How do you simplify #5\frac { 1} { 6} \div ( 2\frac { 2} { 3} \times 1\frac { 3} { 8} )#?

1 Answer
smendyka
Dec 11, 2016

#31/22# or #1 9/22#

Explanation:

First, we must take each Mixed Fraction and convert it into an improper fraction by multiplying the integer by the necessary form of #1# and then adding the result to the fraction:

#((6/6)*5 + 1/6) -: ((3/3)*2 + 2/3) xx (8/8)*1 + 3/8))#

#(30/6 + 1/6) -: ((6/3+ 2/3) xx (8/8 + 3/8))#

#31/6 -: (8/3 xx 11/8)#

The rule for multiplying fractions is:

#color(red)(a/b xx c/d = (a xx c)/(b xx d))#

Using this rule we can multiply the fractions withing the parenthesis:

#31/6 -: ((8 xx 11)/(3 xx 8))#

#31/6 -: 88/24#

We can rewrite this as:

#(31/6)/(88/24)#

The rule for multiplying fractions is:

#color(red)((a/b)/(c/d) = (a xx d)/(b xx c))#

Using this rule we can divide the fractions:

#(31 xx 24)/(6 xx 88)#

#(31 xx (6 xx 4))/(6 xx (4 xx 22))#

#(31 xx (cancel(6) xx cancel(4)))/(cancel(6) xx (cancel(4) xx 22))#

#31/22# or

#(22 + 9)/22#

#22/22 + 9/22#

#1 + 9/22#

#1 9/22#

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