To solve the expression [tex]\( -18 + 3 \frac{4}{5} \)[/tex], follow these steps:
1. Understand the terms:
- The first term is [tex]\(-18\)[/tex].
- The second term is a mixed number, [tex]\(3 \frac{4}{5}\)[/tex].
2. Convert the mixed number to an improper fraction (optional but helpful):
- [tex]\(3 \frac{4}{5}\)[/tex] can be converted to an improper fraction. First, multiply the whole number by the denominator: [tex]\(3 \times 5 = 15\)[/tex].
- Next, add the numerator: [tex]\(15 + 4 = 19\)[/tex].
- Therefore, [tex]\(3 \frac{4}{5} = \frac{19}{5}\)[/tex].
3. Convert the improper fraction to a decimal:
- Divide the numerator by the denominator: [tex]\(\frac{19}{5} = 3.8\)[/tex].
4. Add the two numbers:
- Now, you have the expression [tex]\( -18 + 3.8 \)[/tex].
5. Combine the numbers:
- Adding a positive number to a negative number involves finding the difference between their absolute values and applying the sign of the larger absolute value.
- So, [tex]\(-18 + 3.8\)[/tex] involves finding the difference between [tex]\(18\)[/tex] and [tex]\(3.8\)[/tex], which is [tex]\(18 - 3.8 = 14.2\)[/tex].
6. Determine the sign:
- Since [tex]\(-18\)[/tex] has a larger absolute value than [tex]\(3.8\)[/tex], the result will be negative.
Thus, [tex]\( -18 + 3 \frac{4}{5} = -14.2 \)[/tex].
