How to Divide Fractions | Popular Science Homepage
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Wednesday, January 26, 2022

How to Divide Fractions

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divide fractions	“Dividing fractions is easy if you just remember to keep, change and flip. HowStuffWorks

The math you did in elementary school seems daunting to adults because there are so many rules and special words. And dividing fractions is no different: You have to flip fractions and know words like divisor and dividend and reciprocal. It may seem hard to remember, but it’s not with a little practice.

Because math is all about remembering rules and terms, and if you can do that, dividing fractions is a breeze. Division is the inverse of multiplication, so one thing you have to remember when dividing fractions is the answer is always going to be larger than either of the components of the problem. You’re basically trying to figure out how many of the divisor (second number in the problem) can be found in the dividend (first number).

Step 1: Keep

The first step to dividing fractions is to look at both your fractions, take a deep breath and tell yourself that if a sixth grader can do it, you can probably do it, too.

The other first step is just as simple. Let’s say you’re trying to figure out the answer to 2/3 ÷ 1/6. Don’t do anything! Keep these numbers just as they are.

Step 2: Change

The second step is to multiply the two fractions. So, you simply have to change the ÷ sign to an x sign: 2/3 ÷ 1/6 becomes 2/3 x 1/6.

Step 3: Flip

The third step is to take the reciprocal of the divisor — but don’t panic! That just means you’ve got to flip the numerator (the top number) and the denominator (the bottom number) of the fraction on the right side of the division sign, which is called the divisor.

For instance, if you’re dividing 2/3 by 1/6, you’d begin working on the problem by flipping the divisor: 2/3 x 6/1 = 12/3.

You might notice that the fraction is no longer a proper fraction, in which the numerator is smaller than the denominator; it’s an improper fraction, which means the number the fraction represents is larger than 1.

Is That Your Final Answer?

No, it’s close, but not quite your final answer. All you need to do next is simplify the fraction 12/3. You do this by finding the largest number that divides equally into both the numerator and the denominator, which, in this case, is 3, which means the fraction simplifies to 4/1, or just 4.

Now That’s Interesting

The word fraction comes from the Latin word fractus, or "broken."

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