Question

Explain the associative property of rational numbers under multiplication and

addition​

Answer 1

Answer:

over multiplication,

While multiplying three or more rational numbers, they can be grouped in any order.  

Thus, for any rationals a/b, c/d, and e/f we have:  

(a/b × c/d) × e/f = a/b × (c/d × e/f)  

For example:  

Consider the rationals -5/2, -7/4 and 1/3 we have  

(-5/2 × (-7)/4 ) × 1/3 = {(-5) × (-7)}/(2 × 4) ×1/3} = (35/8 × 1/3)

= (35 × 1)/(8 × 3) = 35/24

and (-5)/2 × (-7/4 × 1/3) = -5/2 × {(-7) × 1}/(4 × 3) = (-5/2 × -7/12)

= {(-5) × (-7)}/(2 × 12) = 35/24

Therefore, (-5/2 × -7/4 ) × 1/3 = (-5/2) × (-7/4 × 1/3)

over addition=

While adding three rational numbers, they can be grouped in any order.  

Thus, for any three rational numbers a/b, c/d and e/f, we have  

(a/b + c/d) + e/f = a/b + (c/d + e/f)  

For example:

Consider three rationals -2/3, 5/7 and 1/6 Then,  

{(-2/3 + 5/7) + 1/6} = {(-14 + 15)/21 + 1/6} = (1/21 + 1/6) = (2 + 7)/42

= 9/42 = 3/14

and {(-2/3 + (5/7 + 1/6)} = {-2/3 + (30 + 7)/42} = (-2/3 + 37/42)

= (-28 + 37)/42 = 9/42 = 3/14

Therefore, {(-2/3 + 5/7) + 1/6} = {-2/3 + (5/7 + 1/6)}

please mark me as brainliest