To solve the expression [tex]\( \frac{2}{3} + \frac{5}{6} - \frac{1}{12} \)[/tex], we follow these steps:
1. Identify a common denominator:
The denominators we have are 3, 6, and 12. The least common multiple (LCM) of these three numbers is 12. Hence, we will convert all fractions to have a denominator of 12.
2. Convert each fraction to the common denominator:
- For [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
- For [tex]\( \frac{5}{6} \)[/tex]:
[tex]\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\][/tex]
- For [tex]\( \frac{1}{12} \)[/tex], it is already in the form with the common denominator, so it remains [tex]\( \frac{1}{12} \)[/tex].
3. Perform the arithmetic operations:
Now add and subtract the fractions with the common denominator:
[tex]\[
\frac{8}{12} + \frac{10}{12} - \frac{1}{12}
\][/tex]
4. Sum the numerators:
Combine the numerators:
[tex]\[
8 + 10 - 1 = 17
\][/tex]
5. Create the final fraction:
Place the combined numerator over the common denominator:
[tex]\[
\frac{17}{12}
\][/tex]
6. Convert the improper fraction to a mixed number:
- Calculate the whole number part by dividing the numerator by the denominator:
[tex]\[
\frac{17}{12} = 1 \text{ (whole number) } + \frac{5}{12} \text{ (remainder)}
\][/tex]
Hence, the mixed number is:
[tex]\[
1 \frac{5}{12}
\][/tex]
In summary, the value of the expression [tex]\( \frac{2}{3} + \frac{5}{6} - \frac{1}{12} \)[/tex] is:
[tex]\[
1 \frac{5}{12}
\][/tex]
