Answer :
To find the sum of the fractions [tex]\(\frac{7}{12}\)[/tex] and [tex]\(\frac{18}{12}\)[/tex], follow these steps:
1. Add the Fractions:
Both fractions have the same denominator of 12, which makes adding them straightforward. You add the numerators together:
[tex]\[
\frac{7}{12} + \frac{18}{12} = \frac{7 + 18}{12} = \frac{25}{12}
\][/tex]
2. Convert to a Mixed Number:
The fraction [tex]\(\frac{25}{12}\)[/tex] is an improper fraction because the numerator is larger than the denominator. We can convert it to a mixed number.
- Divide the numerator by the denominator: [tex]\(25 \div 12\)[/tex]
- This division gives 2 as the whole number (since 12 goes into 25 two times) with a remainder.
- Calculate the remainder: [tex]\(25 - 2 \times 12 = 25 - 24 = 1\)[/tex]
So, the remainder is 1. This means:
[tex]\[
\frac{25}{12} = 2 \frac{1}{12}
\][/tex]
3. Select the Correct Answer:
From the options provided:
- A. [tex]\(1 \frac{1}{24}\)[/tex]
- B. [tex]\(\frac{11}{12}\)[/tex]
- C. [tex]\(2 \frac{1}{12}\)[/tex]
- D. [tex]\(\frac{12}{25}\)[/tex]
The correct answer is C. [tex]\(2 \frac{1}{12}\)[/tex].
So, the solution to the problem is [tex]\(2 \frac{1}{12}\)[/tex].
1. Add the Fractions:
Both fractions have the same denominator of 12, which makes adding them straightforward. You add the numerators together:
[tex]\[
\frac{7}{12} + \frac{18}{12} = \frac{7 + 18}{12} = \frac{25}{12}
\][/tex]
2. Convert to a Mixed Number:
The fraction [tex]\(\frac{25}{12}\)[/tex] is an improper fraction because the numerator is larger than the denominator. We can convert it to a mixed number.
- Divide the numerator by the denominator: [tex]\(25 \div 12\)[/tex]
- This division gives 2 as the whole number (since 12 goes into 25 two times) with a remainder.
- Calculate the remainder: [tex]\(25 - 2 \times 12 = 25 - 24 = 1\)[/tex]
So, the remainder is 1. This means:
[tex]\[
\frac{25}{12} = 2 \frac{1}{12}
\][/tex]
3. Select the Correct Answer:
From the options provided:
- A. [tex]\(1 \frac{1}{24}\)[/tex]
- B. [tex]\(\frac{11}{12}\)[/tex]
- C. [tex]\(2 \frac{1}{12}\)[/tex]
- D. [tex]\(\frac{12}{25}\)[/tex]
The correct answer is C. [tex]\(2 \frac{1}{12}\)[/tex].
So, the solution to the problem is [tex]\(2 \frac{1}{12}\)[/tex].