Math CentralQuandaries & Queries


Question from Jennifer, a student:

I want to know how to get the right answer for this math problem, dividing a fraction in to a whole number , example 3/8 using the whole number 6? Thanks

Hi Jennifer,

Division is the inverse of multiplication so you can often think of a division problem by way of a multiplication problem. For example you know that


is 2 because

\[3 \times 2 = 6.\]

Think of your problem the same way. What is the number x so that

\[\frac{6}{3/8} = x\]

is equivalent to asking what is the number $x$ so that

\[6 = x \times \frac{3}{8}?\]

Now you can see that if you multiply both sides by $\large \frac83$ you get

\[x = 6 \times \frac{8}{3}.\]

The same technique works if you have to divide a fraction by a fraction.


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