can you explain why do we inverse and multiply for dividing fractions?

Answer 1

yawn

Answer 2

Yes, I can.

Look at whole numbers, every whole number, as a fraction. Let's divide 25 by 5.

25/5 is the same as 25/1 divided by 5/1.

With me so far?

This is the important part: When you divide two numbers, what you are doing is multiplying the numerator (actually called the dividend) by the inverse of the divisor.

What an inverse means is "flipping over" the divisor. So the inverse of 5 (which I just said was the same as 5/1) is 1/5.

That's all division is: multiplying by the inverse of the divisor.

So when you divide fractions, that's why you invert the divisor. You're doing the same thing you would do for whole numbers, but with whole numbers you don't have to think about it.

Back to the example: 25/1 divided by 5/1. That's the same as 25/1 times 1/5.

That gives us 25 over 5.

The answer, of course, is 5.

Answer 3

There was a good explanation of this earlier, but the simpliest way is to look at what it means to divide:
"5 divided by 2" = "How many twos fit into 5". The answer is 2.5.

Now:
"5 divided by 1/2" = "How many halves fit into 5". The answer is 10. This, though, is the same as "5 times 2" - 2 being the inverse of 1/2. So when dividing by a fraction, multitplying by its inverse does the same thing (and is often easier).

Answer 4

they ran out of other useless stuff to make us learn. When is the last time you needed to multiply or divide a fraction outside of your math class??????? Sure, we use fractions all of the time to see if we have 1/2 a gallon of milk left....tell mom that you ate 1/4 of the pizza...but when is the last time you used it in any other way???

Answer 5

Division is the inverse of multiplying. This is given... The reason why you inverse to multiply is just a prop to help students get to the answer faster... If you were a math mastermind, you wouldn't need shortcuts, you'd do it in your head. I love math!

Answer 6

The guy who invented dividing fractions tried hard to think of a complicated way to do it. After hours and hours, he just said screw it let's just flip this bad boy and multiply.

Answer 7

I'll use the explanation that my friend Josh gave me to explain the complexity of trigonometry -

Some really smart guys a really long time ago believed that was the way it should be done.

And he believes them too.

He's much better at math than I ever will be.

Answer 8

*sings* Cauz that's just the way it is - ok ok, because division is the inverse of multiplication.

Answer 9

shhhhh... Just do it. Don't ask questions (lol)

Answer 10

because it works.