Answer :
To find the difference between the fractions
[tex]$$\frac{8}{9} \text{ and } \frac{5}{6},$$[/tex]
we start by expressing both fractions with a common denominator.
1. The denominators are 9 and 6. The least common multiple (LCM) of 9 and 6 is 18, which will be our common denominator.
2. Convert each fraction to have the denominator 18:
- For the fraction [tex]$\frac{8}{9}$[/tex], multiply the numerator and denominator by 2:
[tex]$$\frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}.$$[/tex]
- For the fraction [tex]$\frac{5}{6}$[/tex], multiply the numerator and denominator by 3:
[tex]$$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}.$$[/tex]
3. Now, subtract the second fraction from the first:
[tex]$$\frac{16}{18} - \frac{15}{18} = \frac{16-15}{18} = \frac{1}{18}.$$[/tex]
Thus, the difference between the two fractions is
[tex]$$\boxed{\frac{1}{18}}.$$[/tex]
This corresponds to option (A).
[tex]$$\frac{8}{9} \text{ and } \frac{5}{6},$$[/tex]
we start by expressing both fractions with a common denominator.
1. The denominators are 9 and 6. The least common multiple (LCM) of 9 and 6 is 18, which will be our common denominator.
2. Convert each fraction to have the denominator 18:
- For the fraction [tex]$\frac{8}{9}$[/tex], multiply the numerator and denominator by 2:
[tex]$$\frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}.$$[/tex]
- For the fraction [tex]$\frac{5}{6}$[/tex], multiply the numerator and denominator by 3:
[tex]$$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}.$$[/tex]
3. Now, subtract the second fraction from the first:
[tex]$$\frac{16}{18} - \frac{15}{18} = \frac{16-15}{18} = \frac{1}{18}.$$[/tex]
Thus, the difference between the two fractions is
[tex]$$\boxed{\frac{1}{18}}.$$[/tex]
This corresponds to option (A).
