Answer :
Certainly! Let's compare each pair of fractions step by step to determine which is greater.
### a) [tex]\(\frac{1}{6}\)[/tex] vs. [tex]\(\frac{1}{8}\)[/tex]
To compare [tex]\(\frac{1}{6}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex], we cross multiply:
[tex]\[ 1 \times 8 \text{ vs. } 1 \times 6 \][/tex]
This leads to:
[tex]\[ 8 \text{ vs. } 6 \][/tex]
Since 8 is greater than 6, [tex]\(\frac{1}{6}\)[/tex] is greater than [tex]\(\frac{1}{8}\)[/tex].
So, [tex]\(\frac{1}{6}\)[/tex] is the greater fraction.
### b) [tex]\(\frac{3}{4}\)[/tex] vs. [tex]\(\frac{5}{6}\)[/tex]
To compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], we cross multiply:
[tex]\[ 3 \times 6 \text{ vs. } 4 \times 5 \][/tex]
This leads to:
[tex]\[ 18 \text{ vs. } 20 \][/tex]
Since 20 is greater than 18, [tex]\(\frac{5}{6}\)[/tex] is greater than [tex]\(\frac{3}{4}\)[/tex].
So, [tex]\(\frac{5}{6}\)[/tex] is the greater fraction.
### c) [tex]\(\frac{2}{3}\)[/tex] vs. [tex]\(\frac{3}{4}\)[/tex]
To compare [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], we cross multiply:
[tex]\[ 2 \times 4 \text{ vs. } 3 \times 3 \][/tex]
This leads to:
[tex]\[ 8 \text{ vs. } 9 \][/tex]
Since 9 is greater than 8, [tex]\(\frac{3}{4}\)[/tex] is greater than [tex]\(\frac{2}{3}\)[/tex].
So, [tex]\(\frac{3}{4}\)[/tex] is the greater fraction.
### d) [tex]\(\frac{7}{8}\)[/tex] vs. [tex]\(\frac{6}{7}\)[/tex]
To compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex], we cross multiply:
[tex]\[ 7 \times 7 \text{ vs. } 8 \times 6 \][/tex]
This leads to:
[tex]\[ 49 \text{ vs. } 48 \][/tex]
Since 49 is greater than 48, [tex]\(\frac{7}{8}\)[/tex] is greater than [tex]\(\frac{6}{7}\)[/tex].
So, [tex]\(\frac{7}{8}\)[/tex] is the greater fraction.
### e) [tex]\(\frac{2}{5}\)[/tex] vs. [tex]\(\frac{2}{6}\)[/tex]
To compare [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{2}{6}\)[/tex], we cross multiply:
[tex]\[ 2 \times 6 \text{ vs. } 2 \times 5 \][/tex]
This leads to:
[tex]\[ 12 \text{ vs. } 10 \][/tex]
Since 12 is greater than 10, [tex]\(\frac{2}{5}\)[/tex] is greater than [tex]\(\frac{2}{6}\)[/tex].
So, [tex]\(\frac{2}{5}\)[/tex] is the greater fraction.
### Summary:
- For part a), [tex]\(\frac{1}{6}\)[/tex] is greater.
- For part b), [tex]\(\frac{5}{6}\)[/tex] is greater.
- For part c), [tex]\(\frac{3}{4}\)[/tex] is greater.
- For part d), [tex]\(\frac{7}{8}\)[/tex] is greater.
- For part e), [tex]\(\frac{2}{5}\)[/tex] is greater.
The greater fractions from each pair are:
[tex]\[ \left( \frac{1}{6}, \frac{5}{6}, \frac{3}{4}, \frac{7}{8}, \frac{2}{5} \right) \][/tex]
### a) [tex]\(\frac{1}{6}\)[/tex] vs. [tex]\(\frac{1}{8}\)[/tex]
To compare [tex]\(\frac{1}{6}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex], we cross multiply:
[tex]\[ 1 \times 8 \text{ vs. } 1 \times 6 \][/tex]
This leads to:
[tex]\[ 8 \text{ vs. } 6 \][/tex]
Since 8 is greater than 6, [tex]\(\frac{1}{6}\)[/tex] is greater than [tex]\(\frac{1}{8}\)[/tex].
So, [tex]\(\frac{1}{6}\)[/tex] is the greater fraction.
### b) [tex]\(\frac{3}{4}\)[/tex] vs. [tex]\(\frac{5}{6}\)[/tex]
To compare [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], we cross multiply:
[tex]\[ 3 \times 6 \text{ vs. } 4 \times 5 \][/tex]
This leads to:
[tex]\[ 18 \text{ vs. } 20 \][/tex]
Since 20 is greater than 18, [tex]\(\frac{5}{6}\)[/tex] is greater than [tex]\(\frac{3}{4}\)[/tex].
So, [tex]\(\frac{5}{6}\)[/tex] is the greater fraction.
### c) [tex]\(\frac{2}{3}\)[/tex] vs. [tex]\(\frac{3}{4}\)[/tex]
To compare [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], we cross multiply:
[tex]\[ 2 \times 4 \text{ vs. } 3 \times 3 \][/tex]
This leads to:
[tex]\[ 8 \text{ vs. } 9 \][/tex]
Since 9 is greater than 8, [tex]\(\frac{3}{4}\)[/tex] is greater than [tex]\(\frac{2}{3}\)[/tex].
So, [tex]\(\frac{3}{4}\)[/tex] is the greater fraction.
### d) [tex]\(\frac{7}{8}\)[/tex] vs. [tex]\(\frac{6}{7}\)[/tex]
To compare [tex]\(\frac{7}{8}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex], we cross multiply:
[tex]\[ 7 \times 7 \text{ vs. } 8 \times 6 \][/tex]
This leads to:
[tex]\[ 49 \text{ vs. } 48 \][/tex]
Since 49 is greater than 48, [tex]\(\frac{7}{8}\)[/tex] is greater than [tex]\(\frac{6}{7}\)[/tex].
So, [tex]\(\frac{7}{8}\)[/tex] is the greater fraction.
### e) [tex]\(\frac{2}{5}\)[/tex] vs. [tex]\(\frac{2}{6}\)[/tex]
To compare [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{2}{6}\)[/tex], we cross multiply:
[tex]\[ 2 \times 6 \text{ vs. } 2 \times 5 \][/tex]
This leads to:
[tex]\[ 12 \text{ vs. } 10 \][/tex]
Since 12 is greater than 10, [tex]\(\frac{2}{5}\)[/tex] is greater than [tex]\(\frac{2}{6}\)[/tex].
So, [tex]\(\frac{2}{5}\)[/tex] is the greater fraction.
### Summary:
- For part a), [tex]\(\frac{1}{6}\)[/tex] is greater.
- For part b), [tex]\(\frac{5}{6}\)[/tex] is greater.
- For part c), [tex]\(\frac{3}{4}\)[/tex] is greater.
- For part d), [tex]\(\frac{7}{8}\)[/tex] is greater.
- For part e), [tex]\(\frac{2}{5}\)[/tex] is greater.
The greater fractions from each pair are:
[tex]\[ \left( \frac{1}{6}, \frac{5}{6}, \frac{3}{4}, \frac{7}{8}, \frac{2}{5} \right) \][/tex]
