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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (2)/(3)-(5)/(21) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{2}{3}-\frac{5}{21}$ $\newline$ 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{2}{3}-\frac{5}{21}

\newline

Answer:

Find Common Denominator: Find a common denominator for the fractions $(\frac{2}{3})$ and $(\frac{5}{21})$ . $\newline$ The least common multiple (LCM) of the denominators $3$ and $21$ is $21$ .
Convert Fractions: Convert the fractions to have the common denominator of $21$ . $(\frac{2}{3})$ becomes $(\frac{2\times7}{3\times7}) = (\frac{14}{21})$ . $(\frac{5}{21})$ remains the same because it already has the denominator of $21$ .
Subtract Fractions: Subtract the two fractions with the common denominator. $\newline$ $(\frac{14}{21}) - (\frac{5}{21}) = \frac{14 - 5}{21}$ .
Perform Subtraction: Perform the subtraction in the numerator. $\newline$ $14 - 5 = 9$ . $\newline$ So, $(14 - 5)/21 = 9/21$ .
Simplify Fraction: Simplify the fraction $\frac{9}{21}$ to its simplest form. $\newline$ Both the numerator and the denominator are divisible by $3$ . $\newline$ $\frac{9}{21} = \frac{(9/3)}{(21/3)} = \frac{3}{7}.$

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