Verify associativity of multiplication of rational numbers for the
following:
a) 3/7,5/6,14/23
Answers
Answer:
Question:
Verify Associative Property of multiplication on rational numbers:
3/7 , 5/6 , 14/23
Solution:
Associative property of multiplication => a * (b * c) = (a * b) * c
a = 3/7
b = 5/6
c = 14/23
Verification =>
\frac{3}{7} * ( \frac{5}{6} * \frac{14}{23}) = (\frac{3}{7} * \frac{5}{6}) * \frac{14}{23}
7
3
∗(
6
5
∗
23
14
)=(
7
3
∗
6
5
)∗
23
14
\frac{3}{7} * ( \frac{70}{138}) = (\frac{15}{42}) * \frac{14}{23}
7
3
∗(
138
70
)=(
42
15
)∗
23
14
\frac{210}{966} = \frac{210}{966}
966
210
=
966
210
This verifies that the three rational numbers 3/7 , 5/6 , 14/23 are following Associative property of multiplication.
Rational Numbers are those numbers which are in the form p/q where p and q needs to be integer and q can't be 0.
Associative Property of Addition => a + (b + c) = (a + b) + c
Distributivity of Rational Numbers => a * (b + c) = ab + ac , a * (b - c) = ab - ac