Solve the fraction -2/5 + 1/8=

The Correct Answer and Explanation is:

To solve the fraction (-\frac{2}{5} + \frac{1}{8}), we need to find a common denominator and then combine the two fractions. Here’s a step-by-step explanation of the process:

Step 1: Identify the Denominators

The denominators of our fractions are 5 and 8. To add the fractions, we need to find a common denominator, which is the least common multiple (LCM) of these two numbers.

Step 2: Find the Least Common Multiple (LCM)

The LCM of 5 and 8 can be found by listing the multiples:

Multiples of 5: 5, 10, 15, 20, 25, 30, …
Multiples of 8: 8, 16, 24, 32, …

The first common multiple is 40. Therefore, the LCM of 5 and 8 is 40.

Step 3: Convert Each Fraction

Next, we convert each fraction to have the common denominator of 40.

For (-\frac{2}{5}):
[
-\frac{2}{5} = -\frac{2 \times 8}{5 \times 8} = -\frac{16}{40}
]
For (\frac{1}{8}):
[
\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}
]

Step 4: Add the Fractions

Now that both fractions have a common denominator, we can add them:
[
-\frac{16}{40} + \frac{5}{40} = \frac{-16 + 5}{40} = \frac{-11}{40}
]

Step 5: Final Result

The final result of (-\frac{2}{5} + \frac{1}{8}) is:
[
\boxed{-\frac{11}{40}}
]

Conclusion

In this process, we first identified the denominators and found their least common multiple to establish a common ground for the fractions. After converting each fraction to this common denominator, we were able to add them straightforwardly by combining the numerators. This approach highlights the importance of having a common denominator in fraction addition and illustrates the methodical steps needed to perform arithmetic with fractions effectively. The final answer, (-\frac{11}{40}), represents the sum of the two original fractions.