Question

Complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions. Find 1/4 ÷ 3/8. ....................................................................................................................................................
Step 1:rewrite it as 1/4/3/8. ....................................................................................................................................................Step 2:multiply the numerator and the denominator by the reciprocal of blank /blank. 1/4/3/8=1/4/3/8×blank/blank/ blank /blank.                                                                     ....................................................................................................................................................Step 3:simplify the denominator 1/4×8/3/blank                                                                  .................................................................................................................................................Step 4:simplify the fraction blank/blank ×blank/blank.               

Answer 1

To complete the steps to demonstrate why you multiply by the reciprocal when dividing fractions.

To find
$\frac{1}{4}\div\frac{3}8}$

Step 1:
Rewrite it as
$\frac{\frac{1}{4}}{\frac{3}{8}}$.


Step 2:
Multiply the numerator and the denominator by the reciprocal of
$\frac{3}{8}$.

$\frac{\frac{1}{4}}{\frac{3}{8}}=\frac{\frac{1}{4}}{\frac{3}{8}}\times\frac{\frac{8}{3}}{\frac{8}{3}}$


Step 3:
Simplify the denominator
$\frac{\frac{1}{4}\times\frac{8}{3}}{1}$                                                                 

Step 4:
Simplify the fraction
$\frac{1}{4}\times\frac{8}{3}$.

We complete the solution as follows:
$\frac{1}{4}\times\frac{8}{3}=\frac{1\times8}{4\times3}\\ \\=\frac{8}{12}=\frac{4\times2}{4\times3}=\frac{2}{3}$