Question

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

Answer 1

To subtract \( 1 \frac{4}{5} - 5 \frac{1}{10} \), we first convert each mixed number to an improper fraction.

1. Convert \( 1 \frac{4}{5} \):

\[
1 \frac{4}{5} = 1 \times 5 + 4 = 5 + 4 = \frac{9}{5}
\]

2. Convert \( 5 \frac{1}{10} \):

\[
5 \frac{1}{10} = 5 \times 10 + 1 = 50 + 1 = \frac{51}{10}
\]

Now we need to subtract the two improper fractions:

\[
\frac{9}{5} - \frac{51}{10}
\]

To do this, we need a common denominator. The least common denominator (LCD) of 5 and 10 is 10.

We'll 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:

\[
\frac{18}{10} - \frac{51}{10} = \frac{18 - 51}{10} = \frac{-33}{10}
\]

Now, we need to express \( \frac{-33}{10} \) as a mixed number:

\[
-33 \div 10 = -3 \quad \text{(with a remainder of } -3 \text{)}
\]

Thus:

\[
\frac{-33}{10} = -3 \frac{3}{10}
\]

Therefore, the final answer in the form of \( [\text{whole number}] [\text{numerator}]/[\text{denominator}] \) is:

\[
-3 \frac{3}{10}
\]

So we can write the answer as:

\[
[-3] [3]/[10]
\]