To solve the problem [tex]\(\frac{1}{8} - \frac{2}{3}\)[/tex], we need to follow these steps:
1. Identify the Common Denominator:
The denominators of the given fractions are 8 and 3. The least common multiple of these two numbers is 24. This will be our common denominator.
2. Convert the Fractions:
We need to convert both fractions to have this common denominator.
[tex]\[\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}\][/tex]
[tex]\[\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}\][/tex]
3. Subtract the Numerators:
Now with a common denominator, we can subtract the numerators.
[tex]\[\frac{3}{24} - \frac{16}{24} = \frac{3 - 16}{24} = \frac{-13}{24}\][/tex]
4. Simplify the Result if Necessary:
The fraction [tex]\(\frac{-13}{24}\)[/tex] is already in its simplest form.
5. Convert to Decimal Form (Optional):
For additional clarity, we can also convert the fraction to a decimal.
[tex]\[\frac{-13}{24} \approx -0.5416666666666666\][/tex]
Thus, the step-by-step solution to the problem [tex]\(\frac{1}{8} - \frac{2}{3}\)[/tex] is:
1. The common denominator is 24.
2. Convert [tex]\(\frac{1}{8}\)[/tex] to [tex]\(\frac{3}{24}\)[/tex].
3. Convert [tex]\(\frac{2}{3}\)[/tex] to [tex]\(\frac{16}{24}\)[/tex].
4. Subtract the numerators: [tex]\(3 - 16 = -13\)[/tex].
5. The resulting fraction is [tex]\(\frac{-13}{24}\)[/tex].
6. In decimal form, this is approximately [tex]\(-0.5417\)[/tex].
So, [tex]\(\frac{1}{8} - \frac{2}{3} = \frac{-13}{24} \approx -0.5417\)[/tex].
