To simplify the expression [tex]\(\frac{7}{24} + \frac{9}{24} - \frac{1}{24} + \frac{11}{24}\)[/tex], follow these steps:
1. Identify the common denominator:
All fractions have a common denominator of 24.
2. Combine the fractions:
Combine the numerators over the common denominator:
[tex]\[
\frac{7}{24} + \frac{9}{24} - \frac{1}{24} + \frac{11}{24} = \frac{7 + 9 - 1 + 11}{24}
\][/tex]
3. Perform the operations in the numerator:
Add and subtract the numerators step-by-step:
[tex]\[
7 + 9 = 16
\][/tex]
[tex]\[
16 - 1 = 15
\][/tex]
[tex]\[
15 + 11 = 26
\][/tex]
4. Combine the result:
Now, we have:
[tex]\[
\frac{7 + 9 - 1 + 11}{24} = \frac{26}{24}
\][/tex]
5. Simplify the fraction:
Simplify [tex]\(\frac{26}{24}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{26 \div 2}{24 \div 2} = \frac{13}{12}
\][/tex]
Now, if we express [tex]\(\frac{13}{12}\)[/tex] as a mixed number, we get:
[tex]\[
1 \frac{1}{12}
\][/tex]
Thus, the simplified form of the given expression is [tex]\(\frac{13}{12}\)[/tex] or [tex]\(1 \frac{1}{12}\)[/tex].
