I know that you DO, what I'm asking for is a justification. We're always taught that when you have to divide fractions, you just multiply by the reciprocal, but I've never understood why this is so. Thanks for your help.
2007-09-08 16:27:50 · 3 answers · asked by Zowzooma, the Angry Deity 2 in Science & Mathematics ➔ Mathematics
Remember the meaning of division: a/b is the unique number that, when multiplied by b, yields a. In other words a/b=c iff a=cb.
So suppose that b is a fraction x/y. Consider what happens if c=a*y/x. Then cb = a*y/x*x/y = a*(yx)/(xy) = a*1 = a. By the definition of division this means that a*y/x = a/(x/y). Which is why multiplication by the reciprocal works.
2007-09-08 17:11:58 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
The reciprocal capability which you swap the fraction over. case in point, the reciprocal of two/3 is 3/2. so as to divide (4/5)/(one million/3) You multiply the spectacular by the reciprocal of the backside 4/5 * 3/one million = 12/5
2016-12-31 17:21:25 · answer #2 · answered by strassberg 3 · 0⤊ 0⤋
I would say that in our usual math world there are only two arithmetic operations: addition and multiplication.
subtraction is an additive inverse operation
division is a multiplicative inverse operation
(long division of complex fractions gets extremely messy btw)
2007-09-08 17:18:26 · answer #3 · answered by Anonymous · 0⤊ 0⤋