To solve the problem \(\frac{3}{4} - \frac{2}{3}\), we follow these steps:
1. Find a common denominator for the fractions:
To subtract fractions with different denominators, we first need to find a common denominator. The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12. So, we will use 12 as the common denominator.
2. Adjust the numerators based on the common denominator:
- For \(\frac{3}{4}\), we need to convert it to an equivalent fraction with a denominator of 12. To do this, we multiply the numerator and denominator by 3 (since \(4 \times 3 = 12\)):
[tex]\[
\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}
\][/tex]
- For \(\frac{2}{3}\), we need to convert it to an equivalent fraction with a denominator of 12. To do this, we multiply the numerator and denominator by 4 (since \(3 \times 4 = 12\)):
[tex]\[
\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}
\][/tex]
3. Subtract the numerators while keeping the common denominator:
Now that both fractions have the same denominator, we can subtract the numerators:
[tex]\[
\frac{9}{12} - \frac{8}{12} = \frac{9 - 8}{12} = \frac{1}{12}
\][/tex]
So, [tex]\(\frac{3}{4} - \frac{2}{3} = \frac{1}{12}\)[/tex].
