Let a, b, c be the three rational numbers where a = 2/3, b = 4/5 and c = −5/6 Verify: a + (b + c) = (a + b) + c

Calculate b + c: Calculate b + c: b + c = 4/5 + (-5/6) = (24/30) + (-25/30) = -1/30.Calculate a + (b + c): Calculate a + (b + c): a + (b + c) = 2/3 + (-1/30) = (20/30) + (-1/30) = 19/30.Calculate a + b: Calculate a + b: a + b = 2/3 + 4/5 = (10/15) + (12/15) = 22/15.Calculate (a + b) + c: Calculate (a + b) + c: (a + b) + c = 22/15 + (-5/6) = (44/30) + (-25/30) = 19/30.

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

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Math Problems

Algebra 2

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}

\newline

Verify:

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

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 $(a + b) + c$ : $(a + b) + c = \frac{22}{15} + \left(-\frac{5}{6}\right) = \left(\frac{44}{30}\right) + \left(-\frac{25}{30}\right) = \frac{19}{30}$ .