Question

evaluate the expression below. enter the answer as a mixed number or as a fraction.
$2\frac{3}{5} \div 4\frac{3}{4}$
show your work here

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(2\frac{3}{5}\) to an improper fraction, we use the formula: \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(2\frac{3}{5}\), we have \(a = 2\), \(b=3\), \(c = 5\). Then \(\frac{2\times5+3}{5}=\frac{10 + 3}{5}=\frac{13}{5}\).

For \(4\frac{3}{4}\), with \(a = 4\), \(b = 3\), \(c=4\), we get \(\frac{4\times4+3}{4}=\frac{16+3}{4}=\frac{19}{4}\).

Step2: Divide the two improper fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So \( \frac{13}{5}\div\frac{19}{4}=\frac{13}{5}\times\frac{4}{19}\).

Step3: Multiply the numerators and denominators

Multiply the numerators: \(13\times4 = 52\). Multiply the denominators: \(5\times19=95\). So the result is \(\frac{52}{95}\).

Answer:

\(\frac{52}{95}\)