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

2024
Views:

103

Pages:

4
Author:

Delphinixxc3

Question 1 How do you convert 0.16 (6 repeating) to a fraction? Answer 1 Explanation: For recurring decimals, the numerator is the digits that repeat, and the denominator is determined by the recurring part. For 0.16 6 ‾ 0.16 6 , write 166 minus the non-repeating 16 divided by a 9 for each recurring digit, followed by 0 for each non-recurring digit. 0.16 6 ‾ = 166 − 16 990 = 150 990 = 5 33 0.16 6 = 990 166−16 = 990 150 = 33 5 Answer 2 If only some digits recur: For example, in 0.524 6 ‾ 0.524 6 , only the 6 repeats. Numerator: 524 − 524 524−524, Denominator: a 9 for each repeating digit and a 0 for each non-repeating digit: 0.524 6 ‾ = 524 − 524 900 = 472 900 0.524 6 = 900 524−524 = 900 472 Question 2 How do you change 9 12 12 9 to its simplest form? Answer 1 Find the largest number that divides both 9 and 12. The GCD of 9 and 12 is 3. 9 12 = 9 ÷ 3 12 ÷ 3 = 3 4 12 9 = 12÷3 9÷3 = 4 3 Thus, 9 12 12 9 simplifies to 3 4 4 3 . Answer 2 Find the common factor of 9 and 12. Since 3 divides both, 9 12 = 3 4 12 9 = 4 3 Question 3 Write 2.75 as a fraction. Answer 1 2.75 is the same as 275 100 100 275 , which simplifies to 11 4 4 11 . Answer 2 You can write it as 275 100 100 275 , or simplify it to 11 4 4 11 . Question 4 What are the equivalent fractions for 3 4 4 3 ? Answer 1 To find equivalent fractions, multiply both the numerator and denominator by the same number: 3 4 = 6 8 , 9 12 , 12 16 4 3 = 8 6 , 12 9 , 16 12 Answer 2 For instance: 3 4 = 6 8 , 9 12 , 12 16 , 15 20 4 3 = 8 6 , 12 9 , 16 12 , 20 15 Question 5 Convert 0.6666 … 0.6666… to a fraction. Answer 1 Multiply 0.666 … 0.666… by 10 to cancel out the repeating decimal: 10 𝑥 = 6.666 … 10x=6.666… 10 𝑥 − 𝑥 = 6.666 … − 0.666 … 10x−x=6.666…−0.666… 9 𝑥 = 6 9x=6 𝑥 = 6 9 = 2 3 x= 9 6 = 3 2 Answer 2 0.66 6 ‾ = 2 3 0.66 6 = 3 2