Question

- 5 3/10 - -1 31/50

Answer 1

To solve the expression \( -5 \frac{3}{10} - (-1 \frac{31}{50}) \), we can follow these steps:

1. Convert the mixed numbers to improper fractions.
- For \( -5 \frac{3}{10} \):
\[
-5 \frac{3}{10} = -\left(5 \times 10 + 3\right)/10 = -\frac{53}{10}
\]

- For \( -1 \frac{31}{50} \):
\[
-1 \frac{31}{50} = -\left(1 \times 50 + 31\right)/50 = -\frac{81}{50}
\]

2. Rewrite the expression:
\[
-\frac{53}{10} - (-\frac{81}{50}) = -\frac{53}{10} + \frac{81}{50}
\]

3. Find a common denominator to combine the fractions. The least common multiple of 10 and 50 is 50.
- Convert \( -\frac{53}{10} \) to a denominator of 50:
\[
-\frac{53}{10} = -\frac{53 \times 5}{10 \times 5} = -\frac{265}{50}
\]

4. Now we can combine the fractions:
\[
-\frac{265}{50} + \frac{81}{50} = \frac{-265 + 81}{50} = \frac{-184}{50}
\]

5. Simplify the fraction:
\[
\frac{-184}{50} = \frac{-92}{25}
\]

So, the final answer is:
\[
-\frac{92}{25}
\]