Question

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

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(4\frac{3}{5}\) to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So for \(4\frac{3}{5}\), we have \(a = 4\), \(b=3\), \(c = 5\). Then \(\frac{4\times5+3}{5}=\frac{20 + 3}{5}=\frac{23}{5}\).

For \(3\frac{2}{5}\), using the same formula with \(a = 3\), \(b = 2\), \(c=5\), we get \(\frac{3\times5+2}{5}=\frac{15+2}{5}=\frac{17}{5}\).

Step2: Divide the two improper fractions

Dividing fractions is done by multiplying the first fraction by the reciprocal of the second fraction. So \(\frac{23}{5}\div\frac{17}{5}=\frac{23}{5}\times\frac{5}{17}\).

The 5 in the numerator and the 5 in the denominator cancel out, leaving us with \(\frac{23}{17}\).

Step3: Convert to mixed number (optional, but since the problem allows mixed number or fraction)

To convert \(\frac{23}{17}\) to a mixed number, we divide 23 by 17. 17 goes into 23 once with a remainder of 6. So \(\frac{23}{17}=1\frac{6}{17}\).

Answer:

\(1\frac{6}{17}\) (or \(\frac{23}{17}\))