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B Fractions question

  1. Sep 5, 2016 #1
    Can someone please explain why the following equation is true:

    [itex] (7 \div 4) \div (1 \div 2) = 7 \div 4 \div 1 \times 2 [/itex]

    As in, why does the division become multiplication when the parentheses are removed?


    Thanks
     
  2. jcsd
  3. Sep 5, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    Dividing by something is the same as multiplying by the inverse (by definition), and the inverse of 1/2 is 2/1. Therefore, (7/4)/(1/2) = (7/4) * (2/1) = (7/4)*2/1 = ((7/4)/1)*2.
     
  4. Sep 5, 2016 #3
    Thanks!

     
  5. Sep 11, 2016 #4

    Math_QED

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    Homework Helper

    I can't resist to say that ##a \div b## is an ugly and often confusing notation. Rather, we use ##\frac{a}{b}##
     
  6. Sep 19, 2016 #5
    When we divide a fraction by another fraction, we have to multiply first fraction by the reciprocal of second fraction.
    i.e. $$\dfrac{a}{b}\div \dfrac{m}{n}=\dfrac{a}{b}\times \dfrac{n}{m}$$
    so $$(7\div 4)\div (1\div 2)=\dfrac{7}{4}\div \dfrac{1}{2}=\dfrac{7}{4}\times \dfrac{2}{1}$$
     
  7. Sep 19, 2016 #6

    Mark44

    Staff: Mentor

    I totally agree.
     
  8. Oct 20, 2016 #7
    Dividing a fraction by another fraction is same as multiplying reciprocal of another fraction. So,

    ##\dfrac{7}{4}\div\dfrac{1}{2}=\dfrac{7}{4}\times\dfrac{2}{1}=\dfrac{\dfrac{7}{4}}{1}\times2##

    ##\implies\dfrac{7}{4}\div\dfrac{1}{2}=\dfrac{14}{4}##

    ##\implies\dfrac{7}{4}\times\dfrac{2}{1}=\dfrac{14}{4}##

    ##\implies\dfrac{\dfrac{7}{4}}{1}\times2=\dfrac{14}{4}##
     
  9. Oct 20, 2016 #8

    Mark44

    Staff: Mentor

    You have a lot of extra work here that isn't needed.
    ##=\frac 7 2##
    Done...
    With all of this extra, unnecessary work, you at least could have simplfied your final result.
     
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