Question

4. Verify the associative property for addition for the following rational number
4/5,-3/8,11/20​

Answer 1

EXPLANATION.

Verify the associative property for addition of the rational number.

4/5 , -3/8 , 11/20.

As we know that,

Associative property.

• Associative property of addition : (a + b) + c = a + (b + c).
• Associative property of multiplication : (a x b) x c = a x (b x c).

First we verify associative property of addition.

$\sf \displaystyle (a + b) + c = a + (b + c)$

$\sf \displaystyle \bigg[\frac{4}{5} + \bigg(\frac{-3}{8} \bigg) \bigg] + \frac{11}{20} = \frac{4}{5} + \bigg[\frac{-3}{8} + \frac{11}{20} \bigg]$

$\sf \displaystyle \bigg[\frac{(4)(8) + (-3)(5)}{40} \bigg] + \frac{11}{20} = \frac{4}{5} + \bigg[\frac{(-3)(5) + (11)(2)}{40} \bigg]$

$\sf \displaystyle \bigg[\frac{32 - 15}{40} \bigg] + \frac{11}{20} = \frac{4}{5} + \bigg[\frac{- 15 + 22}{40} \bigg]$

$\sf \displaystyle \frac{17}{40} + \frac{11}{20} = \frac{4}{5} + \frac{7}{40}$

$\sf \displaystyle \frac{17 + 2(11)}{40} = \frac{4(8) + 7}{40}$

$\sf \displaystyle \frac{17 + 22}{40} = \frac{32 + 7}{40}$

$\sf \displaystyle \frac{39}{40} =\frac{39}{40}$

Hence proved.

Now, we verify associative property of multiplication.

$\sf \displaystyle ( a \times b) \times c = a \times (b \times c)$

$\sf \displaystyle \bigg[\frac{4}{5} \times \frac{-3}{8} \bigg] \times \frac{11}{20} = \frac{4}{5} \times \bigg[\frac{- 3}{8} \times \frac{11}{20} \bigg]$

$\sf \displaystyle \bigg[\frac{1}{5} \times \frac{-3}{2} \bigg] \times \frac{11}{20} = \frac{4}{5} \times \frac{- 33}{160}$

$\sf \displaystyle\frac{-3}{10} \times \frac{11}{20} = \frac{1}{5} \times \frac{-33}{40}$

$\sf \displaystyle \frac{-33}{200} = \frac{-33}{200}$

Hence proved.