Answer:
Change the mixed numbers into an improper fraction:
[tex]2\frac16 \div 2\frac12=\dfrac{2 \times 6+1}{6}\div \dfrac{2 \times 2+1}{2}=\dfrac{13}{6}\div \dfrac{5}{2}[/tex]
Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. (Reciprocal is when you swap the numerator and denominator). Therefore,
[tex]\dfrac{13}{6}\div \dfrac{5}{2}=\dfrac{13}{6}\times\dfrac{2}{5}[/tex]
Now we simply multiply the numerators and the denominators:
[tex]\dfrac{13}{6}\times\dfrac{2}{5}=\dfrac{13 \times 2}{6\times 5}=\dfrac{26}{30}[/tex]
We can now reduce the fraction to its simplest form by dividing the numerator and denominator by 2:
[tex]\dfrac{26}{30}=\dfrac{26\div 2}{30 \div 2}=\dfrac{13}{15}[/tex]
