Answer:
quotient = 7
Step-by-step explanation:
We are asked to evaluate the following expression:
[tex]4\frac{2}{3} \div \frac{2}{3}[/tex]
• To solve this we can first convert the mixed number [tex]4\frac{2}{3}[/tex] into an improper fraction:
[tex]4\frac{2}{3}[/tex] ⇒ [tex]\frac{14}{3}[/tex]
• Next, we know that dividing by a fraction is the same as multiplying by its reciprocal (the reciprocal of a fraction is what is you get by swapping the numerator and denominator):
reciprocal of [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{2}[/tex].
• Therefore, the expression now becomes:
[tex]4\frac{2}{3} \div \frac{2}{3}[/tex]
⇒ [tex]\frac {14}{3} \div \frac {2}{3}[/tex]
⇒ [tex]\frac {14}{3} \times \frac {3}{2}[/tex]
⇒ 7
