Sure! Let's solve the problem by subtracting [tex]\(\frac{-6}{13}\)[/tex] from [tex]\(\frac{4}{13}\)[/tex] step-by-step.
1. Identify the fractions:
- The first fraction is [tex]\(\frac{4}{13}\)[/tex].
- The second fraction is [tex]\(\frac{-6}{13}\)[/tex].
2. Set up the subtraction:
- We need to subtract [tex]\(\frac{-6}{13}\)[/tex] from [tex]\(\frac{4}{13}\)[/tex].
- This can be written as:
[tex]\[
\frac{4}{13} - \left(\frac{-6}{13}\right)
\][/tex]
3. Simplify the expression:
- Subtracting a negative fraction is equivalent to adding its positive counterpart.
- Thus, subtracting [tex]\(\frac{-6}{13}\)[/tex] is the same as adding [tex]\(\frac{6}{13}\)[/tex].
- So, we rewrite the expression as:
[tex]\[
\frac{4}{13} + \frac{6}{13}
\][/tex]
4. Add the fractions:
- Since the denominators of the fractions are the same (both are 13), we can directly add the numerators.
- The numerator of the resulting fraction will be: [tex]\(4 + 6 = 10\)[/tex].
- The denominator remains the same: 13.
5. Write the resulting fraction:
- Therefore, the resulting fraction is:
[tex]\[
\frac{10}{13}
\][/tex]
6. Convert the result to decimal (if necessary):
- To convert [tex]\(\frac{10}{13}\)[/tex] to a decimal, we divide 10 by 13.
- This gives approximately:
[tex]\[
0.7692307692307693
\][/tex]
So, the detailed steps to subtract [tex]\(\frac{-6}{13}\)[/tex] from [tex]\(\frac{4}{13}\)[/tex] show that:
[tex]\[
\frac{4}{13} - \left(\frac{-6}{13}\right) = \frac{10}{13} \approx 0.7692307692307693
\][/tex]
We have:
- The value of [tex]\(\frac{4}{13}\)[/tex] is approximately [tex]\(0.3076923076923077\)[/tex].
- The value of [tex]\(\frac{-6}{13}\)[/tex] is approximately [tex]\(-0.46153846153846156\)[/tex].
- Subtracting [tex]\(\frac{-6}{13}\)[/tex] from [tex]\(\frac{4}{13}\)[/tex] gives approximately [tex]\(0.7692307692307693\)[/tex].
- The numerator of the resulting fraction after subtraction is 10.
- The final resulting fraction is [tex]\(\frac{10}{13}\)[/tex] which is approximately [tex]\(0.7692307692307693\)[/tex].
