How do you evaluate #(\frac { 1} { 5} \times \frac { 2} { 3} ) - ( 1\frac { 1} { 3} \div 2\frac { 2} { 9} )#?

2 Answers
Shwetank Mauria
Feb 26, 2017

#(1/5xx2/3)-(1 1/3-:2 2/9)=-7/15#

Explanation:

Dividing by a fraction such as #a/b# is equivalent to multiplying by its reciprocal or multiplicative inverse #b/a#. This means that, dividing by #2 2/9# or #(2xx9+2)/9=20/9# means multiplying by #9/20#.

Therefore #(1/5xx2/3)-(1 1/3-:2 2/9)#

= #(1xx2)/(5xx3)-((1xx3+1)/3-:(2xx9+2)/9)#
(converting mixed fractions to improper fractions)

= #2/15-(4/3-:20/9)#

= #2/15-(4/3xx9/20)#

= #2/15-((cancel4^1)/(cancel3^1)xx(cancel9^3)/(cancel20^5))#

= #2/15-3/5#

Now LCD of denominators #5# and #15# is #15#

Hence #2/15-3/5#

= #2/15-(3xx3)/(5xx3)#

= #2/15-9/15#

= #(2-9)/15#

= #-7/15#

Barney V.
Mar 1, 2017

#-7/15#

Explanation:

#(1/5 xx 2/3)-(1 1/3-:2 2/9)#

#:.=(1/5 xx 2/3)-(4/3-:20/9)#

#:.=(2/15)-(cancel4^1/cancel3^1 xx cancel9^3/cancel20^5)#

#:.=2/15-3/5#

L.C.D.#=15#

#:.=(2-9)/15#

#:.=-7/15#

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