Question

Subtract. Answer as a fraction in simplest form.
1 4/5 - 5 1/10 = [__]/[__]

Answer 1

To solve \(1 \frac{4}{5} - 5 \frac{1}{10}\), we first convert the mixed numbers to improper fractions.

1. Convert \(1 \frac{4}{5}\):
\[
1 \frac{4}{5} = 1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5}
\]

2. Convert \(5 \frac{1}{10}\):
\[
5 \frac{1}{10} = 5 + \frac{1}{10} = \frac{50}{10} + \frac{1}{10} = \frac{51}{10}
\]

Now we need to subtract these improper fractions:
\[
\frac{9}{5} - \frac{51}{10}
\]

To perform the subtraction, we need a common denominator. The least common multiple of 5 and 10 is 10. We convert \(\frac{9}{5}\) to have a denominator of 10:
\[
\frac{9}{5} = \frac{9 \times 2}{5 \times 2} = \frac{18}{10}
\]

Now we can perform the subtraction:
\[
\frac{18}{10} - \frac{51}{10} = \frac{18 - 51}{10} = \frac{-33}{10}
\]

To express \(\frac{-33}{10}\) as a fraction in simplest form, we note that \(-33\) and \(10\) have no common factors (except 1). Thus, the simplest form of the fraction is:
\[
\frac{-33}{10}
\]

Therefore, the final answer is:
\[
\frac{-33}{10}
\]

So, in the form \([__]/[__]\), we have \([-33]/[10]\).