Question

Which of the following expressions show that Rational numbers are associative under multiplication?

Answer 1

Answer:

Step-by-step explanation:

Answer is option 2

Answer 2

The correct answer is option a and c.

Given: Expressions of rational numbers.

To Find: Which option follows associative property.

Solution:

Associative property: a x (b x c) = (a x b) x c.

(a) $\frac{2}{3}*(\frac{-6}{7} *\frac{3}{5} ) =(\frac{2}{3}*\frac{-6}{7} )*\frac{3}{5}$

If we consider a = $\frac{2}{3}$, b = $\frac{-6}{7}$ and c = $\frac{3}{5}$.

This is following the property.

(b) $\frac{2}{3}*(\frac{-6}{7} *\frac{3}{5} ) =\frac{2}{3}*(\frac{3}{5}*\frac{-6}{7} )$

If we consider a = $\frac{2}{3}$, b = $\frac{-6}{7}$ and c = $\frac{3}{5}$.

This is not following the associative property. only the terms in brackets are interchanging.

(c) $\frac{2}{3}*(\frac{-6}{7} *\frac{3}{5} ) =(\frac{3}{5}*\frac{2}{3} )*\frac{-6}{7}$

If we consider a = $\frac{2}{3}$, b = $\frac{-6}{7}$ and c = $\frac{3}{5}$.

This is following the property.

(b) $(\frac{2}{3}*\frac{-6}{7}) *\frac{3}{5} =(\frac{-6}{7}*\frac{2}{3})*\frac{3}{5}$

If we consider a = $\frac{2}{3}$, b = $\frac{-6}{7}$ and c = $\frac{3}{5}$.

This is not following the associative property. only the terms in brackets are interchanging.

Hence, the correct answer is a and c option.

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