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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(11)/(6)+(-(3)/(10)) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{11}{6}+\left(-\frac{3}{10}\right)$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

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-\frac{11}{6}+\left(-\frac{3}{10}\right)

\newline

Answer:

Identify common denominator: Identify the common denominator for the fractions. $\newline$ The fractions have denominators of $6$ and $10$ . The least common multiple (LCM) of $6$ and $10$ is $30$ , which will be the common denominator.
Convert to equivalent fractions: Convert each fraction to an equivalent fraction with the common denominator of $30$ . $\newline$ For the first fraction, multiply both the numerator and the denominator by $5$ to get an equivalent fraction with a denominator of $30$ : $\newline$ $-\frac{11}{6} = -\frac{11\times 5}{6\times 5} = -\frac{55}{30}$ $\newline$ For the second fraction, multiply both the numerator and the denominator by $3$ to get an equivalent fraction with a denominator of $30$ : $\newline$ $-\frac{3}{10} = -\frac{3\times 3}{10\times 3} = -\frac{9}{30}$
Add fractions with common denominator: Add the two fractions with the common denominator. $\newline$ Now that both fractions have the same denominator, we can add their numerators: $\newline$ $-\frac{55}{30} + \left(-\frac{9}{30}\right) = -\frac{55}{30} - \frac{9}{30}$ $\newline$ Combine the numerators: $\newline$ $-55 - 9 = -64$ $\newline$ So the combined fraction is $-\frac{64}{30}$ .
Simplify the fraction: Simplify the fraction. $\newline$ The fraction $-\frac{64}{30}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of $64$ and $30$ is $2$ . $\newline$ $-\frac{64}{30} \div \frac{2}{2} = -\frac{32}{15}$