When dividing a fraction by a fraction, the dividing fraction is turned upside down then multiplied. why?
Answers:
Dividing by a number is the same as multiplying by the multiplicative inverse of that number.
The multiplicative inverse of a proper fraction is just the fraction turned upside down. Thus, one fourth divided by two fifths is the same as one fourth times by five halves equals five eighths.
The same is true for integers. Three divided by four is the same as three times one fourth equals three fourths.
BECAUSE I SAY SO.OK?
Good question. I just know it works. I guess it's because division is the opposite of multiplication. Ergo, you invert the fraction.
good question. That is dealing with reciprocals. A number's reciprocal is the same as flipping the number. Multiplying by the reciprocal is the same as dividing by the number.
ex. 6/2= 3
6*(1/2) = 3
1/2 is the reciprocal of 2
The multiplicative inverse of any number is defined as one divided by that number. (Obviously, a multiplicative inverse cannot exist for zero.) It is always true that dividing by something is the same as multiplying by the multiplicative inverse, and the rule for fractions is a special case of this.
When you divide you always multiply by the inverse of the divisor. 10/2 would be the same as 10*(1/2). That is because division and multiplication are inverses of each other.
Why do you seem to be disputing this ?
Just accept it. It works !!
That's just the way it is. That's how to get the correct answer. No reason why, it's just the process you have to use.
It's actually easier that way anyway. Hard to divide fractions by fractions.
Because it gets the result.
because it works.
because that is what our math teachers taught us.
Because dividing by anything is equivalent to multiplying by the inverse of the divisor. Think about it. Hint: half of n == n /2 == n x 1/2
Don't ask me. I failed maths!
I'll give you an example "without multiplying the reciprocal"
If given (1/2)/(2)=?
To get the fraction out of the numerator you would multiply both the top and bottom by 2 or
[(1/2)x2]/(2x2)=
1/4
OK - trying for a relatively easy example.
If you divide 1 by 1/2 you'd get 2 - because there are 2 halves in a whole.
Although you have divided 1 by 1/2, you'll notice that the answer is the same as multiplying 1 by 2 (1x2=2)
1 is an integer (whole number), but it can be written as 1/1, or 2/2. So you could say it's 1/1 mulitplied by 2/1 (the half turned upside down) - answer: 2.
OK, now let's look at a proper fraction:
Take a half (1/2) and divide it by a quarter (1/4). If you think of starting with half a cake, then cut that half into 2 pieces (ie two quarters), you are dividing the half cake into quarters of the original cake and end up with 2 pieces. If you multiplied the original 1/2 by 4/1 (the quarter turned upside down) you end up with 2 - which is the same answer.
Crikey - that all sounds a bit confusing, I hope it helps a little bit. Just keep thinking in terms of pieces of cake.
I see that Deep Thought gave you the right answer, but it is sufficient to remember that you just have to do it to get the right answer. My answer would be "because division is the inverse if multiplication".
3/4 divided by 1/2
3/4 X 2/1= 6/4 reduced is 3/2
3/4 divided by 1/2 is 3/1 over 4/2 which comes out 3/2..same answer is just easier to flip 2nd number and multiply then write fraction over a fraction.also multiplication and division are opposites just like 5/3 is the opposite of 3/5 so if you are to divide by 5/3 then if you multiply by its opposite you arrive at same number
lets say you have
(a/b) = (c/d)x
where as to find x, you have to divide both sides by (c/d), which would give you
(a/b)/(c/d) = (a/b)*(d/c) = (ad)/(bc)
now lets try this a slightly different way
(a/b) = (c/d)x
since you have a "d" in the denominator, to get rid of that, you would have to multiply both sides by "d", which gives you
(ad)/b = cx
now to get "x" by itself, you would have to divide both sides c, which gives you
x = (ad)/(bc)
basically its the result of inverse of operations.
To answer this question I'll start with something basic. That is: dividing by 2 is the same as multiplying by a half. Similarly multiplying by 2 is the same as dividing by a half.
That same prinicple can be extended to full fractions such as 3/7 or whatever.
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