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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(1)/(11)-(1)/(10) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{1}{11}-\frac{1}{10}$ $\newline$ 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{1}{11}-\frac{1}{10}

\newline

Answer:

Identify LCD: Identify the Least Common Denominator (LCD) $\newline$ To add or subtract fractions, we need a common denominator. The denominators here are $11$ and $10$ . The least common denominator (LCD) for $11$ and $10$ is their product since they are coprime (have no common factors other than $1$ ). $\newline$ LCD = $11 \times 10 = 110$ .
Rewrite with LCD: Rewrite the fractions with the LCD as the new denominator $\newline$ We convert each fraction to an equivalent fraction with the LCD as the denominator. $\newline$ $-\frac{1}{11}$ becomes $-\frac{10}{110}$ because $11 \times 10 = 110$ . $\newline$ $-\frac{1}{10}$ becomes $-\frac{11}{110}$ because $10 \times 11 = 110$ .
Add fractions: Add the fractions $\newline$ Now that we have common denominators, we can combine the numerators. $\newline$ $-\frac{10}{110} - \frac{11}{110} = -\frac{10 + 11}{110} = -\frac{21}{110}$ .
Simplify fraction: Simplify the fraction $\newline$ We look for any common factors between the numerator and the denominator to simplify the fraction. The numbers $21$ and $110$ do not have any common factors other than $1$ , so the fraction is already in its simplest form.

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