Question

simplify with addition and subtraction
which expression is equivalent to $\frac{4}{5}a + \frac{2}{3}b + \frac{1}{8} - \frac{7}{6}b - \frac{3}{4} - \frac{2}{5}a$?
$\bigcirc$ $\frac{6}{5}a + \frac{11}{6}b + \frac{7}{8}$
$\bigcirc$ $\frac{2}{5}a + \frac{11}{6}b + \frac{7}{8}$
$\bigcirc$ $\frac{2}{5}a - \frac{1}{2}b - \frac{5}{8}$
$\bigcirc$ $\frac{6}{5}a - \frac{1}{2}b - \frac{5}{8}$

Explanation:

Step1: Combine like terms for \(a\)

We have \(\frac{4}{5}a\) and \(-\frac{2}{5}a\). Combining them: \(\frac{4}{5}a - \frac{2}{5}a=\frac{4 - 2}{5}a=\frac{2}{5}a\)

Step2: Combine like terms for \(b\)

We have \(\frac{2}{3}b\) and \(-\frac{7}{6}b\). First, convert \(\frac{2}{3}b\) to sixths: \(\frac{2}{3}b=\frac{4}{6}b\). Then combine: \(\frac{4}{6}b-\frac{7}{6}b=\frac{4 - 7}{6}b=-\frac{3}{6}b = -\frac{1}{2}b\)

Step3: Combine like terms for constants

We have \(\frac{1}{8}\) and \(-\frac{3}{4}\). Convert \(-\frac{3}{4}\) to eighths: \(-\frac{3}{4}=-\frac{6}{8}\). Then combine: \(\frac{1}{8}-\frac{6}{8}=\frac{1 - 6}{8}=-\frac{5}{8}\)

Step4: Combine all results

Putting together the results from steps 1, 2, and 3, we get \(\frac{2}{5}a-\frac{1}{2}b-\frac{5}{8}\)

Answer:

\(\frac{2}{5}a - \frac{1}{2}b - \frac{5}{8}\) (corresponding to the option with this expression)