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

giorgiana1976 | Student

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

(3/5) x (2/3)=(3x2)/(5x3)

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

neela | Student

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.

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The text contains a mathematical question and a detailed solution provided by two different students. The question involves a series of arithmetic operations with fractions, and the solution walks through the steps to simplify the expression.
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Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
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# (3/5) x (2/3) - (1/5) + (2/5) / 3 of (1/5) please solve it.

giorgiana1976 | Student

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

(3/5) x (2/3)=(3x2)/(5x3)

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

neela | Student

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.

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The text contains a mathematical question and a detailed solution provided by two different students. The question involves a series of arithmetic operations with fractions, and the solution walks through the steps to simplify the expression.

TYPE: SINGLE_QUESTION_WITH_ANSWER