Question

How do you divide `1 2/ 6\div 1/ 3`?

Answer 1

`4`

Explanation:

The key to division of fractions is to reciprocate the divisor (what comes after the division sign) and change the division sign to multiplication.

In this case, we have a mixed fraction so we change it to an improper fraction first.

How do we do that?

Simple!

Take the denominator of the mixed fraction, multiply it by the whole number and add the numerator.

Whatever value you get becomes the numerator of the improper fraction over the denominator of the mixed fraction.

So for `1(2)/6`, we multiply `6` by `1` and add the product to `2`

`(6*1)+2`

`6+2`

`8`

So our numerator is `8` over our denominator which is `6`

`:.`Our improper fraction is `8/6=4/3`

Back to our question;

`1(2)/6-:1/3`

`4/3-:1/3`

Reciprocate `1/3` and change the division sign to multiplication.

`4/3xx3/1`

Multiply the numerators and the denominators.

`12/3`

Reduce the fraction if possible

`=(4xxcancel(3))/cancel3`

`rArr4`