What you do is the KCF method. Keep, Change, Flip. Friend would store the #1/3#. Climate you change the divide authorize to a main point sign. Climate you upper and lower reversal the #4# come #1/4#. You execute that due to the fact that #1/4# is the mutual of #4#.

You are watching: What is 1/3 of 4

#1/3 div 4 = 1/3 xx 1/4#

You can work the out using the normal fraction department process, or just through what is happening...

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

If you take it #1/6# and also cut that 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 brief cut: To division a fraction in half, one of two people halve the height (if the is even) or dual the bottom:

#2/3 div 2 = 1/3#

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

#5/9 div 2 = 5/18#

#7/8 div 2 = 7/16#

In the very same way: To division a fraction by #3# in half, either division the through #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#

Tony B
Apr 7, 2018

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

Explanation:

#color(blue)("Answering the concern 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 together that us have:

#("numerator")/("denominator") ->("count")/("size indicator that what you are counting")#

YOU deserve to NOT #color(red)(ul("DIRECTLY"))# ADD, SUBTRACT OR DIVIDE just THE COUNTS unless THE SIZE indications ARE THE SAME.

You have actually been applying this rule for year without realising it!Consider the numbers: 1,2,3,4,5 and also so on. Did you know that it mathematically correct to compose them as: #1/1,2/1,3/1,4/1,5/1# and so on. So your SIZE indicators ARE THE SAME.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#color(blue)("Explaining the principle using a different example")#

#color(brown)("I have actually chosen to usage a different example as I wished")##color(brown)("to stop using 1"s. In preventing 1"s the plot is an ext obvious.") #

Consider the example #color(green)(3/color(red)(4)-:2/color(red)(8)")#

Turn upside down and readjust the authorize to multiply

#color(green)(3/color(red)(4)xxcolor(red)(8)/2 larr" together per the method"#

Note that: #4xx2=8 =2xx4.# This is commutative.

Using the principle of gift commutative swap the 4 and also 2 round the other means 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 separation 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 initial 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 make the size indications the same and also adjusting the counts to suit.

See more: 1974 Half Dollar No Mint Mark, 1974 Kennedy Half Dollar 50C About Uncirculated

#color(red)("IT IS A switch FACTOR")#So by turning upside down" and multiplying girlfriend are applying a conversion and directly dividing the counts every at once.