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

Question

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: $$\frac{1}{10}n-(-\frac{3}{10})$$

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: $$\frac{1}{10}n-\frac{3}{10}$$