how do u divide 72 divided by 3/4

 

Golden Leaf, you did get the right answer but you did a lot of very unnecessary working.

You do not need to get a common denominator when you multiply  fractions!

 

$$72\div \frac{3}{4}\\\\ =\frac{72}{1}\div \frac{3}{4}\\\\ =\frac{72}{1}\times \frac{4}{3}\\\\ \mbox{cancel the 3 on the bottom and the 72 on the top by dividing by 3}\\\\ =\frac{24}{1}\times \frac{4}{1}\\\\ =\frac{24\times4}{1\times1}\\\\ =96\\\\$$

There is no dividing by a fraction. Thus, you must 'flip' the fraction (or take the inverse) and change the division sign to a multiplication sign. This makes:

 

$${\frac{{\mathtt{72}}}{\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right)}}$$

 

Into:

 

$${\mathtt{72}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{4}}}{{\mathtt{3}}}}\right)$$

 

This because, similar to subtraction and how subtracting a negative number from a positive number makes it addition, dividing a number that is already being divided just makes the two division signs cancel each other out and become a multiplication sign.

 

It is wise to make the 72 into a like fraction: That is, make the denominators similar between the two fractions. In order to do this, multiply 72 by 3, and then put that number over 3.

 

$${\mathtt{72}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{216}}$$

$${\frac{{\mathtt{216}}}{{\mathtt{3}}}}$$

 

This now makes like denominators between the fractions, and thus the whole thing can be put over 9 once the fractions are multiplied together.

 

$${\frac{\left({\mathtt{216}}{\mathtt{\,\times\,}}{\mathtt{4}}\right)}{{\mathtt{9}}}}$$

 

Multiply to make it a simpler fraction.

 

$${\mathtt{216}}{\mathtt{\,\times\,}}{\mathtt{4}} = {\mathtt{864}}$$

$${\frac{{\mathtt{864}}}{{\mathtt{9}}}}$$

 

Now simplify the fraction. This means dividing 864 by 9.

 

$${\frac{{\mathtt{864}}}{{\mathtt{9}}}} = {\mathtt{96}}$$

 

Your final answer is 96.