SOLUTION: Please help me to solve this fraction. Divide {{{15}}}{{{15/16}}} ÷ {{{3}}}{{{3/4}}}

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Please help me to solve this fraction. Divide {{{15}}}{{{15/16}}} ÷ {{{3}}}{{{3/4}}}      Log On


   



Question 89410: Please help me to solve this fraction.
Divide
1515%2F16 ÷ 33%2F4

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me to solve this fraction. 
Divide 

1515%2F16 ÷ 33%2F4

Change these mixed fractions to improper fractions
by this rule:

---------------------------------------------------

To change the mixed number 

WN%2FD

to an improper fraction, where W = whole part, 
N = numerator, D = denominator

IMPROPER FRACTION = %28DW+%2B+N%29%2FD

----------------------------------------------------                        

Following the above rule with 1515%2F16

W = 15, N = 15, D = 16

IMPROPER FRACTION = %28DW+%2B+N%29%2FD = %2816%2A15+%2B+15%29%2F16 = 255%2F16

-----------------------

Following the rule with 33%2F4

W = 3, N = 3, D = 4

IMPROPER FRACTION = %28DW+%2B+N%29%2FD = %284%2A3+%2B+3%29%2F4 = 15%2F4

------------------------

So the original problem

1515%2F16 ÷ 33%2F4

is now

255%2F16÷15%2F4

Now we use the principle of inverting the second fraction
and changing the ÷ to ×

 255      4
----- × ----
  16     15

Cancel the 15 into the 255 and get 17 in the top

  17       
 255      4
----- × ----
  16     15
          1

Cancel the 4 into the 16 and get 4 in the bottom

  17      1           
 255      4
----- × ----
  16     15
   4      1

So you end up eith the improper fraction

17%2F4

Now since the original problem was given
as mixed fractions, we change this to
an improper fraction, by using this rule:

-------------------------------------------

To change the improper fraction N%2FD to
a mixed fraction,
 
perform the division
 __ 
D)N

then the mixed fraction will be:

N%2FD = QR%2FD

where N = the numerator, D = the denominator, 
Q = the quotient, R = the remainder 

--------------------------------------------
                            __
So we perform the division D)N 

 ` 4
4)17
  16
   1  

Here, N = 17, D = 4, Q = 4, R = 1 so 

N%2FD = QR%2FD becomes

17%2F4 = 41%2F4

Edwin