Let a,b,c be the three rational numbers where a=(2)/(3)quad b=(4)/(5) and c=(-5)/(6) and Verify: (i) a+(b+c)=(a+b)+c (Associative property of addition)

Calculate Sum of Fractions: First, we will calculate the sum of b and c, and then add a to the result. b + c = (4/5) + (-5/6) To add these fractions, we need a common denominator, which is 30. So, we convert the fractions to have the same denominator: b = (4/5) * (6/6) = (24/30) c = (-5/6) * (5/5) = (-25/30) Now, we add b and c: b + c = (24/30) + (-25/30) = (24 - 25)/30 = -1/30Add a to the Result: Next, we add a to the result of b + c. a + (b + c) = (2/3) + (-1/30) Again, we need a common denominator, which is 30. So, we convert a to have the same denominator: a = (2/3) * (10/10) = (20/30) Now, we add a to the result of b + c: a + (b + c) = (20/30) + (-1/30) = (20 - 1)/30 = 19/30Calculate Sum of Fractions: Now, we will calculate the sum of a and b, and then add c to the result. a + b = (2/3) + (4/5) To add these fractions, we need a common denominator, which is 15. So, we convert the fractions to have the same denominator: a = (2/3) * (5/5) = (10/15) b = (4/5) * (3/3) = (12/15) Now, we add a and b: a + b = (10/15) + (12/15) = (10 + 12)/15 = 22/15Add c to the Result: Finally, we add c to the result of a + b. (a + b) + c = (22/15) + (-5/6) To add these fractions, we need a common denominator, which is 30. So, we convert the fractions to have the same denominator: (a + b) = (22/15) * (2/2) = (44/30) c = (-5/6) * (5/5) = (-25/30) Now, we add (a + b) and c: (a + b) + c = (44/30) + (-25/30) = (44 - 25)/30 = 19/30

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Let
a,b,c be the three rational numbers where
a=(2)/(3)quad b=(4)/(5) and
c=(-5)/(6) and Verify:
(i)
a+(b+c)=(a+b)+c (Associative property of addition)

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

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Algebra 1

Transformations of quadratic functions

Full solution

Q. Let

a, b, c

be the three rational numbers where

a=\frac{2}{3} \quad b=\frac{4}{5}

and

c=\frac{-5}{6}

and Verify:

\newline

(i)

\mathrm{a}+(\mathrm{b}+\mathrm{c})=(\mathrm{a}+\mathrm{b})+\mathrm{c}

(Associative property of addition)

Calculate Sum of Fractions: First, we will calculate the sum of $b$ and $c$ , and then add $a$ to the result. $b + c = \left(\frac{4}{5}\right) + \left(-\frac{5}{6}\right)$ To add these fractions, we need a common denominator, which is $30$ . So, we convert the fractions to have the same denominator: $b = \left(\frac{4}{5}\right) \cdot \left(\frac{6}{6}\right) = \left(\frac{24}{30}\right)$ $c = \left(-\frac{5}{6}\right) \cdot \left(\frac{5}{5}\right) = \left(-\frac{25}{30}\right)$ Now, we add $b$ and $c$ : $b + c = \left(\frac{24}{30}\right) + \left(-\frac{25}{30}\right) = \left(\frac{24 - 25}{30}\right) = -\frac{1}{30}$
Add $a$ to the Result: Next, we add $a$ to the result of $b + c$ . $\newline$ $a + (b + c) = \frac{2}{3} + \left(-\frac{1}{30}\right)$ $\newline$ Again, we need a common denominator, which is $30$ . $\newline$ So, we convert $a$ to have the same denominator: $\newline$ $a = \left(\frac{2}{3}\right) * \left(\frac{10}{10}\right) = \frac{20}{30}$ $\newline$ Now, we add $a$ to the result of $b + c$ : $\newline$ $a + (b + c) = \frac{20}{30} + \left(-\frac{1}{30}\right) = \frac{20 - 1}{30} = \frac{19}{30}$
Calculate Sum of Fractions: Now, we will calculate the sum of $a$ and $b$ , and then add $c$ to the result. $a + b = \frac{2}{3} + \frac{4}{5}$ To add these fractions, we need a common denominator, which is $15$ .So, we convert the fractions to have the same denominator: $a = \frac{2}{3} \times \frac{5}{5} = \frac{10}{15}$ $b = \frac{4}{5} \times \frac{3}{3} = \frac{12}{15}$ Now, we add $a$ and $b$ : $a + b = \frac{10}{15} + \frac{12}{15} = \frac{10 + 12}{15} = \frac{22}{15}$
Add $c$ to the Result: Finally, we add $c$ to the result of $a + b$ . $(a + b) + c = \left(\frac{22}{15}\right) + \left(-\frac{5}{6}\right)$ To add these fractions, we need a common denominator, which is $30$ . So, we convert the fractions to have the same denominator: $(a + b) = \left(\frac{22}{15}\right) * \left(\frac{2}{2}\right) = \left(\frac{44}{30}\right)$ $c = \left(-\frac{5}{6}\right) * \left(\frac{5}{5}\right) = \left(-\frac{25}{30}\right)$ Now, we add $(a + b)$ and $c$ : $(a + b) + c = \left(\frac{44}{30}\right) + \left(-\frac{25}{30}\right) = \frac{44 - 25}{30} = \frac{19}{30}$