To solve the sum of the fractions [tex]\(\frac{4}{3} + \frac{1}{5} + \frac{6}{7}\)[/tex], follow these steps:
1. Convert the fractions to decimals for easier handling:
- [tex]\(\frac{4}{3} \approx 1.3333333333333333\)[/tex]
- [tex]\(\frac{1}{5} = 0.2\)[/tex]
- [tex]\(\frac{6}{7} \approx 0.8571428571428571\)[/tex]
2. Add the decimal values:
- [tex]\( 1.3333333333333333 + 0.2 = 1.5333333333333332 \)[/tex]
- [tex]\( 1.5333333333333332 + 0.8571428571428571 \approx 2.3904761904761904 \)[/tex]
Therefore, the sum of the fractions is approximately: [tex]\(2.3904761904761904\)[/tex].
3. Now, convert the sum back to a fraction:
- The exact sum can be represented by the fraction [tex]\(\frac{251}{105}\)[/tex].
4. Verify the fraction and simplify if necessary:
- The fraction [tex]\(\frac{251}{105}\)[/tex] is already in its simplest form (as 251 and 105 have no common factors other than 1).
5. Summarize the results:
- The individual fractions and their decimal forms are:
- [tex]\(\frac{4}{3} \approx 1.3333333333333333\)[/tex]
- [tex]\(\frac{1}{5} = 0.2\)[/tex]
- [tex]\(\frac{6}{7} \approx 0.8571428571428571\)[/tex]
- The sum of these fractions is [tex]\( \frac{251}{105} \)[/tex] which is approximately [tex]\(2.3904761904761904\)[/tex].
In conclusion, adding the fractions [tex]\(\frac{4}{3} + \frac{1}{5} + \frac{6}{7}\)[/tex] results in [tex]\(\frac{251}{105}\)[/tex], with a decimal approximation of [tex]\(2.3904761904761904\)[/tex].
