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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(6)/(7)+(-(2)/(21)) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{6}{7}+\left(-\frac{2}{21}\right)$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

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

\newline

-\frac{6}{7}+\left(-\frac{2}{21}\right)

\newline

Answer:

Identify common denominator: Identify the common denominator for the fractions. $\newline$ The fractions $\frac{6}{7}$ and $\frac{2}{21}$ have different denominators. To add or subtract fractions, we need a common denominator. The least common denominator (LCD) for $7$ and $21$ is $21$ .
Convert first fraction: Convert the first fraction to have the common denominator. $\newline$ The first fraction $\frac{6}{7}$ needs to be converted to have the denominator of $21$ . To do this, we multiply both the numerator and the denominator by $3$ , because $21$ is $3$ times $7$ . $\newline$ $\frac{6}{7} \times \frac{3}{3} = \frac{18}{21}$
Rewrite with converted fraction: Rewrite the expression with the converted first fraction. $\newline$ Now that we have a common denominator, we can rewrite the expression as: $\newline$ $-\frac{18}{21} + \left(-\frac{2}{21}\right)$
Add fractions: Add the fractions. $\newline$ Since both fractions now have the same denominator, we can add the numerators together, keeping the denominator the same. $\newline$ $-\frac{18}{21} + \left(-\frac{2}{21}\right) = -\frac{18 + 2}{21}$
Simplify numerator: Simplify the numerator. $\newline$ Add the numerators together. $\newline$ $-\frac{18 + 2}{21} = -\frac{20}{21}$
Check for simplification: Check for any possible simplification. $\newline$ The fraction $-\frac{20}{21}$ is already in its simplest form because $20$ and $21$ have no common factors other than $1$ .

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