Need Help to Know if Answer is Correct?

Question

My daughter already worked the problem out I just want to make sure it is correct. Thank you.

(1/3 / 4 1/2) * (1 5/8 * 5 2/3)
---------------------------------------
(1/2 * 3/9) + (3/4 / 6)

My daughters answer is 2 193/567. It just doesn't seem right to me. Thank you again.

Answer 1

you first need to convert all the "whole number fractions" (mixed fractions) to improper fractions.... for example... 4 1/2 is equal to the mixed fraction 9/2.... [(4*2) + 1]/2 = 9/2 i.e. [(whole number * denom) + num]/denom

sooo.... the given should now look like this with mixed fractions...

(1/3 / 9/2) * (13/8 * 17/3)
----------------------------------
(1/2 * 1/3) + (3/4 / 6)

now to divide a fraction by another fraction you simply take the first fraction... and multiply by the 'flip' (or reciprocal) of the second fraction... i.e. reversing the num and denom of the second fraction...

your problem should turn from looking like this...

(1/3 / 9/2) * (13/8 * 17/3)
----------------------------------
(1/2 * 1/3) + (3/4 / 6)

to looking like this...

(1/3 * 2/9) * (13/8 * 17/3)
----------------------------------
(1/2 * 1/3) + (3/4 * 1/6) .... where given 3/9 is same as 1/3

which then should look like this...

(2/27) * (221/24)
------------------------
(1/6) + (3/24)

then on top in the numerator... you can 'cancel' terms... 2 goes into 24... so 2 becomes 1 and 24 is now 12

and on bottom... the LCM (lowest common denom) is 24... so 1/6 is the same as 4/24... combine with the 3/24 and you get 7/24 in the denominator of above...

221/324
------------
7/24

now remember what I said up above about dividing one fraction by another?.... use that principle of 'flipping' here...

so now you have...

221/324 * 24/7....

but wait... 324 in the denom and 24 in the num are both divisible by 12.... so 324 becomes 27 and 24 become 2...

so now you have...

221/27 * 2/7 = 442/189 reduced...

basically what I did was take 221/324 * 24/7.... and divide both top and bottom above by 12

442/189 should be your daughter's final answer... not what she has...

or... 2 and 64/ 189 ths...

hope this helps...

BTW... I just compared my answer to the above person's to see if we came out with the same result....

notice that he has 334 in the denom of num... it is a typo... and should be '324'... and so that is who the person's answer is 'off' ... because the person 'carried' the 334 through...

Answer 2

numerator is 221/334
denominator is 7/24
221/334 x 24/7 = 2652/1169