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

2024
Views:

188

Pages:

3
Author:

Delphinixxc3

Question 1 Find the difference by converting the mixed numbers to improper fractions: 4 4 9 − 3 7 9 4 9 4 −3 9 7 Answer 1 Calculation: Writing the mixed numbers as improper fractions: 4 4 9 = ( 9 ) ( 4 ) + 4 9 = 36 + 4 9 = 40 9 4 9 4 = 9 (9)(4)+4 = 9 36+4 = 9 40 3 7 9 = ( 9 ) ( 3 ) + 7 9 = 27 + 7 9 = 34 9 3 9 7 = 9 (9)(3)+7 = 9 27+7 = 9 34 To subtract, we need the denominators to be equal: 4 4 9 − 3 7 9 = 40 9 − 34 9 = 40 − 34 9 = 6 9 = 2 3 4 9 4 −3 9 7 = 9 40 − 9 34 = 9 40−34 = 9 6 = 3 2 Therefore, 4 4 9 − 3 7 9 = 2 3 4 9 4 −3 9 7 = 3 2 Question 2 Additive property of equality with fractions and mixed numbers "I am unable to solve 𝑣 + 4 5 = 3 4 v+ 5 4 = 4 3 ." "I don’t understand how to subtract and rename 4 15 15 4 as 35 20 20 35 ." Answer 1 Step 1 Given: 𝑣 + 4 5 = 3 4 v+ 5 4 = 4 3 Find: value of 𝑣 v Step 2 We have, 𝑣 + 4 5 = 3 4 v+ 5 4 = 4 3 𝑣 = 3 4 − 4 5 v= 4 3 − 5 4 Rewrite both fractions with a common denominator of 20: 𝑣 = 3 × 5 4 × 5 − 4 × 4 5 × 4 v= 4×5 3×5 − 5×4 4×4 𝑣 = 15 20 − 16 20 v= 20 15 − 20 16 𝑣 = 15 − 16 20 = − 1 20 v= 20 15−16 = 20 −1 Thus, 𝑣 = − 1 20 v=− 20 1 Question 3 A parabola opening up or down has vertex ( 0 , 4 ) (0,4) and passes through ( − 12 , − 8 ) (−12,−8). Write its equation in vertex form. 𝑦 = ? y=? Answer 1 We have: vertex ( 0 , 4 ) (0,4) and point ( − 12 , − 8 ) (−12,−8) Solution: 𝑦 = 𝑎 ( 𝑥 − ℎ ) 2 + 𝑘 y=a(x−h) 2 +k − 8 = 𝑎 ( − 12 − 0 ) 2 + 4 −8=a(−12−0) 2 +4 − 8 = 144 𝑎 + 4 −8=144a+4 144 𝑎 = − 8 − 4 144a=−8−4 𝑎 = − 12 144 a= 144 −12 𝑎 = − 1 12 a=− 12 1 Result: 𝑦 = − 1 12 𝑥 2 + 4 y=− 12 1 x 2 +4 Question 4 Convert Percent to Fractions and Decimals. In the following exercises, convert each percent to a fraction and simplify all fractions. 125% Answer 1 Formula used: Convert a percent to a fraction: Step 1: Write the percent as a ratio with the denominator 100. Step 2: Simplify the fraction if possible. Calculation: Consider 125%. Let us write the percent as a ratio with the denominator 100. 125 % = 125 100 125%= 100 125 Now let us simplify by cancelling out the common factors. 125 100 = 5 ⋅ 5 5 ⋅ 4 = 5 4 100 125 = 5⋅4 5⋅5 = 4 5 Question 5 Convert Percent to Fractions and Decimals. In the following exercises, convert each percent to a fraction and simplify all fractions. 37.5% Answer 1 Formula used: Convert a percent to a fraction: Step 1: Write the percent as a ratio with the denominator 100. Step 2: Simplify the fraction if possible. Calculation: Consider 37.5%. Let us write the percent as a ratio with the denominator 100. 37.5 % = 37.5 100 = 375 1000 37.5%= 100 37.5 = 1000 375 Now let us simplify by cancelling out the common factors. 375 1000 = 3 8 1000 375 = 8 3