Rational Numbers — Previous Year Questions (Class 8 Mathematics)
Master rational numbers, their properties, and operations. Build advanced fraction and decimal manipulation skills.
TL;DR: Master rational numbers, their properties, and operations. Build advanced fraction and decimal manipulation skills.
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Master rational numbers, their properties, and operations. Build advanced fraction and decimal manipulation skills.
Rational Numbers — Previous Year Questions with Solutions
Q (2023, 2 marks): Which of the following is a rational number? -2/3, pi, sqrt(2), 0.5
Answer: A rational number can be expressed as p/q where p and q are integers and q ≠ 0.
-2/3: Rational (is a fraction)
pi: Irrational (cannot be expressed as fraction)
sqrt(2): Irrational
0.5 = 1/2: Rational
Rational numbers: -2/3 and 0.5
Q (2022, 2 marks): Add: -3/5 + 4/7
Answer: LCM of 5 and 7 = 35
-3/5 = (-3×7)/35 = -21/35
4/7 = (4×5)/35 = 20/35
Sum = -21/35 + 20/35 = -1/35
Q (2023, 2 marks): Multiply: (-5/8) × (3/4) and simplify.
Answer: (-5/8) × (3/4) = (-5×3)/(8×4) = -15/32
This is already in simplest form.
Q (2022, 2 marks): Find the multiplicative inverse of -3/4.
Answer: The multiplicative inverse (reciprocal) of -3/4 is -4/3.
Verification: (-3/4) × (-4/3) = 12/12 = 1
Q (2023, 3 marks): Simplify: (2/3 + 1/4) × (3/5)
Answer: First, add: 2/3 + 1/4
LCM of 3 and 4 = 12
2/3 = 8/12; 1/4 = 3/12
2/3 + 1/4 = 8/12 + 3/12 = 11/12
Now multiply: (11/12) × (3/5) = 33/60 = 11/20
Q (2022, 2 marks): Between which two integers does -5/2 lie on a number line?
Answer: -5/2 = -2.5
-3 < -2.5 < -2
So -5/2 lies between -3 and -2.
Frequently Asked Questions
What is the difference between a rational and an irrational number?
Rational numbers can be expressed as p/q where p and q are integers (e.g., 3/4, -2, 0.5). Irrational numbers cannot be expressed as fractions (e.g., pi, sqrt(2)). All integers and fractions are rational.
Is zero a rational number?
Yes, zero is a rational number because it can be expressed as 0/1, 0/2, or any non-zero denominator. It is both an integer and a rational number.
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