# (3/5) x (2/3) - (1/5) + (2/5) / 3 of (1/5) please solve it.

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To simplify (3/5) x (2/3) - (1/5) + (2/5) / 3 of (1/5)

Solution:

The expressions like this could be solved by followig the rule of priority of operations in the order of BODMAS (bracket, Division or mutiplication, subtraction or Additon).

Here in the expression there are 3 terms: First term (3/5) x (2/3) - Secon term: 1/5 + 3rd term:(2/5) / 3 of (1/5)

So.

(3/5) x (2/3) - (1/5) + (2/5) / 3 of (1/5)

First term:(3/5)(2/3) =3*2/15= 2/5

Second term: 1/5 to be subtracted.

Third term: (2/5) / 3 of (1/5) = [(2/5)/3]*(1/5) =2/15]*(1/5)=2/75.

The sum of the three terms = 2/5-1/5+2/75= 1/5-2/75

LCM of the denominators (5,75) = 75. So 1/5 is converted into an equivalent factor 15/75 and the expression comes to:

15/75-2/75 =13/75

Note with reference to the 3rd term,(2/5) / 3 **of** (1/5):

The word** of **is nomally is used in mathematical operations like part of another expression. Fraction of something. 2/3 of 6 = (2/3)*6 = 2. But we nomally say 5 times 6 =30 and not like:5 of 6 = 30. 1/5 of 10 = (1/5)*10 or (1/5) times 10 =(1/5)*10 =2.

Knowing the rule about order of algebraic operations, we'll deal with multiplications and division first:

(3/5) x (2/3)=(**3**x2)/(5x**3**)

As you can see (I've written the value bold), we have the number 3 at the numerator and denominator, too, so we can divide the numerator and denominator with 3.

(3/5) x (2/3)=(2/5)

(2/5) / 3 of (1/5)=[2/(5x3)] x (1/5)=(2 x1)/(5x3x5)=2/75

So the relation will become:

(2/5)-(1/5)+(2/75)=(1/5)+(2/75)

In order to sum the 2 resulted ratios, they have to have same denominator, which is 75.

1/5=15x1/15x5=15/75

**15/75 + 2/75= (15+2)/75=17/75**