To solve the equation \(4 \frac{4}{5}=\frac{\square}{15}=\square\), we'll go through the process step-by-step:
1. Convert the mixed fraction to an improper fraction:
- The mixed fraction provided is \( 4 \frac{4}{5} \).
- To convert this mixed fraction to an improper fraction, first multiply the whole number part (4) by the denominator (5):
[tex]\[
4 \times 5 = 20
\][/tex]
- Next, add the numerator of the fractional part (which is 4):
[tex]\[
20 + 4 = 24
\][/tex]
- The improper fraction is thus \(\frac{24}{5}\).
2. Convert the improper fraction to an equivalent fraction with a denominator of 15:
- We need to express \(\frac{24}{5}\) with a denominator of 15.
- To do this, determine what number needs to multiply the current denominator (5) to make it 15:
[tex]\[
5 \times 3 = 15
\][/tex]
- To maintain equivalence, we must also multiply the numerator (24) by the same number (3):
[tex]\[
24 \times 3 = 72
\][/tex]
- Thus, \(\frac{24}{5}\) is equivalent to \(\frac{72}{15}\).
3. Express the result:
- The final simplified fraction \(\frac{72}{15}\) maintains the same value as the original mixed fraction \(4 \frac{4}{5}\).
- Hence, in the form \(\frac{\square}{15}\), we have:
[tex]\[
4 \frac{4}{5} = \frac{72}{15}
\][/tex]
- The box filled in for this problem is \(\boxed{72}\).
In conclusion, the full equation with the converted fraction is:
[tex]\[
4 \frac{4}{5} = \frac{72}{15} = 72
\][/tex]
