What is the value of? 1/3÷4

Question

Noah Archer · Accepted Answer

#1/12# is the value.

What you do is the KCF method. Keep, Change, Flip. You would keep the #1/3#. Then you change the divide sign to a multiply sign. Then you flip the #4# to #1/4#. You do that since #1/4# is the reciprocal of #4#. #1/3 div 4 = 1/3 xx 1/4#

Genesis Amaya · Answer

#1/12#

You can work it out using the usual fraction division process, or just through what is happening...

If you take one third and cut it in half ( same as dividing by #2#), then each piece will be #1/6#. (More pieces, therefore they get smaller)

If you take #1/6# and cut it in half, the pieces get smaller again. Each piece will be #1/12#

#1/3 div 4 = 1/3 div 2 div 2 = 1/12#

A nifty short cut: To divide a fraction in half, either halve the top (if it is even) or double the bottom:

#2/3 div 2 = 1/3#

#4/11 div 2 = 2/11" "larr# pretty obvious if you think about it!!

#5/9 div 2 = 5/18#

#7/8 div 2 = 7/16#

In the same way: To divide a fraction by #3# in half, either divide the by #3# (if possible) or treble the bottom:

#6/11 div 3 = 2/11" "larr# share out #6# portions equally.

#5/8 div 3 = 5/24#

Julian Avila · Answer

This is why the 'turn upside down and multiply' works.

#color(blue)("Answering the question using the shortcut method")# Write as #1/3-: 4/1# giving: #1/3xx1/4= (1xx1)/(3xx4)=1/12# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(white)()# #color(blue)("The teaching bit")# A fraction structure is such that we have: #("numerator")/("denominator") ->("count")/("size indicator of what you are counting")# YOU CAN NOT #color(red)(ul("DIRECTLY"))# ADD, SUBTRACT OR DIVIDE ONLY THE COUNTS UNLESS THE SIZE INDICATORS ARE THE SAME. You have been applying this rule for years without realising it! Consider the numbers: 1,2,3,4,5 and so on. Did you know that it mathematically correct to write them as: #1/1,2/1,3/1,4/1,5/1# and so on. So their SIZE INDICATORS ARE THE SAME. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Explaining the principle using a different example")# #color(brown)("I have chosen to use a different example as I wished")##color(brown)("to avoid using 1's. In avoiding 1's the behaviour is more obvious.") # Consider the example #color(green)(3/color(red)(4)-:2/color(red)(8)")# Turn upside down and change the sign to multiply #color(green)(3/color(red)(4)xxcolor(red)(8)/2 larr" as per the method"# Note that: #4xx2=8 =2xx4.# This is commutative. Using the principle of being commutative swap the 4 and 2 round the other way giving: #color(green)(color(white)("ddd")ubrace(3/2)color(white)("ddd")xxcolor(white)("ddd")color(red)(ubrace(8/4)) # #color(green)("directly dividing ") color(red)("Converting the")# #color(green)(color(white)("dd")"the counts")color(white)("ddddddd") color(red)("counts")# Now split them up like this: #( color(green)( 3)xxcolor(red)(8/4)) -:color(green)(2)# #color(magenta)(color(white)("ddd") 6 color(white)("dddd")-:2)# And compare to the original of #color(green)([3/color(red)(4)]-:2/color(red)(8)")# #color(white)()# #color(green)([3/color(red)(4)color(black)(xx2/2)] color(green)(-:)2/color(red)(8))color(white)("dddd")->color(white)("dddd")color(magenta)(6)/8-:color(magenta)(2)/8# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ So the #color(red)(8/4)# is the equivalent action of making the size indicators the same and adjusting the counts to suit. #color(red)("IT IS A CONVERSION FACTOR")# So by turning upside down' and multiplying you are applying a conversion and directly dividing the counts all at once.

Zoe Adams · Answer

undefined The value of $ \frac{1}{3} \div 4 $ is $ \frac{1}{12} $.