Dividing Fractions has actually A weird Rule

Dividing fractions can be a tiny tricky. It’s the just operation that calls for using the reciprocal. Utilizing the mutual simply means you flip the portion over, or invert it.

You are watching: Do you divide by the numerator or denominator

For example, the reciprocal of 2/3 is 3/2.

After we offer you the division rule, we will show you WHY you need to use the mutual in the very first place.

But for now…

Here’s the ascendancy for Division

To divide, convert the fraction division process come a multiplication procedure by using the complying with steps.

Change the “÷” (division sign) come “x” (multiplication sign) and invert the number to the right of the sign.Multiply the numerators.Multiply the denominators.Re-write her answer in its simplified or lessened form, if needed

Once you finish Step #1 for splitting fractions, the difficulty actually alters from division come multiplication.

Example 1: splitting Fractions by Fractions

1/2 ÷ 1/3 = 1/2 x 3/1

1/2 x 3/1 = 3/2

Simplified prize is 1 1/2

Example 2: splitting Fractions by totality Numbers

1/2 ÷ 5 = 1/2 ÷ 5/1

(Remember come convertwhole number to fractions, FIRST!)

1/2 ÷ 5/1 = 1/2 x 1/5

1/2 x 1/5 = 1/10

Example 3: splitting Whole numbers by Fractions

6 ÷ 1/3 = 6/1 ÷ 1/3

(Remember to convertwhole number to fractions, FIRST!)

6/1 ÷ 1/3 = 6/1 x 3/1

6/1 x 3/1 = 18/1 = 18

Now that’s every there is to it. The main things you need to remember once you divide is to convert whole numbers to fractions first, then invert the fraction to the right of the department sign, and change the authorize to multiplication.

The “divisor” has some other considerationsyou must keep in mind…

Special Notes!Remember to just invert the divisor.The divisor’s numerator or denominator can not be “zero”.Convert the procedure to multiplication BEFORE performing any kind of cancellations.

I promised to try to explain why the dominion requires inverting the divisor.

Here goes..

Why splitting Fractions calls for Inverting The Divisor

Let’s use our an easy example to actually validate this strange dominion for division.

If you yes, really think about it, us are dividing a fraction by a fraction, which forms what is called a “complex fraction”. It actually looks favor this…


When working with complicated fractions, what we desire to do first is get rid that the denominator (1/3), therefore we can work this trouble easier.

You might recall that any number multiply by its reciprocal is same to 1. And since, 1/3 x 3/1 = 1, we deserve to use the reciprocal home of 1/3, (3/1), to do the value of the denominator equal to 1.

You might likewise recall that every little thing we carry out to the fraction’s denominator, us must also do to its numerator, so as not to adjust the overall portion “value”.

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So let’s main point both the numerator and also denominator by 3/1…


Which offers us…


Here’s what happened…

By multiply the numerator and also denominator of our complex fraction by 3/1, we were then able to use the reciprocal home of a portion to eliminate the denominator. Actually, there is no our advantageous Rule, we would have to use every one of the measures above.

So, the Rule for separating fractions really conserves us a most steps!

Now that’s the most basic explanation I might come up with for WHY and also HOW we end up with a Rule that says whenever we division fractions, we must invert the divisor!