Question #bc12d

1/4 th of 1/4
#=1/4xx1/4=1/16#
1/4 th of 1/4 means fourth part of 1/4 which is equal to 1/16.

#color(blue)("The teaching bit")#

A fractions' structure is that of:

#("count")/("size indicator of what is being counted")#

The count and size indicator form a fixed ratio in that
for example:

#1/2=2/4=4/8=32/64# and so on. They all have the same intrinsic value.

To obtain a quarter we need to be able to change the top number into one that is easily divided by 4.

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#color(blue)("Answering your question - using first principle")#

Multiply by 1 and you do not change the value. However, 1 comes in many forms

Note that multiply by #1/4# is the same effect as dividing by #4# so we have:

#[1/4color(red)(xx1)]xx1/4 color(white)("ddd") ->color(white)("ddd") [1/4color(red)(xx1)]-:4#

#color(white)("dddddddddddddd") ->color(white)("ddd") [1/4color(red)(xx4/4)]-:4#

#color(white)("dddddddddddddd") ->color(white)("ddd") [4/16]-:4#

#color(white)("dddddddddddddd") ->color(white)("ddd") [1/16+1/16+1/16+1/16]-:4#

#color(white)("dddddddddddddd") ->color(white)("ddd") 1/16#

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#color(blue)("Answering your question - shortcut method")#

#1/4" of "1/4color(white)("dd") ->color(white)("dd") 1/4xx1/4color(white)("dd")->color(white)("dd")(1xx1)/(4xx4)=1/16#