Question

what is a common denominator of this equation 3n/4-1/4 n=3/8

Answer 1

To find a common denominator for the equation

\[
\frac{3n}{4} - \frac{1}{4}n = \frac{3}{8},
\]

let's look at the denominators involved, which are 4 and 8. The least common multiple (LCM) of 4 and 8 is 8.

Now, let's rewrite each term with 8 as the common denominator:

1. The term \(\frac{3n}{4}\) can be rewritten as:
\[
\frac{3n}{4} = \frac{3n \cdot 2}{4 \cdot 2} = \frac{6n}{8}.
\]

2. The term \(-\frac{1}{4}n\) can also be rewritten as:
\[
-\frac{1}{4}n = -\frac{1 \cdot 2}{4 \cdot 2}n = -\frac{2n}{8}.
\]

Now we can substitute these into the equation:

\[
\frac{6n}{8} - \frac{2n}{8} = \frac{3}{8}.
\]

Combining the left side gives:

\[
\frac{6n - 2n}{8} = \frac{3}{8}.
\]

This simplifies to:

\[
\frac{4n}{8} = \frac{3}{8}.
\]

Now we can eliminate the denominators (since both sides are over 8):

\[
4n = 3.
\]

Finally, solve for \(n\):

\[
n = \frac{3}{4}.
\]

So the common denominator for the original equation is 8, and the solution for \(n\) is \(\frac{3}{4}\).