1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    2017 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

    User Avatar
    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...