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

2024
Views:

13

Pages:

3
Author:

Delphinixxc3

Question 1 Fill in the blank with the correct term or example in the sentence: "A fraction is written in simplest form when the GCF of the numerator and the denominator is ___." Answer 1 A fraction is written in simplest form when the GCF of the numerator and the denominator is 1. Question 2 How to convert decimals into fractions? Answer 1 Step 1: Write the decimal as a fraction with a denominator of 1. Step 2: Multiply both the numerator and denominator by 10 for every decimal place. For example, if there are two decimal places, multiply by 100. Step 3: Simplify (or reduce) the fraction if possible. Question 3 Simplify a complex rational expression by writing it as division. Simplify: 𝑥 𝑥 + 5 2 + 5 𝑥 − 5 2+ x−5 5 x+5 x Answer 1 Step 1: Write the given expression: 𝑥 𝑥 + 5 2 + 5 𝑥 − 5 2+ x−5 5 x+5 x Step 2: Combine the terms in the denominator: 2 + 5 𝑥 − 5 = 2 ( 𝑥 − 5 ) + 5 𝑥 − 5 = 2 𝑥 − 10 + 5 𝑥 − 5 = 2 𝑥 − 5 𝑥 − 5 2+ x−5 5 = x−5 2(x−5)+5 = x−5 2x−10+5 = x−5 2x−5 Step 3: Now write the complex expression as: 𝑥 𝑥 + 5 2 𝑥 − 5 𝑥 − 5 = 𝑥 ( 𝑥 − 5 ) ( 𝑥 + 5 ) ( 2 𝑥 − 5 ) x−5 2x−5 x+5 x = (x+5)(2x−5) x(x−5) Step 4: Simplified result: 𝑥 ( 𝑥 − 5 ) ( 𝑥 + 5 ) ( 2 𝑥 − 5 ) (x+5)(2x−5) x(x−5) Question 4 Order of operations with fractions. Simplify: 5 9 × 7 2 + 7 19 ÷ 18 19 9 5 × 2 7 + 19 7 ÷ 19 18 Answer 1 Step 1: Solve multiplication and division first. 5 9 × 7 2 = 35 18 , 7 19 ÷ 18 19 = 7 19 × 19 18 = 7 18 9 5 × 2 7 = 18 35 , 19 7 ÷ 19 18 = 19 7 × 18 19 = 18 7 Step 2: Now add the results: 35 18 + 7 18 = 42 18 = 7 3 18 35 + 18 7 = 18 42 = 3 7 Final answer: 7 3 3 7 Question 5 To multiply two rational expressions, we multiply their ___? together and multiply their ___? Answer 1 We multiply their numerators together and multiply their denominators.