How do you simplify #3 2/3 + 1 1/4 - 2 5/12#?

1 Answer
Sep 1, 2017

Answer:

Method broken down into a lot of detail. Once you get used to these you can do a lot of it in your head and rattle the answer off in a couple of lines.

#2 1/2#

Explanation:

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

Stating the obvious: When adding and subtracting you are dealing with counts.

A fractions structure is such that we have:

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

You can not DIRECTLY add or subtract counts unless the size indicators are the same. This is why 2+3 works as really it is #2/1+3/1# The size indicator of their #ul("unit size")# are the same.

Consider #3/16# the count is 3 and the unit size is #1/16#

So you have 3 of unit size #1/16 = 3xx1/16=3/16#
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#color(blue)("Answering the question")#

In the end I make them all have the same 'unit size' (denominator)

Consider #3 2/3 larr" Detailed explanation"#

Write as #3+2/3# this is the same as

#color(green)([3color(red)(xx1)]+2/3#

#color(green)([3/1color(red)(xx3/3)]+2/3#

#color(green)([(3color(red)(xx3))/(1color(red)(xx3))]+2/3#

#[9/3]+2/3=11/3#
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Consider #1 1/4#

Using the same method as above this is #5/4#
................................................................
Consider #2 5/12#

Using the same method this is #29/12#
....................................................................
Putting it all together

#11/3+5/4-29/12#

Again using the above approach we have

#44/12+15/12-29/12" "=" "(44+15-29)/12#

#=30/12#

#=(30-:6)/(12-:6) #

#= 5/2 color(white)("ddd") rarr color(white)("ddd")(2+2+1)/2#

# = 2/2+2/2+1/2" " =" " 2 1/2#