Cross-Product Rule and Representation on Rational Number Class 8 OP Malhotra Maths Solutions Exe-1A Ch-Rational Number. We Provide Step by Step Solutions on Cross-Product Rule and Representation of Rational Number in very simple and easy way. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.
Class 8 OP Malhotra Maths Solutions Exe-1A Rational Number
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 8th |
| Chapter-1 | Rational Number |
| Writer | OP Malhotra |
| Exe-1(A) | Cross-Product Rule and Representation |
| Edition | 2026-2027 |
Cross-Product Rule and Representation on Rational Number
Cross-Product Rule and Representation on Rational Number ICSE Class 8 Maths OP Malhotra (2026-27)
Que-1: Fill in the blanks.
(i) 3/-4 expressed as a rational number with denominator 24 = 18/24.
(ii) -4/7 ………… 4/-11 (<,>,=)
(iii) The absolute value of -21/-29 = ……….
(iv) The rational numbers whose absolute value is 7/8 are ………………
(v) he rational number which is neither positive nor negative is …………
Sol: (i) Since 4 × 6 = 24,
3/4 = (3 × 6)/(4 × 6)
= 18/2
(ii) 4/-11 = -4/11
Now compare -4/7 and -4/11.
Since 4/7 > 4/11, therefore −4/7 < −4/11.
Hence,
−4/7 < 4/−11.
(iii) The absolute value of a rational number is always positive.
|−21/−29| = |21/29| = 21/29.
(iv) A number having absolute value 7/8 can be either positive or negative.
Therefore, the rational numbers are:
7/8 and −7/8.
(v) Zero is neither a positive rational number nor a negative rational number.
Therefore, the answer is 0.
Que-2: Answer True (T) or False (F).
(i) Every rational number is a whole number.
Answer: False (F)
Solution: Every whole number is a rational number, but every rational number is not a whole number. For example, 1/2 is a rational number but not a whole number.
(ii) 0 is the smallest rational number.
Answer: False (F)
Solution: There is no smallest rational number because rational numbers can be negative and can be smaller than any given rational number.
(iii) Every fractional number is a rational number.
Answer: True (T)
Solution: A rational number is a number which can be expressed in the form p/q, where p and q are integers and q ≠ 0. Hence, every fractional number is a rational number.
(iv) 4/0 is a rational number.
Answer: False (F)
Solution: In a rational number, the denominator cannot be zero. Therefore, 4/0 is not a rational number.
(v) |x| = −x, if x < 0.
Answer: True (T)
Solution: The absolute value of a negative number is its positive value. Therefore, if x < 0, then |x| = −x.
Que-3: Write four rational numbers equivalent to each of the following rational numbers.
(i) 3/7
Answer: 6/14, 9/21, 12/28, 15/35
Solution:
3/7 × 2/2 = 6/14
3/7 × 3/3 = 9/21
3/7 × 4/4 = 12/28
3/7 × 5/5 = 15/35
(ii) −7/9
Answer: −14/18, −21/27, −28/36, −35/45
Solution:
−7/9 × 2/2 = −14/18
−7/9 × 3/3 = −21/27
−7/9 × 4/4 = −28/36
−7/9 × 5/5 = −35/45
(iii) 5/−12
Answer: 10/−24, 15/−36, 20/−48, 25/−60
Solution:
Multiply the numerator and denominator by 2, 3, 4 and 5 respectively.
(iv) −12/13
Answer: −24/26, −36/39, −48/52, −60/65
Solution:
Multiply the numerator and denominator by 2, 3, 4 and 5 respectively.
Que-4: Which of the two rational numbers is greater?
(i) −8/13 or 6/13
Answer: 6/13
Solution: Since 6/13 is positive and −8/13 is negative, 6/13 is greater.
(ii) −5/16 or −6/8
Answer: −5/16
Solution:
−6/8 = −3/4 = −12/16
Therefore, −5/16 > −12/16.
(iii) −11/25 or 0
Answer: 0
Solution: 0 is greater than every negative rational number. Therefore, 0 is greater than −11/25.
(iv) −22/−33 or 45/−65
Answer: −22/−33
Solution:
−22/−33 = 2/3
45/−65 = −9/13
Since 2/3 is positive and −9/13 is negative,
2/3 > −9/13.
Que-5: Which of the two rational numbers is smaller?
(i) −11/8 or 17/−8
Answer: 17/−8
Solution:
17/−8 = −17/8
Since −17/8 < −11/8,
17/−8 is smaller.
(ii) 12/19 or −9/−19
Answer: −9/−19
Solution:
−9/−19 = 9/19
Since 9/19 < 12/19,
−9/−19 is smaller.
(iii) 21/−5 or 1
Answer: 21/−5
Solution:
21/−5 = −21/5
Since −21/5 < 1,
21/−5 is smaller.
(iv) −11/1111 or 1/−103
Answer: 1/−103
Solution:
−11/1111 = −1/101
1/−103 = −1/103
Since −1/103 < −1/101,
1/−103 is smaller.
Que-6: Which of the symbols =, < or >, should replace the blank space?
(i) 10/3 ….. (1)
Answer: >
Solution: 10/3 = 3⅓, which is greater than 1.
Therefore, 10/3 > 1.
(ii) −1/2 ….. −3/5
Answer: >
Solution:
−1/2 = −5/10 and −3/5 = −6/10.
Therefore, −5/10 > −6/10.
−1/2 > −3/5.
(iii) −3/4 ….. −2/3
Answer: <
Solution:
−3/4 = −9/12 and −2/3 = −8/12.
