Question

Which expression is equivalent to ⅖ + 4/5n - 7/10n - 1/10

1/10n -10/10
-3/10n - 1/10
6/5n - 8/10n
1/10n - 3/10

Answer 1

To simplify the expression \( \frac{2}{5} + \frac{4}{5}n - \frac{7}{10}n - \frac{1}{10} \), we will first find a common denominator for the fractions.

The denominators are 5 and 10. The common denominator is 10.

Convert \( \frac{2}{5} \) to have a denominator of 10:
\[
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
\]

Now we rewrite the expression:
\[
\frac{4}{10} + \frac{4}{5}n - \frac{7}{10}n - \frac{1}{10}
\]
Convert \( \frac{4}{5}n \) to have a denominator of 10:
\[
\frac{4}{5}n = \frac{4 \times 2}{5 \times 2}n = \frac{8}{10}n
\]

Now substitute it back into the expression:
\[
\frac{4}{10} + \frac{8}{10}n - \frac{7}{10}n - \frac{1}{10}
\]

Now combine the \( n \) terms:
\[
\frac{8}{10}n - \frac{7}{10}n = \frac{1}{10}n
\]

Now combine the constant terms:
\[
\frac{4}{10} - \frac{1}{10} = \frac{3}{10}
\]

So the entire expression simplifies to:
\[
\frac{1}{10}n + \frac{3}{10}
\]

However, we can rewrite it to emphasize the negative sign:
\[
\frac{1}{10}n - \left(-\frac{3}{10}\right)
\]

From the provided options, it appears the equivalent expression is:
- \(-\frac{3}{10} n - \frac{1}{10}\) is not correct,
- \( \frac{1}{10}n - \frac{3}{10}\) is correct.

So the correct answer is:
\[
\frac{1}{10}n - \frac{3}{10}
\]