What does the unknown number z represent in 118 / 13 equals 59 / z
Accepted Solution
A:
Answer:z= 13/2= 6.500Step-by-step explanation:Step 1 : 59 Simplify —— z Equation at the end of step 1 : 118 59 ——— - —— = 0 13 z Step 2 : 118 Simplify ——— 13 Equation at the end of step 2 : 118 59 ——— - —— = 0 13 z Step 3 :Calculating the Least Common Multiple : 3.1 Find the Least Common Multiple The left denominator is : 13 The right denominator is : z Number of times each prime factor appears in the factorization of: Prime Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} 13 1 0 1 Product of all Prime Factors 13 1 13 Number of times each Algebraic Factor appears in the factorization of: Algebraic Factor Left Denominator Right Denominator L.C.M = Max {Left,Right} z 0 1 1 Least Common Multiple: 13z Calculating Multipliers : 3.2 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_Deno Left_M = L.C.M / L_Deno = z Right_M = L.C.M / R_Deno = 13Making Equivalent Fractions : 3.3 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value.For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier. L. Mult. • L. Num. 118 • z —————————————————— = ——————— L.C.M 13z R. Mult. • R. Num. 59 • 13 —————————————————— = ——————— L.C.M 13z Adding fractions that have a common denominator : 3.4 Adding up the two equivalent fractionsAdd the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible: 118 • z - (59 • 13) 118z - 767 ——————————————————— = —————————— 13z 13z Step 4 :Pulling out like terms : 4.1 Pull out like factors : 118z - 767 = 59 • (2z - 13) Equation at the end of step 4 : 59 • (2z - 13) —————————————— = 0 13z Step 5 :When a fraction equals zero : 5.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here's how: 59•(2z-13) —————————— • 13z = 0 • 13z 13z Now, on the left hand side, the 13z cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape : 59 • (2z-13) = 0Equations which are never true : 5.2 Solve : 59 = 0This equation has no solution.A a non-zero constant never equals zero.Solving a Single Variable Equation : 5.3 Solve : 2z-13 = 0 Add 13 to both sides of the equation : 2z = 13Divide both sides of the equation by 2: z = 13/2 = 6.500One solution was found : z = 13/2 = 6.500