# Find out the value of given expression,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + 15 + }}\dfrac{{39}}{2}{\text{ }} - {\text{ 15 }}\]

Answer

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Hint:- First perform arithmetic operations on integers and then perform arithmetic operations rational numbers after that perform arithmetic operations on the result.

As we know that integers are the sets of numbers starting from negative infinity and goes on till positive infinity.

Integers are {……………., –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, ………………}

And fractional numbers are the sets of numbers which can be changed to decimal numbers by dividing the numerator by denominator and they can also be negative or positive.

Some fractional numbers are \[\left\{ {{\text{ }}\dfrac{4}{3},{\text{ }}\dfrac{5}{4},{\text{ }}\dfrac{7}{2},{\text{ }}\dfrac{9}{6}{\text{ }}} \right\}\]

Integers are special cases of fractional numbers with denominators equal to 1.

So, first we calculate integers in the given equation.

So, \[{\text{ + 15 }} - {\text{ 15 = 0}}\] (1)

And then calculating the fractional numbers given in the equation. We get,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + }}\dfrac{{39}}{2}{\text{ = }}\dfrac{{ - 21{\text{ + 39}}}}{2}{\text{ = }}\dfrac{{18}}{2}{\text{ = 9}}\] (2)

So, now the given equation is,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + 15 + }}\dfrac{{39}}{2}{\text{ }} - {\text{ 15 }}\] (3)

So, putting the value of equation 1 and equation 2 in equation 3.

We get,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + 15 + }}\dfrac{{39}}{2}{\text{ }} - {\text{ 15 = + 15 }} - {\text{ 15 }} - {\text{ }}\dfrac{{21}}{2}{\text{ + }}\dfrac{{39}}{2}{\text{ = 0 + 9 }}\]

Now, solving the above equation. We get,

\[0{\text{ + 9 = 9}}\]

Hence, the required value of the given equation is 9.

Note:- Whenever we come up with this type of problem then to solve the given equation by other method, first we need to change the fractional numbers to decimal numbers by dividing numerator by the denominator. And after that we will get an equation with integers and decimal numbers. So, now we can apply the given arithmetic operations easily.

As we know that integers are the sets of numbers starting from negative infinity and goes on till positive infinity.

Integers are {……………., –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, ………………}

And fractional numbers are the sets of numbers which can be changed to decimal numbers by dividing the numerator by denominator and they can also be negative or positive.

Some fractional numbers are \[\left\{ {{\text{ }}\dfrac{4}{3},{\text{ }}\dfrac{5}{4},{\text{ }}\dfrac{7}{2},{\text{ }}\dfrac{9}{6}{\text{ }}} \right\}\]

Integers are special cases of fractional numbers with denominators equal to 1.

So, first we calculate integers in the given equation.

So, \[{\text{ + 15 }} - {\text{ 15 = 0}}\] (1)

And then calculating the fractional numbers given in the equation. We get,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + }}\dfrac{{39}}{2}{\text{ = }}\dfrac{{ - 21{\text{ + 39}}}}{2}{\text{ = }}\dfrac{{18}}{2}{\text{ = 9}}\] (2)

So, now the given equation is,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + 15 + }}\dfrac{{39}}{2}{\text{ }} - {\text{ 15 }}\] (3)

So, putting the value of equation 1 and equation 2 in equation 3.

We get,

\[ - {\text{ }}\dfrac{{21}}{2}{\text{ + 15 + }}\dfrac{{39}}{2}{\text{ }} - {\text{ 15 = + 15 }} - {\text{ 15 }} - {\text{ }}\dfrac{{21}}{2}{\text{ + }}\dfrac{{39}}{2}{\text{ = 0 + 9 }}\]

Now, solving the above equation. We get,

\[0{\text{ + 9 = 9}}\]

Hence, the required value of the given equation is 9.

Note:- Whenever we come up with this type of problem then to solve the given equation by other method, first we need to change the fractional numbers to decimal numbers by dividing numerator by the denominator. And after that we will get an equation with integers and decimal numbers. So, now we can apply the given arithmetic operations easily.

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