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

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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?

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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)

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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


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