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# Math 098 Math 098

Minnesota State University, Mankato

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This 5 page Class Notes was uploaded by Alyssa Notetaker on Tuesday January 26, 2016. The Class Notes belongs to Math 098 at Minnesota State University - Mankato taught by Soo Leon Shin in Winter 2016. Since its upload, it has received 20 views. For similar materials see Intermidiate Algerbra in Math at Minnesota State University - Mankato.

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Date Created: 01/26/16

Math 098 Multiplying and Dividing Fra:tions 1. 3/5 x 1/6 first factor the numerators and denominators (3)/(5) x (1)/(2 x 3) then cross out numbers that are the same in each fraction (3)/(5) x (1)/3) x multiply the numerators and then the denominators 1/10 2. 20/4 x 4/10 = (2 x 2 x 5)/(2 x 2) x (2 x 2)/(2 x 5) (2 x x5/2 x ) x2x 2)2x) 2/1 or 2 1. 6/5 ÷ 4/15 first you have to change division to multiplication by multiplying it by the reciprocal 6/5 x 15/4 then you have to find the multiples (2 x 3)/(5) x (3 x 5)/(2 x 2) then cross out the numbers that are the same in each fraction (2x3)/(5) x3x)/(22) multiply the numerators and denominators 1/2 Adding and Subtracting Fractions: 1. 2/5 - 1/3 first you have to find a common denominator and in order to do that you have to find the least common multiple in this case the LCM is 15, so we have to multiply each fraction to get a denominator of 15 2(3)/5(3) - 1(5)/3(5) = 6/15 - 5/15 next, you subtract the numerators to get the answer 1/15 2. 5/6 - 8/5 = 5(5)/6(5) - 8(6)/5(6) = 25/30 - 48/30 -23/30 1. 5/8 + 4/5 first you have to find a common denominator and in order to do that you have to find the least common multiple in this case the LCM is 40, so we have to multiply each fraction to get a denominator of 40 5(5)/8(5) + 4(8)/5(8) = 25/40 + 32/40 next, you add the numerators to get the answer 57/40 2. (x + 8)/3 + 4/5 first you have to find a common denominator and in order to do that you have to find the least common multiple in this case the LCM is 15, so we have to multiply each fraction to get a denominator of 15 (x + 8)(5)/3(5) + 4(3)/5(3) = (5x + 40)/15 + 12/15 next you will just add the numerators (5x + 52)/15 Dividing with Zero: 0÷ 5 = 0/5 = 0 3 ÷0 = 3/0 = undefined 0÷ 0 = 0/0 = indeterminate Distributive Property: 1. 1/3 (6 - 9x) you have to multiply 1/3 by what's in the parentheses (which is the same as dividing by 3) 2 - 3x 2. 1/8(64 + 24x) = 8+ 3x Solving Linear Equations in One Variable: 1. 7 (x + 3) - 5 = 15 first you have to distribute the 7 into what’s in the parentheses 7x + 21 - 5 = 15 then subtract 5 from 21 7x + 16 = 15 then subtract 16 from 15 7x = -1 then divide by 7 to get x alone x = -1/7 2. 3 (x + 2) - 4 = 3 (x + 3) - 7 3x + 6 - 4 = 3x + 9 -7 3x + 2 = 3x + 2 0 = 0 Formulas: 1. P = 3w + 4l solve for l first you have to to move 3w to the other side so l is the only variable on the right side P = 3w + 4l -3w -3w P-3w = 4l then you have to divide by for to get l alone l =P-3w 4 2.- 4= 7/3 x x (y - 4= (7/3)x y - 4 = 7/3x y = 7/3x + 4

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