Rational Numbers MCQs Class 8 RS Aggarwal Exe-1E Goyal Brothers Prakashan ICSE Foundation Maths Solutions. Ch-1. We provides step by step solutions of famous publications textbook for ICSE board. Our Solutions contain all type Questions to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

## Rational Numbers MCQs Class 8 RS Aggarwal Exe-1E Goyal Brothers ICSE Maths Solutions

Board | ICSE |

Publications | Goyal Brothers Prakshan |

Subject | Maths |

Class | 8th |

writer | RS Aggarwal |

Book Name | Foundation |

Topics | MCQs on Rational Numbers |

Edition | 2024-2025 |

### MCQs on Rational Numbers

Rational Numbers Class 8 RS Aggarwal Exe-1E Goyal Brothers Prakashan ICSE Foundation Maths Solutions. Ch-1

**Page- 24,25**

**Exercise- 1E**

(MCQs on Rational Numbers)

**Multiple Choice Questions :**

**Que-1: A number of the form p/q is said to be rational number if**

**(a) p and q are whole numbers and q ≠ 0.**

**(b) p is a whole number and q is a natural number.**

**(c) p and q are integers and q ≠ 0.**

**(d) p and q are integers and p ≠ 0, q ≠ 0.**

**Solution- **(c) p and q are integers and q ≠ 0.

**Reason : **

**Que-2: The additive inverse -5/12 is**

**(a) 5/12 (b) 12/5 (c) -12/5 (d) 2/15**

**Solution- **(a) 5/12

**Reason : **Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

**Que-3: The multiplicative inverse of -5/12 is**

**(a) 5/12 (b) 12/5 (c) -12/5 (d) 2/15**

**Solution- **(c) -12/5

**Reason : **The multiplicative inverse of a fraction a/b is b/a.

**Que-4: The product of additive inverse and multiplicative inverse of -1/4 is**

**(a) 1 (b) -1 (c) 0 (d) -1/16**

**Solution-** (b) -1

**Reason : **Additive inverse of -1/4 = 1/4

The multiplicative inverse of -1/4 = -4

So, the product is 1/4 x -4 = -1

**Que-5: The reciprocal of a negative rational number **

**(a) is a positive rational number**

**(b) is a negative rational number**

**(c) can be either a positive or a negative rational number.**

**(d) does not exist**

**Solution- **(b) is a negative rational number

**Reason :**

**Que-6: Which rational number are equal to their reciprocals?**

**(a) 0,1 (b) -1,0 (c) -1,1 (d) -1,0**

**Solution- **(c) -1,1

**Reason :** because reciprocal of -1/1 is -1/1.

**Que-7: Which of the following expressions show that rational numbers are associative under under multiplication ?**

**(a) 4/5 x [-6/7 x 8/9] = [4/5 x -6/7] x 8/9**

**(b) 4/5 x [-6/7 x 8/9] = 4/5 x [8/9 x -6/7]**

**(c) 4/5 x [6/7 x 8/9] = [8/9 x 4/5] x -6/7**

**(d) [4/5 x -6/7] x 8/9 = [-6/7 x 4/5] x 8/9**

**Solution- **(a) 4/5 x [-6/7 x 8/9] = [4/5 x -6/7] x 8/9

**Reason : ** 2/3×(−6/7×35/) = (2/3×−6/7)×3/5

Associative property states that if a, b and c are three rational numbers, then

(a×b)×c = a×(b×c).

Hence the expression:

2/3×(−6/7×3/5) = (2/3×−6/7)×3/5

represents associative property.

**Que-8: 1/4 X [2/5 + (-5/6)] = ?**

**(a) [-1/4 x 2/5] + [-1/4 x (-5/6)]**

**(b) [-1/4 x 2/5] – [-5/6]**

**(c) 2/5 + (-1/4) x (-5/6)**

**(d) [2/5 + (-5/6)] – 1/4**

**Solution- **(a) [-1/4 x 2/5] + [-1/4 x (-5/6)]

**Reason : **[-1/4 x 2/5] + [-1/4 x (-5/6)]

**Que-9: By what rational number should -5/24 be multiplied to get 10?**

**(a) 12 (b) -12 (c) 48 (d) -48**

**Solution- **(d) -48

**Reason : **Let that number be x

A.T.Q

x × -5/24 = 10

-5x/24 = 10

-5x = 24 × 10

-5x = 240

-x = 240/5

-x = 48

x = -48

**Que-10- What should be added to -3/4 to get 7/6?**

**(a) 11/24 (b) 9/24 (c) 10/25 (d) 23/12**

**Solution-** (d) 23/12

**Reason : **the least common multiple of 6 and 4, which is 12.

Now, convert both fractions to have a denominator of 12:

7/6 = (7/6) * (2/2) = 14/12

3/4 = (3/4) * (3/3) = 9/12

Now, add them:

