Question

1\frac{1}{2}\div1\frac{1}{3}=1\frac{1}{2}\div2\frac{2}{3}
?\times1\frac{1}{3}=

Explanation:

Step1: Convert mixed - numbers to improper fractions

$1\frac{1}{2}=\frac{1\times2 + 1}{2}=\frac{3}{2}$, $1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{4}{3}$, $2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3}$

Step2: Calculate the first division

$\frac{3}{2}\div\frac{4}{3}=\frac{3}{2}\times\frac{3}{4}=\frac{9}{8}$

Step3: Calculate the second division

$\frac{3}{2}\div\frac{8}{3}=\frac{3}{2}\times\frac{3}{8}=\frac{9}{16}$

Step4: Calculate the multiplication for the blank on the right

$\frac{9}{16}\times\frac{4}{3}=\frac{9\times4}{16\times3}=\frac{3}{4}$

Step5: Calculate the multiplication for the blank on the left

$\frac{9}{8}\times\frac{4}{3}=\frac{9\times4}{8\times3}=\frac{3}{2}$

Answer:

$\frac{3}{2}$; $\frac{3}{4}$