# algebra - equation

5/8 divided by n/3=5/8(n/3), What is the value of n.

### Comments for algebra - equation

 Jan 13, 2011 Algebra - Equation by: Staff The question: 5/8 divided by n/3=5/8(n/3), What is the value of n. The answer: 5/8 divided by n/3=5/8(n/3), what is the value of n? ------------------------------------------------------------ You didn’t specify what 5/8(n/3) means. It could mean 5/[8*(n/3)] Or, it could mean (5/8)*(n/3) I am going to assume you mean (5/8)*(n/3) ------------------------------------------------------------ That being the case, your equation can be written: 5/8 divided by n/3=5/8(n/3) (5/8)/(n/3)=(5/8)*(n/3) (5/8)*(3/n)=(5*n)/(8*3) (5/8)*(3/n)=(5*n)/(24) (5*3)/(8*n)=(5*n)/(24) (15)/(8*n)=(5*n)/(24) (15/8)*(1/n)=(5*n)/(24) Multiply each side of the equation by n to remove the 1/n from the left hand side of the equation (15/8)*(1/n)=(5*n)/(24) n*(15/8)*(1/n)=n*[(5*n)/(24)] (15/8)*(n/n)=n*[(5*n)/(24)] (15/8)*(1)=n*[(5*n)/(24)] (15/8)*1=n*[(5*n)/(24)] 15/8=n*[(5*n)/(24)] 15/8=(5*n*n)/(24) 15/8=(5/24)*n*n 15/8=(5/24)*(n^2) Multiply each side of the equation by 1/5 to remove the 5 from the right side of the equation (1/5)*(15/8)=(1/5)*(5/24)*(n^2) (15/5)*(1/8)=(1/5)*(5/24)*(n^2) (3)*(1/8)=(1/5)*(5/24)*(n^2) (3/8)=(1/5)*(5/24)*(n^2) (3/8)=(5/5)*(1/24)*(n^2) (3/8)=(1)*(1/24)*(n^2) (3/8)=(1/24)*(n^2) Multiply each side of the equation by 24 to remove the 1/24 from the right side of the equation (3/8)=(1/24)*(n^2) 24*(3/8)=24*(1/24)*(n^2) (24/1)*(3/8)=24*(1/24)*(n^2) (24/8)*(3/1)=24*(1/24)*(n^2) (3)*(3/1)=24*(1/24)*(n^2) (3)*(3)=24*(1/24)*(n^2) 9=24*(1/24)*(n^2) 9=(24/24)*(n^2) 9=(1)*(n^2) 9=1*(n^2) 9=(n^2) The last step . . . take the square root of each side of the equation 9=(n^2) Sqrt(9) = Sqrt(n^2) 3 = n The final answer: n = 3 Check the answer. Substitute 3 for every n in the original equation. Original equation: (5/8)/(n/3)=(5/8)*(n/3) Substituting 3 for every n: (5/8)/(3/3)=(5/8)*(3/3) (5/8)/(3/3)=(5/8)*(3/3) (5/8)/(1)=(5/8)*(1) (5/8)=(5/8) Since the equation is in balance for n=3, the solution of n=3 is correct Thanks for writing. Staff www.solving-math-problems.com