Question

8/5 x -5/16 find the lowest term

Answer 1

To simplify the expression \( \frac{8}{5} x - \frac{5}{16} \), we need to find a common denominator to combine the two fractions.

The denominators here are 5 and 16. The least common multiple (LCM) of 5 and 16 is 80.

Now, we rewrite each fraction with a denominator of 80:

1. For \( \frac{8}{5} x \):
\[
\frac{8}{5} x = \frac{8 \times 16}{5 \times 16} x = \frac{128}{80} x
\]

2. For \( \frac{5}{16} \):
\[
\frac{5}{16} = \frac{5 \times 5}{16 \times 5} = \frac{25}{80}
\]

Now we can rewrite the expression \( \frac{8}{5} x - \frac{5}{16} \) as:
\[
\frac{128}{80} x - \frac{25}{80}
\]

Since both terms now have a common denominator, we can combine them:
\[
\frac{128x - 25}{80}
\]

This is the expression in the simplest form. However, we also want to find if \( 128x - 25 \) can be simplified further. The numerator \( 128x - 25 \) does not have any common factors with 80, so we leave it as is.

The final result is:
\[
\frac{128x - 25}{80}
\]

Thus, the simplified expression is \( \frac{128x - 25}{80} \).