# Simplify,{(3/6)+(2/3)x(1/3)}-(1/3)/(3/2)

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To solve this problem you need to use PEMDAS, working the part within the parenthesis or brackets first.

Within the brackets, work the multiplication or division before doing any other part of the problem.

{3/6 + 2/3 *1/3} -(1/3) / (3/2)

2/3 * 1/3 or 2 *1 over 3*3 .... 2/9

{3/6 + 2/9} - (1/3) / (3/2)

To add 3/6 and 2/9, common denominators have to be found and equivalent fractions formed.

6, 12, 18, 24, ...

9, 18, 27,...

18 is the common denominator. so the equivalent fractions to 3/6 and 2/9 are 9/18 and 4/18

{9/18 + 4/18} - (1/3) / (3/2)

Still working inside the brackets, 9/18 + 4/18 equals 13/18.

Now your eqation looks like 13/18 - (1/3) / (3/2).

The next part of PEMDAS which applies to this problem is multiplication or division... from left to right...

(1/3) / (3/2)

To divide fractions, simply leave the first as is and use the reciprical of the second. This means switch the numberator and denominator. And change the division to multiplication.

(1/3) * (2/3)

1 times 2... 3 times 3.........2/9

Now the eqation looks like

13/18 - 2/9

Again, find common denominator, this time it is 18.

13/18 - 4/18 = 9/18

Simplify... by finding greatest common factor of 9 and 18....

1, 3, 9 1, 2, 3, 6, 9, 18

Divide both numerator and denominator by the GCF 9 and your answer is

1/2

To simplify {(3/6)+(2/3)x(1/3)}-(1/3)/(3/2)

Solution:

{(3/6)+(2/3)x(1/3)}-(1/3)/(3/2)

In the innermost bracket, we have 3/6 which is equal to 1/2 and (2/3)*(1/3) is equal to 2/9.

So the given expression becomes:

={(1/2+2/9)}-(1/3)/(3/2),

=3/6+2/9-2/9 , as (1/3)/(3/2) is equalto (1/3)(2/3)=2/9

=3/6

=1/2

So the given expression simplifies to the value 1/2.

{(3/6) + (2/3)*(1/3)} - (1/3)/(3/2)

= {3/6 + (2*1)/(3*3)} - (1*2)/(3*3)

(Please not that in multiplication of two fractions. the numerator is multiplied by numerator and denominator is multiplied denominator. In case of one fraction is divided by another fraction then the division operation (/)can be changed to multiplication (*) by keeping the first fraction as it is and reversing the numerator and denominator of the second fraction.)

= 3/6 + 2/9 - 2/9

= 3/6

=1/2 ... Answer.