Sure, let's break down the process of converting the mixed number [tex]\( 24 \frac{3}{5} \)[/tex] into an improper fraction step-by-step.
1. Identify the components of the mixed number:
- The whole number part is [tex]\( 24 \)[/tex].
- The fractional part is [tex]\( \frac{3}{5} \)[/tex].
2. Convert the whole number part to a fraction having the same denominator as the fractional part:
- Since [tex]\( 24 \)[/tex] is a whole number, we can represent it as [tex]\( \frac{24}{1} \)[/tex].
- To give it the same denominator as the fractional part ([tex]\(5\)[/tex]), we need to multiply both the numerator and the denominator by 5:
[tex]\[
24 = \frac{24 \times 5}{1 \times 5} = \frac{120}{5}
\][/tex]
3. Add the fractional part to the converted whole number fraction:
- The fractional part already has the denominator, which is [tex]\( \frac{3}{5} \)[/tex].
- Now, add the two fractions:
[tex]\[
\frac{120}{5} + \frac{3}{5} = \frac{120 + 3}{5} = \frac{123}{5}
\][/tex]
Therefore, the equivalent improper fraction of the mixed number [tex]\( 24 \frac{3}{5} \)[/tex] is [tex]\( \frac{123}{5} \)[/tex].
Out of the given options, the correct one is:
[tex]\[
\frac{123}{5}
\][/tex]
