Let's solve each problem step by step to find the correct matches.
1. [tex]\(\frac{5}{7} - \frac{3}{7}\)[/tex]:
- The fractions have the same denominator, so we can subtract the numerators directly.
- [tex]\(\frac{5-3}{7} = \frac{2}{7}\)[/tex].
- This matches with option B [tex]\(\frac{2}{7}\)[/tex].
2. [tex]\(\frac{1}{6} + \frac{3}{6}\)[/tex]:
- The fractions have the same denominator, so we can add the numerators directly.
- [tex]\(\frac{1+3}{6} = \frac{4}{6} = \frac{2}{3}\)[/tex] (simplified).
- This matches with option C [tex]\(\frac{2}{3}\)[/tex].
3. [tex]\(\frac{1}{2} + \frac{1}{4}\)[/tex]:
- Here, the denominators are different, so we first find a common denominator.
- The common denominator of 2 and 4 is 4.
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{2}{4}\)[/tex].
- Now, add the fractions: [tex]\(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex].
- This matches with option E [tex]\(\frac{3}{4}\)[/tex].
4. [tex]\(\frac{1}{5} + \frac{1}{2}\)[/tex]:
- The denominators are different, so we find a common denominator.
- The common denominator of 5 and 2 is 10.
- Convert [tex]\(\frac{1}{5}\)[/tex] to [tex]\(\frac{2}{10}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{5}{10}\)[/tex].
- Now, add the fractions: [tex]\(\frac{2}{10} + \frac{5}{10} = \frac{7}{10}\)[/tex].
- This matches with option D [tex]\(\frac{7}{10}\)[/tex].
5. [tex]\(\frac{1}{6} - \frac{1}{8}\)[/tex]:
- The denominators are different, so we find a common denominator.
- The common denominator of 6 and 8 is 24.
- Convert [tex]\(\frac{1}{6}\)[/tex] to [tex]\(\frac{4}{24}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex] to [tex]\(\frac{3}{24}\)[/tex].
- Now, subtract the fractions: [tex]\(\frac{4}{24} - \frac{3}{24} = \frac{1}{24}\)[/tex].
- This matches with option A [tex]\(\frac{1}{24}\)[/tex].
Therefore, the matches are:
- [tex]\(\frac{5}{7} - \frac{3}{7}\)[/tex] matches with B [tex]\(\frac{2}{7}\)[/tex].
- [tex]\(\frac{1}{6} + \frac{3}{6}\)[/tex] matches with C [tex]\(\frac{2}{3}\)[/tex].
- [tex]\(\frac{1}{2} + \frac{1}{4}\)[/tex] matches with E [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{1}{5} + \frac{1}{2}\)[/tex] matches with D [tex]\(\frac{7}{10}\)[/tex].
- [tex]\(\frac{1}{6} - \frac{1}{8}\)[/tex] matches with A [tex]\(\frac{1}{24}\)[/tex].
