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

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(1) Evaluate. Express Your Answer as a Rational Number in Its Lowest Form

(a)

(b)

(c)

(2) Evaluate. Express Your Answer as a Rational Number in Its Lowest Form

(a)

(b)

(c)

(3) Evaluate. Express Your Answer as a Rational Number in Its Standard Form

(a)

(b)

(c)

(4) Evaluate. Express Your Answer as a Rational Number in Its Standard Form

(a)

(b)

(c)

(5) Evaluate. Express Your Answer as a Rational Number in Its Lowest Form

(a)

(b)

(c)

(6) Find the Value of X. Express Your Answer as a Rational Number in Its Lowest Form

(a)

(b)

(7) Find the Value of X. Express Your Answer as a Rational Number in Its Standard Form

(a)

(b)

(8) Find the Value of X. Express Your Answer as a Rational Number in Its Lowest Form

(a)

(b)

(9) Find the Value of X. Express Your Answer as a Rational Number in Its Standard Form

(a)

(b)

(10) P, Q, R, and S Are Rational Numbers, Where P < 0, Q > 0, R < 0, and S > 0. Find the Sign of the Given Expressions. Write + for Positive, – for Negative, and X to Indicate That the Sign Cannot be Determined

(a)

(b)

(C)

(11) a, B, C, and D Are Rational Numbers, Where a > 0, B < 0, C > 0, and D < 0. Find the Sign of the Given Expressions. Write + for Positive, – for Negative, and X to Indicate That the Sign Cannot be Determined

(a)

(b)

(C)

(12) T, U, V, and W Are Rational Numbers, Where T < 0, U > 0, V < 0, and W > 0. Find the Sign of the Given Expressions. Write + for Positive, – for Negative, and X to Indicate That the Sign Cannot be Determined

(a)

(b)

(C)

(13) W, X, Y, and Z Are Rational Numbers, Where W < 0, X > 0, Y < 0, and Z > 0. Find the Sign of the Given Expressions. Write + for Positive, – for Negative, and X to Indicate That the Sign Cannot be Determined

(a)

(b)

(C)

(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 .

(19) Evaluate. Write the Answer in the Decimal Form

(a)

(b)

(20) Evaluate. Write the Answer in the Decimal Form

(a)

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

(a)

(22) If , evaluate the following.

(23) If , evaluate the following.

Answers and Explanations

Answer 1 (A)

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

Answer 1 (B)

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

Answer 1 (C)

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

Answer 2 (A)

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

Answer 2 (B)

  • So,
  • And for lowest form

  • So, lowest form of derived rational number

Answer 2 (C)

  • So,
  • For lowest form,

  • So, lowest form of evaluated rational number is

Answer 3 (A)

  • So,
  • For Standard form,

  • So, standard form of evaluated rational number

Answer 3 (B)

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

Answer 3 (C)

  • So,
  • For standard form,

)

  • So, standard form of evaluated rational number

Answer 4 (A)

  • So,
  • For Standard form

  • So, standard form of evaluated rational number

Answer 4 (B)

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

Answer 4 (C)

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

Answer 5 (A)

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

Answer 5 (B)

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

Answer 5 (C)

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

Answer 6 (A)

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

  • So, lowest form of rational number is

Answer 6 (B)

  • So, lowest form of evaluated rational number is

Answer 7 (A)

  • For, Standard form of evaluated rational number;

  • So, standard form of evaluated rational number

Answer 7 (B)

  • Now, for Standard form of evaluated rational number;

  • So, standard form of evaluated rational number

Answer 8 (A)

  • For, lowest form of evaluated x value;

  • So, lowest form of evaluated x value is

Answer 8 (B)

  • For, lowest form of evaluated x value;

  • So, lowest form of evaluated x value

Answer 9 (A)

  • Now, for standard form of evaluated x value,

  • So, standard form of evaluated x value is

Answer 9 (B)

  • Now, for standard form of evaluated x value,

  • So, standard form of evaluated x value

Answer 10 (A)

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

Answer 10 (B)

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

Answer 10 (C)

  • 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,

Answer 11 (A)

  • 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,

Answer 11 (B)

  • 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,

Answer 11 (C)

  • 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,

Answer 12 (A)

  • 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,

Answer 12 (B)

  • 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,

Answer 12 (C)

  • 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,

Answer 13 (A)

  • 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,

Answer 13 (B)

  • 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,

Answer 13 (C)

  • 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,

Answer 14 (A)

  • 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.

Answer 14 (B)

  • 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.

Answer 15 (A)

  • 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.

Answer 15 (B)

  • 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.

Answer 16 (A)

  • 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.

Answer 16 (B)

  • 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

  • Here positive sign indicate lift 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.

Answer (17)

  • 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

Answer (18)

  • The number lies between and ;

  • Now, Number lies between and ;

  • Now, Number lies between and ;

  • So, three number lies between and are

Answer 19 (A)

  • 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,

Answer 19 (B)

  • 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,

Answer 20 (A)

  • 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,

Answer 21 (A)

  • 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,

Answer (22)

  • Here, given
  • Now,

  • So,

Answer (23)

  • So,

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