Question:
Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $-(1 / 4) \times\{(2 / 3)+(-4 / 7)\}=[-(1 / 4) \times(2 / 3)]+[(-1 / 4) \times(-4 / 7)]$
(b) $-(1 / 4) \times\{(2 / 3)+(-4 / 7)\}=[(1 / 4) \times(2 / 3)]-(-4 / 7)$
(c) $-(1 / 4) \times\{(2 / 3)+(-4 / 7)\}=(2 / 3)+(-1 / 4) \times(-4 / 7)$
(d) $-(1 / 4) \times\{(2 / 3)+(-4 / 7)\}=\{(2 / 3)+(-4 / 7)\}-(1 / 4)$
Solution:
(a) $-(1 / 4) \times\{(2 / 3)+(-4 / 7)\}=[-(1 / 4) \times(2 / 3)]+[(-1 / 4) \times(-4 / 7)]$
Because, we know the rule of distributive law, i.e. $a \times(b+c)]=[(a \times b)+(a \times c)$