# Grade 8 Operations on Rational Numbers Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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## (14) a Crane Lifts the Material According Signal It Receives from Signal Man. When Man Given Green Signal Operator Lift Material by 1/4 Meter and Man Give Red Signal Operator down Material by 1/5 Meter

Now write a sequence of signal that moves the material accordingly.

(a) Material lifted up to 6m.

(b) Material down by 4m.

## (15) a Crane Lift the Material According Signal It Receive from Signal Man. When Man Given Green Signal Operator Lift Material by 1/4 Meter and Man Give Red Signal Operator down Material by 1/5 Meter

Now write a sequence of signal that moves the material accordingly.

(a) Material lifted up to 8m

(b) Material down by 1m

## (16) a Crane Lift the Material According Signal It Receive from Signal Man. When Man Given Green Signal Operator Lift Material by 1/4 Meter and Man Give Red Signal Operator down Material by 1/5 Meter

(a) Due to mistake of signal man material was at same place hanged from when man start giving signal, so write a sequence of that signal.

(b) Can a sequence of signals lift or down material by meter? If yes, write that sequence. Otherwise, explain why it is not possible.

(17) Find rational number that lies between and .

(18) Find three rational number that lies between and .

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## (21) Evaluate. Write the Answer in the Decimal Form

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(22) If , evaluate the following.

(23) If , evaluate the following.

• So,
• And lowest form of evaluated rational number is

• So,
• And lowest form of evaluated rational number is

• So,
• And lowest form of evaluated rational number is

• So,
• And lowest form of evaluated rational number is

• So,
• And for lowest form

• So, lowest form of derived rational number

• So,
• For lowest form,

• So, lowest form of evaluated rational number is

• So,
• For Standard form,

• So, standard form of evaluated rational number

• So,
• So, standard form of evaluated rational number is

• So,
• For standard form,

)

• So, standard form of evaluated rational number

• So,
• For Standard form

• So, standard form of evaluated rational number

• So,
• So, Standard form of evaluated rational number is

• So,
• So, Standard form of evaluated rational number is

• So,
• So, lowest form of evaluated rational number is

• So,
• So, lowest form of evaluated rational number is

• So,
• So, lowest form of evaluated rational number is

• Now, for the lowest form of evaluated rational number:

• So, lowest form of rational number is

• So, lowest form of evaluated rational number is

• For, Standard form of evaluated rational number;

• So, standard form of evaluated rational number

• Now, for Standard form of evaluated rational number;

• So, standard form of evaluated rational number

• For, lowest form of evaluated x value;

• So, lowest form of evaluated x value is

• For, lowest form of evaluated x value;

• So, lowest form of evaluated x value

• Now, for standard form of evaluated x value,

• So, standard form of evaluated x value is

• Now, for standard form of evaluated x value,

• So, standard form of evaluated x value

• And given.
• Here P and R both are minus rational number.
• So, their summations also have minus rational number.
• Therefore,

• And given.
• Here Q and S both are Positive rational number.
• So, its Multiplication also has positive rational number.
• Therefore,

• Here given
• So, Q is positive rational number and R is negative rational number.
• So, we cannot exactly know the sign of its summation until we know its value.
• Therefore,

• Here, A > 0 and B < 0 given.
• So, A is positive rational number and B is negative rational number.
• So, Division of one positive rational by another negative rational number is a negative rational number.
• Therefore,

• Here, A > 0 and C > 0 given.
• So, A is positive rational number and C is also a positive rational number.
• So, multiplication of one positive rational by another positive rational number is a positive rational number.
• So,

• Here, B < 0 and D < 0 given.
• So, B is negative rational number and D is also a negative rational number.
• So, Summation of one negative rational to another negative rational number is a negative rational number.
• So,

• Here, T < 0 and U > 0 given.
• So, T is negative rational number and U is Positive rational number.
• So, Subtraction from one negative rational to another positive rational number is a negative rational number.
• So,

• Here, V < 0 and W > 0 given.
• So, V is negative rational number and W is Positive rational number.
• So, for summation of one negative rational to another positive rational number one cannot judge the answer՚s sign it may be a positive rational number or may be a negative rational number.
• So,

