Question

2/3 2 ÷ 3/4 3

Explanation:

Step1: Convert mixed numbers to improper fractions

The mixed number \(2\frac{2}{3}\) can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator. So, \(2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{6+2}{3}=\frac{8}{3}\).
The mixed number \(3\frac{3}{4}\) is converted as \(3\frac{3}{4}=\frac{3\times4+3}{4}=\frac{12 + 3}{4}=\frac{15}{4}\).

Step2: Divide the improper fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So, \(\frac{8}{3}\div\frac{15}{4}=\frac{8}{3}\times\frac{4}{15}\).

Step3: Multiply the numerators and denominators

Multiply the numerators: \(8\times4 = 32\).
Multiply the denominators: \(3\times15=45\).
So, the result is \(\frac{32}{45}\).

Answer:

\(\frac{32}{45}\)