Which of the following expressions shows that rational numbers are associative under multiplication
(a) 2/3 × (-6/7 × 3/5) = (2/3 × -6/7) × 3/5
(b) 2/3 × (-6/7 × 3/5) = 2/3 × (3/5 × -6/7)
(c) 2/3 × (-6/7 × 3/5) = (3/5 × 2/3) × -6/7
(d) (2/3 × -6/7) × 3/5 = (-6/7 × 2/3) × 3/5
Solution:
We know that associative property under multiplication states as follows:
A × (B × C) = (A × B) × C, without change in order of elements
By comparing, we can say that 2/3 × (-6/7 × 3/5) = (2/3 × -6/7) × 3/5.
✦ Try This: Which of the following expressions shows that rational numbers are associative under multiplication.
(a) 2/5 × (1/7 × 3/5) = (2/5 × 1/7) × 3/5
(b) 2/5 × (1/7 × 3/5) = 2/5 × (3/5 × 1/7)
(c) 2/5 × (1/7 × 3/5) = (3/5 × 2/5) × 1/7
(d) (2/5 × 1/7) × 3/5 = (1/7 × 2/5) × 3/5
We know that associative property under multiplication states as follows:
A × (B × C) = (A × B) × C, without change in the order of elements
By comparing, we can say that 2/5 × (1/7 × 3/5) = (2/5 × 1/7) × 3/5.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1
NCERT Exemplar Class 8 Maths Chapter 1 Problem 6
Which of the following expressions shows that rational numbers are associative under multiplication (a) 2/3 × (-6/7 × 3/5) = (2/3 × -6/7) × 3/5, (b) 2/3 × (-6/7 × 3/5) = 2/3 × (3/5 × -6/7), (c) 2/3 × (-6/7 × 3/5) = (3/5 × 2/3) × -6/7, (d) (2/3 × -6/7) × 3/5 = (-6/7 × 2/3) × 3/5
Summary:
2/3 × (-6/7 × 3/5) = (2/3 × -6/7) × 3/5 shows that rational numbers are associative under multiplication
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