Sure, let's solve the given problem step-by-step:
We start with the given expression:
[tex]\[
-\frac{4}{5} + \frac{-8}{-3} - \frac{2}{4}
\][/tex]
### Step 1: Simplify Each Fraction
First, let's simplify each fraction individually.
1. \(-\frac{4}{5}\)
- This fraction is already in its simplest form. It equals \(-0.8\).
2. \(\frac{-8}{-3}\)
- Both the numerator and the denominator are negative. When dividing two negative numbers, the result is positive.
[tex]\[
\frac{-8}{-3} = \frac{8}{3}
\][/tex]
- \(\frac{8}{3}\) in decimal form is approximately \(2.6666666666666665\).
3. \(-\frac{2}{4}\)
- Let's simplify the fraction first. \(\frac{2}{4}\) simplifies to \(\frac{1}{2}\).
- Therefore,
[tex]\[
-\frac{2}{4} = -\frac{1}{2} = -0.5
\][/tex]
### Step 2: Combine the Simplified Fractions
Now that we have simplified each fraction, we can add them together:
[tex]\[
-\frac{4}{5} + \frac{8}{3} - \frac{1}{2} \approx -0.8 + 2.6666666666666665 - 0.5
\][/tex]
### Step 3: Perform the Addition
Let's perform the addition step-by-step:
1. Add \(-0.8\) and \(2.6666666666666665\):
[tex]\[
-0.8 + 2.6666666666666665 = 1.8666666666666665
\][/tex]
2. Subtract \(0.5\) from \(1.8666666666666665\):
[tex]\[
1.8666666666666665 - 0.5 = 1.3666666666666665
\][/tex]
### Conclusion
Therefore, the result of the expression \(-\frac{4}{5} + \frac{-8}{-3} - \frac{2}{4}\) is approximately \(1.3666666666666665\). The values of each fraction and the sum are as follows:
- \(-\frac{4}{5} \approx -0.8\)
- \(\frac{8}{3} \approx 2.6666666666666665\)
- \(-\frac{1}{2} \approx -0.5\)
- The total sum is approximately [tex]\(1.3666666666666665\)[/tex]