Therefore, −9/12 < −8/12.
−3/4 < −2/3.
(iv) (−23/7) ….. (−23/5)
Answer: >
Solution:
−2 3/7 = −17/7 and −2 3/5 = −13/5.
−17/7 ≈ −2.43 and −13/5 = −2.6.
Therefore,
−2 3/7 > −2 3/5.
(v) 8/7 ….. 12/9
Answer: <
Solution:
8/7 = 72/63 and 12/9 = 84/63.
Therefore, 8/7 < 12/9.
(vi) −2/3 ….. 4/−7
Answer: <
Solution:
4/−7 = −4/7.
−2/3 ≈ −0.667 and −4/7 ≈ −0.571.
Therefore, −2/3 < 4/−7.
(vii) 13/−15 ….. 10/−11
Answer: >
Solution:
−13/15 ≈ −0.867 and −10/11 ≈ −0.909.
Therefore, 13/−15 > 10/−11.
(viii) 0 ….. −5/−9
Answer: <
Solution:
−5/−9 = 5/9.
Since 0 < 5/9,
0 < −5/−9.
Que-7: Arrange in order from least to greatest.
(i) −1/4, 3/8, −2/5, 9/40, 7/10
Sol: We take LCM of 4, 8, 5, 40 and 10 = 40
(-1/4)×(10/10) = -10/40,
(3/8)×(5/5) = 15/40
(-2/5)×(8/8) = -16/40
(9/40)×(1/1) = 9/40
(7/10)×(4/4) = 28/40
Since, -16 < -10 < 9 < 15 < 28,
therefore, -16/40 < -10/40 < 9/40 < 15/40 < 28/40
Therefore, the required order is:
−2/5 < −1/4 < 9/40 < 3/8 < 7/10.
(ii) -4/5, 9/-10, 5/6, 3/-4, 9/16
Sol: We take LCM of 5, 10, 6, 4 and 16 = 240
(-4/5)×(48/48) = -192/240,
(-9/10)×(24/24) = -216/240
(5/6)×(40/40) = 200/240
(-3/4)×(60/60) = -180/240
(9/16)×(15/15) = 135/240
Since, -216 < -192 < -180 < 135 < 200,
therefore, -216/240 < -192/240 < -180/240 < 135/240 < 200/240
Therefore, the required order is:
−9/10 < −4/5 < −3/4 < 9/16 < 5/6.
Que-8: Arrange in descending order.
(i) 3/4, 6/7, -9/14, -7/8, -1/6
Sol: We take LCM of 4, 7, 14, 8 and 6 = 168
(3/4)×(42/42) = 126/168,
(6/7)×(24/24) = 144/168
(-9/14)×(12/12) = -108/168
(-7/8)×(21/21) = -147/168
(-1/6)×(28/28) = -28/168
Since, 144 > 126 > -28 > -108 > -147,
therefore, 144/168 > 126/168 > -28/168 > -108/168 > -147/168
Therefore, the required order is:
6/7 > 3/4 > −1/6 > −9/14 > −7/8.
(ii) 1/15, -1/3, -3/12, 18/25, 3/-10
Sol: We take LCM of 15, 3, 12, 25 and 10 = 300
(1/15)×(20/20) = 20/300,
(-1/3)×(100/100) = -100/300
(-3/12)×(25/25) = -75/300
(18/25)×(12/12) = 216/300
(-3/10)×(30/30) = -90/300
Since, 216 > 20 > -75 > -90 > -100,
therefore, 216/300 > 20/300 > -75/300 > -90/300 > -100/300
Therefore, the required order is:
18/25 > 1/15 > −1/4 > −3/10 > −1/3.
Que-9: Write the absolute value of each of the following.
(i) −13/25
Answer: 13/25
Solution: |−13/25| = 13/25.
(ii) −35/−47
Answer: 35/47
Solution:
−35/−47 = 35/47.
Therefore, |−35/−47| = 35/47.
(iii) 0
Answer: 0
Solution: |0| = 0.
(iv) 23/−58
Answer: 23/58
Solution:
23/−58 = −23/58.
Therefore, |23/−58| = 23/58.
Multiple Choice Questions (MCQs)
10. Which of the following is not a rational number?
(a) 3/17
(b) −4/19
(c) 0/9
(d) 4/0
Answer: (d) 4/0
Solution:
A rational number is of the form p/q, where q ≠ 0.
In 4/0, the denominator is zero. Therefore, 4/0 is not a rational number.
Que-11: −32/56 expressed as a rational number with numerator 4 is
(a) 4/7
(b) 4/14
(c) 4/−7
(d) 4/−14
Answer: (c) 4/−7
Solution:
−32/56 = −4/7
To make the numerator 4, multiply both numerator and denominator by −1:
−4/7 × −1/−1
= 4/−7
Therefore, the correct option is (c).
Que-12: Which of the following sets of rational numbers is arranged in ascending order?
(a) −1/2, −3/7, −5/14, −25/28
(b) −25/28, −1/2, −3/7, −5/14
(c) 25/28, −5/14, −3/7, 1/2
(d) −5/14, −25/28, −3/7, 1/2
Answer: (b)
Solution: Convert the numbers into decimals:
−25/28 ≈ −0.893
−1/2 = −0.5
−3/7 ≈ −0.429
−5/14 ≈ −0.357
Thus,
−25/28 < −1/2 < −3/7 < −5/14.
Therefore, the set arranged in ascending order is option (b).
— : End of Cross-Product Rule and Representation on Rational Number ICSE Class 8 Maths OP Malhotra (2026-27) :–
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