College

What is the difference between [tex]$\frac{8}{9}$[/tex] and [tex]$\frac{5}{6}$[/tex]?

A. [tex][tex]$\frac{1}{18}$[/tex][/tex]
B. [tex]$\frac{1}{6}$[/tex]
C. [tex]$\frac{1}{2}$[/tex]
D. [tex][tex]$\frac{13}{15}$[/tex][/tex]

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).