Question

verify associative of multiplication on rational numbers 3/7 5/6 14/23​

Answer 1

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 =>

$\frac{3}{7} * ( \frac{5}{6} * \frac{14}{23}) = (\frac{3}{7} * \frac{5}{6}) * \frac{14}{23}$

$\frac{3}{7} * ( \frac{70}{138}) = (\frac{15}{42}) * \frac{14}{23}$

$\frac{210}{966} = \frac{210}{966}$

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

Answer 2

Answer:

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}73∗(65∗2314)=(73∗65)∗2314

\frac{3}{7} * ( \frac{70}{138}) = (\frac{15}{42}) * \frac{14}{23}73∗(13870)=(4215)∗2314

\frac{210}{966} = \frac{210}{966}966210=966210

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