To simplify the expression \( \frac{3}{8}x - \frac{9}{10}y + \frac{3}{8}x + \frac{7}{10}y \), we will follow these steps:
-
Combine the like terms involving \( x \):
\[
\frac{3}{8}x + \frac{3}{8}x = \frac{6}{8}x
\]
-
Combine the like terms involving \( y \):
\[
-\frac{9}{10}y + \frac{7}{10}y = -\frac{2}{10}y
\]
Putting it all together, we get:
\[
\frac{6}{8}x - \frac{2}{10}y
\]
Next, we can simplify the coefficients further:
- \( \frac{6}{8}x \) simplifies to \( \frac{3}{4}x \) (dividing the numerator and the denominator by 2).
- \( -\frac{2}{10}y \) simplifies to \( -\frac{1}{5}y \) (dividing the numerator and the denominator by 2).
Thus, the simplified expression can also be written as:
\[
\frac{3}{4}x - \frac{1}{5}y
\]
Now, let's compare this with the provided options:
- \(\frac{6}{8}x + \frac{2}{10}y = \frac{3}{4}x + \frac{1}{5}y\)
- \(\frac{6}{8}x - \frac{2}{10}y = \frac{3}{4}x - \frac{1}{5}y\)
- \(\frac{6}{16}x + \frac{2}{20}y = \frac{3}{8}x + \frac{1}{10}y\)
- \(\frac{6}{16}x - \frac{2}{20}y = \frac{3}{8}x - \frac{1}{10}y\)
From the simplified expression \( \frac{6}{8}x - \frac{2}{10}y \), we can directly see that this matches option 2:
\(\frac{6}{8}x - \frac{2}{10}y = \frac{3}{4}x - \frac{1}{5}y\).
1 answer