# why do you multiply by the reciprocal when dividing fractions

The Math You Need to Know You chose the format in which to complete the problem. Any number multiplied by its (its is 1. Any number multiplied by 1 is the number. One is the multiplicative. Any number divided by one, is that number. Another way of saying this is "If 1 is the denominator of a fraction, just use the numerator. "
The goal is to make the division expression look like just one number, perhaps a fraction or mixed number, but, still just one number.

Multiplying by the reciprocal and multiplying by 1 result in "the product of the first fraction and the reciprocal of the second" -- "copy the first, then, invert and multiply. " If you're not sure whether anything can be cancelled off, you can always factor the numerator and denominator, and check for any duplicated factors: Nothing is duplicated between the top and the bottom, so nothing cancels.

Often, though, something will cancel: Dividing fractions is just about as easy as multiplying them; there's just one extra step.

When you divide by a fraction, the first thing you do is "flip-n-multiply". That is, you take the second fraction, flip it upside-down (that is, you "find the reciprocal"), and then you multiply the first fraction by this flipped fraction. Note: When the inputs are mixed numbers, as in the last example above, the book (or instructor, or grader) usually expects a mixed number as the output, too.

So, if your answer is an impropr fraction, you'll need to convert it back to mixed-number form. Don't forget this step! Next, we move on to the much-more-difficult of fractions.

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