Question

set 5 divide
divide. show
1 $2\frac{2}{3} \div \frac{2}{3}$

Explanation:

Step1: Convert mixed number to improper fraction

To divide a mixed number by a fraction, first convert the mixed number \(2\frac{2}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{2}{3}\), we have \(a = 2\), \(b = 2\), \(c = 3\). Then \(\frac{2\times3 + 2}{3}=\frac{6 + 2}{3}=\frac{8}{3}\).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction \(\frac{2}{3}\) is the same as multiplying by its reciprocal. The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\). So we have \(\frac{8}{3}\div\frac{2}{3}=\frac{8}{3}\times\frac{3}{2}\).

Step3: Simplify the multiplication

When we multiply \(\frac{8}{3}\times\frac{3}{2}\), the 3 in the numerator and the 3 in the denominator cancel out. Then we have \(\frac{8\times1}{1\times2}=\frac{8}{2}\).

Step4: Final simplification

Simplify \(\frac{8}{2}\) to get 4.

Answer:

4