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

`(1)/(4)/\frac{3}8}`

Step 1:
Rewrite it as

`((1)/(4))/((3)/(8))`.


Step 2:
Multiply the numerator and the denominator by the reciprocal of

`(3)/(8)`.


`((1)/(4))/((3)/(8))=((1)/(4))/((3)/(8))*((8)/(3))/((8)/(3))`


Step 3:
Simplify the denominator

`((1)/(4)*(8)/(3))/(1)`

Step 4:
Simplify the fraction

`(1)/(4)*(8)/(3)`.

We complete the solution as follows:

`(1)/(4)*(8)/(3)=(1*8)/(4*3)\\ \\=(8)/(12)=(4*2)/(4*3)=(2)/(3)`