Sure, let's solve the given expression step by step:
We have the expression:
[tex]\[
\frac{3}{8} - \left( \frac{1}{6} + \frac{1}{12} \right)
\][/tex]
First, we need to simplify the part inside the parentheses, which is [tex]\(\frac{1}{6} + \frac{1}{12}\)[/tex].
To add these fractions, we need a common denominator. The denominators are 6 and 12. The least common denominator (LCD) of 6 and 12 is 12.
We convert [tex]\(\frac{1}{6}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
\][/tex]
Now, we can add [tex]\(\frac{2}{12}\)[/tex] and [tex]\(\frac{1}{12}\)[/tex]:
[tex]\[
\frac{2}{12} + \frac{1}{12} = \frac{2 + 1}{12} = \frac{3}{12}
\][/tex]
Next, we simplify [tex]\(\frac{3}{12}\)[/tex]:
[tex]\[
\frac{3}{12} = \frac{1}{4}
\][/tex]
So, the expression inside the parentheses simplifies to:
[tex]\[
\frac{1}{6} + \frac{1}{12} = \frac{1}{4}
\][/tex]
Now, we need to subtract this result from [tex]\(\frac{3}{8}\)[/tex]:
[tex]\[
\frac{3}{8} - \frac{1}{4}
\][/tex]
To subtract these fractions, we again need a common denominator. The denominators are 8 and 4. The least common denominator (LCD) of 8 and 4 is 8.
We convert [tex]\(\frac{1}{4}\)[/tex] to a fraction with a denominator of 8:
[tex]\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\][/tex]
Now, we can subtract [tex]\(\frac{2}{8}\)[/tex] from [tex]\(\frac{3}{8}\)[/tex]:
[tex]\[
\frac{3}{8} - \frac{2}{8} = \frac{3 - 2}{8} = \frac{1}{8}
\][/tex]
So, the final result is:
[tex]\[
\frac{3}{8} - \left( \frac{1}{6} + \frac{1}{12} \right) = \frac{1}{8}
\][/tex]
In decimal form, this is:
[tex]\[
0.125
\][/tex]
To summarize:
- Simplified [tex]\(\frac{1}{6} + \frac{1}{12}\)[/tex] as [tex]\(\frac{1}{4}\)[/tex] or 0.25.
- Subtracted [tex]\(\frac{1}{4}\)[/tex] or 0.25 from [tex]\(\frac{3}{8}\)[/tex] or 0.375 to get [tex]\(\frac{1}{8}\)[/tex] which is 0.125.
So, the expression [tex]\(\frac{3}{8} - \left( \frac{1}{6} + \frac{1}{12} \right)\)[/tex] evaluates to 0.125.
