To subtract the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], follow these steps:
1. Find a common denominator:
The denominators of the fractions are 6 and 4. The least common multiple (LCM) of 6 and 4 is 12. Therefore, we will use 12 as the common denominator.
2. Convert the fractions to have the common denominator:
- For [tex]\(\frac{5}{6}\)[/tex], you need to make the denominator 12. To do this, multiply both the numerator and the denominator by 2:
[tex]\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\][/tex]
- For [tex]\(\frac{3}{4}\)[/tex], you need to make the denominator 12. To do this, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\][/tex]
3. Subtract the fractions:
Now that both fractions have the same denominator, you can subtract the numerators:
[tex]\[
\frac{10}{12} - \frac{9}{12} = \frac{10 - 9}{12} = \frac{1}{12}
\][/tex]
4. Convert the result to a decimal form if needed:
The fraction [tex]\(\frac{1}{12}\)[/tex] in decimal form is approximately [tex]\(0.0833333333333334\)[/tex].
Thus, the result of [tex]\(\frac{5}{6} - \frac{3}{4}\)[/tex] is [tex]\(\frac{1}{12} \approx 0.0833333333333334\)[/tex].