14/12 + 9/12 = 23/12

**Que-11: What should be subtracted from -7/8 so as to get 5/12 ?**

**(a) 31/24 (b) 8/5 (c) -31/24 (d) -6/8**

**Solution- **(c) -31/24

**Reason :**we can subtract 5/12 from −7/8.

So, the calculation is:

−7/8 − 5/12

To subtract these fractions, we need to find a common denominator, which is 24 in this case (the least common multiple of 8 and 12)

(−7/8 − 5/12)

= −21/24 − 10/24

= (−21−10)/24

= -31/24

**Que-12: The sum of two rational number is -3. If one of the number is -7/5, then the other number is **

**(a) -8/5 (b) 8/5 (c) -6/5 (d) 6/5**

**Solution- **(a) -8/5

**Reason : **Let the other number be y.

Sum of two rational number = -3

= -7/5 + y = -3

y = -3 – (-7/5)

y = [-15 – (-7)]/5

y = (-15+7)/5

y = -8/5

**Que-13: The product of two numbers is -16/35. If one of the number is -15/14, then the other is**

**(a) -2/5 (b) -8/3 (c) 8/15 (d) 32/75**

**Solution- **(d) 32/75

**Reason : **We have been given that product of two numbers = (-16 / 35)

One of the numbers = (-15 / 14)

Let us assume that the other number is ‘a’.

According to our given condition,

( -15/14 ) x a = (-16 / 35)

a = (-16 / 35) / ( -15/14 )

a = (- 16 x 14) / (35 x -15)

a = 224/525 = 32/75

**∴ The other number is 32/75.**

**Que-14: Which of the following number is in standard form?**

**(a) -12/26 (b) -49/70 (c) -9/16 (d) 28/-105**

**Solution- **(c) -9/16

**Reason : **

**Que-15: (-9/16 x 8/15) = ?**

**(a) -3/10 (b) -4/15 (c) -9/25 (d) -2/5**

**Solution- **(a) -3/10

**Reason :** −9/16 × 8/15

= (−9×8)/(16×15)

= −72/240

= (−72÷24)/(240÷24)

= −3/10

**Que-16: [-5/9 ÷ 2/3] = ?**

**(a) -5/2 (b) -5/6 (c) -10/27 (d) -6/5**

**Solution-** (b) -5/6

**Reason : **So, we have:

= −5/9÷2/3

= (−5/9×3/2)

Now, let’s simplify this expression:

= (−5/9×3/2)

= (−5×3)/(9×2)

= −15/18 = -5/6

**Que-17: 4/9 ÷ ? = -8/15**

**(a) -32/45 (b) -8/5 (c) -9/10 (d) -5/6**

**Solution- **(d) -5/6

**Reason : **Let the fraction which divides 4/9 be ‘f’.

According to the question,

4/9 ÷ f = -8/15

f = 4/9 ÷ -8/15

f = (4/9) × (-15/8)

f = -(4×15)/(9×8)

f = -(5)/(3×2)

f = -5/6

**Que-18: Between any two given rational numbers we can find **

**(a) one and only one rational number (b) only two rational number**

**(c) only ten rational number (d) infinitely many rational numbers**

**Solution- **(d) infinitely many rational numbers

**Que-19: A rational number between 1/5 and 1/2 is **

**(a) 1/10 (b) 1/20 (c) 7/10 (d) 7/20**

**Solution- **(d) 7/20

**Reason : **average

= (1/5+1/2)/2

Calculating this:

= (2/10+5/10)/2

= (7/10)/2

= 7/20

**Que-20: Identify a rational number between 1/3 and 4/5**

**(a) 1/4 (b) 9/10 (c) 17/30 (d) 1*(7/10)**

**Solution- **(c) 17/30

**Reason : **The average of 1/3 and 4/5 is:

= (1/3+4/5)/2

Calculating this:

= (5/15+12/15)/2

= (17/15)/2

= 17/30

**Que-21: The arrangement of rational numbers -7/10, 5/-8, 2/-3, in ascending order is **

**(a) 2/-3, 5/-8, -7/10 (b) -7/10, 2/-3, 5/-8 ****(c) 5/-8, -7/10, 2/-3 (d) -7/10, 5/-8, 2/-3**

**Solution- **(b) -7/10, 2/-3, 5/-8

**Reason :** Given rational numbers are −7/10, 5/−8, 2/−3

∴ LCM of 10, 8, 3 is 120.

So, (−7×12)/(10×12), (5×15)/(−8×15), (2×40)/(−3×40)

= −84/120, 75/−120, 80/−120

= −84/120, −75/120, −80/120

Since, denominators are same so ascending order of numerators are – 84, -80, -75

Hence, −84/120 < −80/120 < −75/120

i.e. −7/10 < 2/−3 < 5/−8

**— : End of Rational Numbers MCQs Class 8 RS Aggarwal Exe-1E Goyal Brothers Prakashan:–**

**Return to :- ICSE Class -8 RS Aggarwal Goyal Brothers Math Solutions**

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