from least to greatest numerator, − 720 , 30 240 , 90 240 , 102 240 , 150 240 −720, 240 30 , 240 90 , 240 102 , 240 150 Hence the given numbers arranged from least to greatest − 3 , 1 8 , 6 16 , 17 40 , 15 24 −3, 8 1 , 16 6 , 40 17 , 24 15