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Let $a$ , $b$ , $c$ be the three rational numbers where $a = \frac{2}{3}$ , $b = \frac{4}{5}$ and $c = -\frac{5}{6}$ Verify: (i) $A + (b + c) = (a + b) + c$ (Associative property of addition)

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Descartes' Rule of Signs

Full solution

Q. Let

a

,

b

,

c

be the three rational numbers where

a = \frac{2}{3}

,

b = \frac{4}{5}

and

c = -\frac{5}{6}

Verify: (i)

A + (b + c) = (a + b) + c

(Associative property of addition)

Calculate $b + c$ : Calculate $b + c$ : $b + c = \frac{4}{5} + \left(-\frac{5}{6}\right) = \left(\frac{24}{30}\right) + \left(-\frac{25}{30}\right) = -\frac{1}{30}$ .
Calculate $a + (b + c)$ : Calculate $a + (b + c)$ : $a + (b + c) = \frac{2}{3} + \left(-\frac{1}{30}\right) = \left(\frac{20}{30}\right) + \left(-\frac{1}{30}\right) = \frac{19}{30}$ .
Calculate $a + b$ : Calculate $a + b$ : $a + b = \frac{2}{3} + \frac{4}{5} = \left(\frac{10}{15}\right) + \left(\frac{12}{15}\right) = \frac{22}{15}$ .
Calculate $(a + b) + c$ : Calculate $(a + b) + c$ : $(a + b) + c = \frac{22}{15} + \left(-\frac{5}{6}\right) = \left(\frac{44}{30}\right) + \left(-\frac{25}{30}\right) = \frac{19}{30}$ .

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