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

2024
Views:

380

Pages:

5
Author:

Delphinixxc3

Question 1 What fraction is equivalent to 1/3? Answer 1 There are an infinite number of fractions that are equal to 1 3 3 1 . You can multiply the numerator and denominator of 1 3 3 1 by any number and the resulting fraction would be equal to 1 3 3 1 , so long as you are multiplying both by the same number. For example: 1 3 × 2 2 = 2 6 3 1 × 2 2 = 6 2 1 3 × 200 200 = 200 600 3 1 × 200 200 = 600 200 1 3 × 4000 4000 = 4000 12000 3 1 × 4000 4000 = 12000 4000 and so on. Answer 2 Explanation: There are many fractions which are equivalent to 1 3 3 1 , but this is the simplest form. To find an equivalent fraction, multiply 1 3 3 1 by 1, but with 1 written as 2 2 , 3 3 , 4 4 , 2 2 , 3 3 , 4 4 , etc. Multiplying the numerator and denominator by the same number does not change the value of a fraction. 13 39 = 26 78 = 77 231 = 4 12 = 5 15 39 13 = 78 26 = 231 77 = 12 4 = 15 5 Question 2 How do you change 9/16 into a percentage? Answer 1 Explanation: A percentage can be obtained from a fraction with a denominator with a power of 10, or from a decimal. 9 ÷ 16 = 0.5625 9÷16=0.5625 0.5625 × 100 = 56.25 0.5625×100=56.25 Therefore, 9 16 16 9 simplified to a percentage is 56.25%. Answer 2 Explanation: 9 16 × 100 % = 56.25 % 16 9 ×100%=56.25% Note that as this is an exact decimal, it should not be rounded to 56.3%. Answer 3 100 ÷ 16 = 6.25 100÷16=6.25 Once we have that, we can multiply both the numerator and denominator by this multiple: 9 × 6.25 16 × 6.25 = 56.25 100 16×6.25 9×6.25 = 100 56.25 Now we see that our fraction is 56.25/100, which means that 9 16 16 9 as a percentage is 56.25%. Alternatively, we can divide 9 16 = 0.5625 16 9 =0.5625, then multiply by 100 to get 56.25%. Question 3 Please, can you convert 3.16 (6 repeating) to a fraction? Answer 1 10 𝑥 = 31.666 … 10x=31.666… 9 𝑥 = 31.666 … − 𝑥 9x=31.666…−x 9 𝑥 = 28.5 9x=28.5 𝑥 = 28.5 9 = 285 90 = 19 6 x= 9 28.5 = 90 285 = 6 19 Answer 2 3.1666 … = 19 6 3.1666…= 6 19 Answer 3 19 6 6 19 Explanation: To convert the decimal number 3.166666\ldots to a fraction, we use the following method: Let 𝑥 = 3.166666 … x=3.166666…. Then we can write: 10 𝑥 = 31.666666 … 10x=31.666666… Subtracting both sides, we get: 9 𝑥 = 28.5 9x=28.5 Now, simplifying the fraction 285 90 90 285 , we get: 19 6 6 19 Answer 4 We can express the decimal 3.166666\ldots as 19 6 6 19 using the same method shown. Question 4 How do you convert 3/20 into a decimal and percent? Answer 1 Divide the numerator by the denominator to change to a decimal. Then multiply the decimal by 100% to change to a percent. 3 20 = 0.15 20 3 =0.15 0.15 × 100 % = 15 % 0.15×100%=15% Answer 2 Method 1: Divide to get 0.15, then multiply by 100 to get 15%. Method 2: Write as 15 100 100 15 to directly get the percentage. Question 5 What is 1.6 as a fraction? Answer 1 1.6 = 16 10 1.6= 10 16 Simplify: 16 10 = 8 5 10 16 = 5 8 Thus, 1.6 = 8 5 1.6= 5 8 . Answer 2 We can express 1.6 as 1 + 6 10 1+ 10 6 , which simplifies to 8 5 5 8 .