Class 8 Maths Chapter 1 Question Answers - Rational Numbers

Q1: Calculate the following:

Ans:


Q2: Find 7 rational numbers between 1/3 and 1/2.
Ans: Express both the numbers in same denominator 

 
Thus, the required rational numbers between


Q3: If x = 1/2, y = −2/3 and z = 1/4, verify that x × (y × z) = (x × y) × z.
Ans:  We have x = 1/2, y = −2/3 and z = 1/4
LHS = x × (y × z)


Q4: The product of two rational numbers is 15/56. If one of the numbers is −5/48, find the other.
Ans:
Product of two rational numbers = 15/56
One number = −5/48
Other number = Product ÷ First number

Hence, the other number = −18/7

Q5: Represent the following rational numbers on number lines.
(a) −2/3
(b) 3/4
(c) 3/2
Ans:


Q6: Show that:

Ans:


Q7: If the cost of  litres of milk is ₹, find the cost of 1 litre of milk.
Ans:


Q8: Let O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between O and P such that OQ = QR = RS = SP.
What are the rational numbers represented by the points Q, R and S. Next choose a point T between Z and 0 so that ZT = TO. Which rational number does T represent?
Ans:
As OQ = QR = RS = SP and OQ + QR + RS + SP = OP therefore Q, R and S divide OP into four equal parts.


Q9: Let a, b, c be the three rational numbers where a = 2/3, b = 4/5 and c = −5/6
Verify:
(i) a + (b + c) = (a + b) + c (Associative property of addition)
(ii) a × (b × c) – (a × b) × c (Associative property of multiplication)
Ans: (i) L.H.S = a + (b + c)

R.H.S of (i) = (a + b) + c