• Here, T < 0 and W > 0 given.
• So, T is negative rational number and W is Positive rational number.
• So, Division of one negative rational by another positive rational number is a negative rational number.
• So,

• Here, W < 0 and X > 0 given.
• So, W is negative rational number and X is Positive rational number.
• So, Multiplication of one negative rational with another positive rational number is a negative rational number.
• So,

• Here, X > 0 and Z > 0 given.
• So, X is Positive rational number and Z is also a Positive rational number.
• So, Division of one Positive rational with another positive rational number is also a positive rational number.
• So,

• Here, Y < 0 and Z > 0 given.
• So, Y is negative rational number and Z is also a Positive rational number.
• So, subtraction of one negative rational by another positive rational number is also a negative rational number.
• So,

• Material lifted up to 6m.
• Now, when operator receive green signal from signal man than he lift material only by meter.
• So,

• Operator receive green signal number of times

• So, sequence of signal that will lift material by 6 meter is 24 times green signal.

• Material down by 4m.
• When operator receive red signal from signal man than he down the material by meter.

So,

• So, operator receives red signal number of times.

• So, sequence of signal that will Down material by 4 meter is 20 times red signal.

• Material lifted up to 8m.
• Now, when operator receive green signal from signal man than he lift material only by meter.
• So,

• Operator receive green signal number of times

• So, sequence of signal that will lift material by 6 meter is 32 times green signal.

• Material down by 1m.
• When operator receive red signal from signal man than he down the material by meter.

So,

• So, operator receives red signal number of times.

• So, sequence of signal that will Down material by 1 meter is 5 times red signal.

• When operator receive green signal he lift material by meter and when receive red signal he down material by meter.
• So, to lift the material by 1 meter operator receive 4 green signals and to down material 1 meter operator should receive 5 red signals.
• So, in another way one can say that operator received 4 green signal and 5 red signal from signal man that՚s why material as hanged at same place since starting of activity.
• So sequence of signal is, 4 green signals and 5 red signals.

• When operator receive green signal he lift material by meter and when receive red signal he down material by meter.
• So, material was lifted by number of meter is in multiplication of meter, because one cannot give half signal.
• Same way material was down by number of meter is in multiplication of meter, because one cannot give half signal.
• So, by summation of green and red signal material was lifted/down by,

• here we give minus sign to red signal to identify actual movement direction of material

• So, by one green and one red signal will lift the material by meter.
• Here 20 is H. C. F of 5 and 4 and is not dividable by 3 (here we consider 3 because we have to movement the material by meter) so one cannot lift or down the material by meter by giving any sequence of red or green signal.

• Here given two rational number are and .
• So, the rational number that lies between this given two rational number is;

• So, the rational number that lies between and is

• The number lies between and ;

• Now, Number lies between and ;

• Now, Number lies between and ;

• So, three number lies between and are

• Here in , 45 is given in the bar form that means 45 is repetitive number after decimal point,
• So in another way we can write this decimal number as below.

• Same way for decimal number we can write as below.

• Now for summation of this two decimal bar number we can write as below,

• Now, for , here 81 is repetitive number after decimal point
• So, in another way we can write this decimal number as below,

• So,

• Here in , 67 is given in the bar form that means 67 is repetitive number after decimal point,
• So in another way we can write this decimal number as below.

• Same way for decimal number we can write as below.

• Now for Subtraction of this two decimal bar number we can write as below,

• Now, for , here 4 is repetitive number after decimal point
• So, in another way we can write this decimal number as below,

• So,

• For multiplication of bar number; we cannot directly multiply this bar number with given number 2.
• For that first we have to convert this bar number in to rational number than multiply this rational number with given number to get answer.
• So,

• Now, for multiplication;

• Now, for , here 90 is repetitive number after decimal point
• So, in another way we can write this decimal number as below,

• So,

• For Division of bar number; we cannot directly divide bar number by given number 3.
• For that first we have to convert this bar number in to rational number than Divide this rational number by given number to get answer.
• So,

• Now for division,

• Now, for , here 23 is repetitive number after decimal point
• So, in another way we can write this decimal number as below,

• So,