To solve the expression [tex]\(\frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}\)[/tex], we can break it down into a step-by-step calculation process.
1. Identify the given fractions:
- [tex]\(\frac{1}{3}\)[/tex]
- [tex]\(\frac{1}{4}\)[/tex]
- [tex]\(\frac{1}{5}\)[/tex]
- [tex]\(\frac{1}{6}\)[/tex]
2. Convert the fractions to decimal form for easier calculation:
- [tex]\(\frac{1}{3} = 0.3333333333333333\)[/tex]
- [tex]\(\frac{1}{4} = 0.25\)[/tex]
- [tex]\(\frac{1}{5} = 0.2\)[/tex]
- [tex]\(\frac{1}{6} = 0.16666666666666666\)[/tex]
3. Perform the operations step-by-step:
First, add [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
0.3333333333333333 + 0.25 = 0.5833333333333333
\][/tex]
Then, subtract [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
0.5833333333333333 - 0.2 = 0.3833333333333333
\][/tex]
Finally, add [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
0.3833333333333333 + 0.16666666666666666 = 0.5499999999999999
\][/tex]
4. Express the result:
Therefore, the value of the expression [tex]\(\frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}\)[/tex] is approximately [tex]\(0.5499999999999999\)[/tex].
Summarizing all the steps, here are the key intermediate steps again:
- [tex]\(\frac{1}{3} = 0.3333333333333333\)[/tex]
- [tex]\(\frac{1}{4} = 0.25\)[/tex]
- [tex]\(\frac{1}{5} = 0.2\)[/tex]
- [tex]\(\frac{1}{6} = 0.16666666666666666\)[/tex]
- Result of the operation: [tex]\(0.5499999999999999\)[/tex]
Hence, [tex]\(\frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6} = 0.5499999999999999\)[/tex].
