Solve the expression (a) (5)/(6)+((-2)/(3))+(1)/(3)-((-2)/(3)÷(3)/(2))=

Simplify Division: We will first simplify the division part of the expression before adding and subtracting the fractions. (-2/3) ÷ (3/2) can be simplified by multiplying the first fraction by the reciprocal of the second fraction. (-2/3) ÷ (3/2) = (-2/3) * (2/3)Multiply Numerators and Denominators: Now, we multiply the numerators and the denominators separately. (-2 * 2) / (3 * 3) = -4 / 9Add and Subtract Fractions: Next, we will add and subtract the fractions (5/6), (-2/3), (1/3), and (-4/9). To add and subtract fractions, they must have a common denominator. The least common multiple (LCM) of 6, 3, and 9 is 18. We will convert each fraction to have a denominator of 18.Convert Fractions to Common Denominator: Convert (5/6) to a fraction with a denominator of 18 by multiplying both the numerator and denominator by 3. (5/6) * (3/3) = 15/18Add and Subtract Fractions with Common Denominator: Convert (-2/3) to a fraction with a denominator of 18 by multiplying both the numerator and denominator by 6. (-2/3) * (6/6) = -12/18Combine Numerators: Convert (1/3) to a fraction with a denominator of 18 by multiplying both the numerator and denominator by 6. (1/3) * (6/6) = 6/18Perform Addition and Subtraction: Convert (-4/9) to a fraction with a denominator of 18 by multiplying both the numerator and denominator by 2. (-4/9) * (2/2) = -8/18Final Combined Fraction: Now, we can add and subtract the fractions with the common denominator of 18. (15/18) + (-12/18) + (6/18) - (-8/18)Combine the numerators while keeping the common denominator. (15 - 12 + 6 + 8) / 18Perform the addition and subtraction in the numerator. (15 - 12 + 6 + 8) = 17 So, the combined fraction is 17/18.

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Solve the expression $\newline$ $\frac{5}{6}+\left(-\frac{2}{3}\right)+\frac{1}{3}-\left(-\frac{2}{3}\div\frac{3}{2}\right)=$

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Algebra 1

Multiplication with rational exponents

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Q. Solve the expression

\newline

\frac{5}{6}+\left(-\frac{2}{3}\right)+\frac{1}{3}-\left(-\frac{2}{3}\div\frac{3}{2}\right)=

Simplify Division: We will first simplify the division part of the expression before adding and subtracting the fractions. $\newline$ $(-\frac{2}{3}) \div (\frac{3}{2})$ can be simplified by multiplying the first fraction by the reciprocal of the second fraction. $\newline$ $(-\frac{2}{3}) \div (\frac{3}{2}) = (-\frac{2}{3}) \times (\frac{2}{3})$
Multiply Numerators and Denominators: Now, we multiply the numerators and the denominators separately. $(-2 \times 2) / (3 \times 3) = -4 / 9$
Add and Subtract Fractions: Next, we will add and subtract the fractions $(\frac{5}{6}), (\frac{-2}{3}), (\frac{1}{3}),$ and $(\frac{-4}{9})$ . To add and subtract fractions, they must have a common denominator. The least common multiple (LCM) of $6, 3,$ and $9$ is $18$ . We will convert each fraction to have a denominator of $18$ .
Convert Fractions to Common Denominator: Convert $(\frac{5}{6})$ to a fraction with a denominator of $18$ by multiplying both the numerator and denominator by $3$ . $(\frac{5}{6}) \times (\frac{3}{3}) = \frac{15}{18}$
Add and Subtract Fractions with Common Denominator: Convert $(-\frac{2}{3})$ to a fraction with a denominator of $18$ by multiplying both the numerator and denominator by $6$ . $(-\frac{2}{3}) \times (\frac{6}{6}) = -\frac{12}{18}$
Combine Numerators: Convert $(\frac{1}{3})$ to a fraction with a denominator of $18$ by multiplying both the numerator and denominator by $6$ . $(\frac{1}{3}) \times (\frac{6}{6}) = \frac{6}{18}$
Perform Addition and Subtraction: Convert $(-\frac{4}{9})$ to a fraction with a denominator of $18$ by multiplying both the numerator and denominator by $2$ . $(-\frac{4}{9}) \times (\frac{2}{2}) = -\frac{8}{18}$
Final Combined Fraction: Now, we can add and subtract the fractions with the common denominator of $18$ . $\frac{15}{18}$ + $\left(-\frac{12}{18}\right)$ + $\frac{6}{18}$ - $\left(-\frac{8}{18}\right)$
Final Combined Fraction: Now, we can add and subtract the fractions with the common denominator of $18$ . $\newline$ $\left(\frac{15}{18}\right) + \left(-\frac{12}{18}\right) + \left(\frac{6}{18}\right) - \left(-\frac{8}{18}\right)$ Combine the numerators while keeping the common denominator. $\newline$ $\left(15 - 12 + 6 + 8\right) / 18$
Final Combined Fraction: Now, we can add and subtract the fractions with the common denominator of $18$ . $(\frac{15}{18}) + (\frac{-12}{18}) + (\frac{6}{18}) - (\frac{-8}{18})$ Combine the numerators while keeping the common denominator. $(15 - 12 + 6 + 8) / 18$ Perform the addition and subtraction in the numerator. $(15 - 12 + 6 + 8) = 17$ So, the combined fraction is $\frac{17}{18}$ .