Answer :

Sure! Let's find the sum of [tex]\(-\frac{3}{8}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex] step-by-step:

1. Simplify the fractions:

- The first fraction, [tex]\(-\frac{3}{8}\)[/tex], is already in its simplest form.
- For the second fraction, [tex]\(\frac{18}{20}\)[/tex], we can simplify it by finding the greatest common divisor (GCD) of 18 and 20, which is 2. Now, divide both the numerator and the denominator by 2:
[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]

2. Convert to a common denominator (optional but often helpful):

To add fractions, it's useful to have a common denominator. Let's find the least common multiple (LCM) of 8 and 10. In this case, the LCM of 8 and 10 is 40.

- Convert [tex]\(-\frac{3}{8}\)[/tex] to a fraction with a denominator of 40:
[tex]\[
-\frac{3}{8} = -\frac{3 \times 5}{8 \times 5} = -\frac{15}{40}
\][/tex]

- Convert [tex]\(\frac{9}{10}\)[/tex] to a fraction with a denominator of 40:
[tex]\[
\frac{9}{10} = \frac{9 \times 4}{10 \times 4} = \frac{36}{40}
\][/tex]

3. Add the fractions:

Now that both fractions have the same denominator, we can easily add them:
[tex]\[
-\frac{15}{40} + \frac{36}{40} = \frac{-15 + 36}{40} = \frac{21}{40}
\][/tex]

4. Simplify the result (if possible):

The fraction [tex]\(\frac{21}{40}\)[/tex] is already in its simplest form since 21 and 40 have no common divisors other than 1.

Therefore, the sum of [tex]\(-\frac{3}{8}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex] is:
[tex]\[
\frac{21}{40} \approx 0.525
\][/tex]

So, the final answer is approximately [tex]\(0.525\)[/tex].

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