To determine which of the given fractions is the smallest, let's compare each fraction step-by-step. We need to identify the smallest fraction among the following: [tex]\(\frac{7}{24}\)[/tex], [tex]\(\frac{5}{12}\)[/tex], [tex]\(\frac{1}{4}\)[/tex], [tex]\(\frac{1}{3}\)[/tex], and [tex]\(\frac{3}{4}\)[/tex].
First, let's list the fractions:
- A: [tex]\(\frac{7}{24}\)[/tex]
- B: [tex]\(\frac{5}{12}\)[/tex]
- C: [tex]\(\frac{1}{4}\)[/tex]
- D: [tex]\(\frac{1}{3}\)[/tex]
- E: [tex]\(\frac{3}{4}\)[/tex]
Now, we need to compare these fractions to find the smallest one. Comparing fractions typically involves converting them to a common denominator or converting them to decimal form.
We know from a reliable calculation that the smallest fraction among the given options is [tex]\(\frac{1}{4}\)[/tex].
Step-by-step process:
1. Compare [tex]\(\frac{7}{24}\)[/tex] and [tex]\(\frac{5}{12}\)[/tex]:
- Convert to a common denominator: The common denominator of 24 and 12 is 24.
- [tex]\(\frac{5}{12} = \frac{10}{24}\)[/tex].
- Compare [tex]\(\frac{7}{24}\)[/tex] and [tex]\(\frac{10}{24}\)[/tex]: [tex]\(\frac{7}{24}\)[/tex] is smaller.
2. Compare [tex]\(\frac{7}{24}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
- Convert to a common denominator: The common denominator of 24 and 4 is 24.
- [tex]\(\frac{1}{4} = \frac{6}{24}\)[/tex].
- Compare [tex]\(\frac{7}{24}\)[/tex] and [tex]\(\frac{6}{24}\)[/tex]: [tex]\(\frac{6}{24} = \frac{1}{4}\)[/tex] is smaller.
3. Compare [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
- Convert to a common denominator: The common denominator of 4 and 3 is 12.
- [tex]\(\frac{1}{3} = \frac{4}{12}\)[/tex] and [tex]\(\frac{1}{4} = \frac{3}{12}\)[/tex].
- Compare [tex]\(\frac{3}{12}\)[/tex] and [tex]\(\frac{4}{12}\)[/tex]: [tex]\(\frac{3}{12} = \frac{1}{4}\)[/tex] is smaller.
4. Compare [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]:
- Comparing [tex]\(\frac{1}{4}\)[/tex] (which equals 0.25) with [tex]\(\frac{3}{4}\)[/tex] (which equals 0.75): [tex]\(\frac{1}{4}\)[/tex] is smaller.
From these comparisons, it is evident that [tex]\(\frac{1}{4}\)[/tex] is the smallest fraction.
Therefore, among the fractions given, the smallest one is:
[tex]\[
\boxed{\frac{1}{4} \text{ (C)}}
\][/tex]
