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Chapter 4: Problem 20

Perform the indicated operation. Write all results in lowest terms. $$-\frac{2}{7}-\frac{1}{21}$$

Short Answer

Expert verified
Answer: \(-\frac{5}{21}\)

Step by step solution

01

Find the Common Denominator

To subtract fractions, we need to have the same denominator. The common denominator between \(7\) and \(21\) is their least common multiple (LCM), which, in this case, is \(21\).
02

Rewrite the Fractions

Now that we know the common denominator, we can rewrite the fractions to have the same denominator. To do this, we multiply the fractions to make their denominators equal to \(21\). We have: $$-\frac{2}{7} \times \frac{3}{3} = -\frac{6}{21} \qquad \text{and} \qquad -\frac{1}{21}$$ So the expression becomes: $$-\frac{6}{21}-\frac{1}{21}$$
03

Subtract the Numerators

Now that the fractions have the same denominator, we can subtract the numerators: $$-\frac{6}{21}-\frac{1}{21} = -\frac{6-1}{21}$$
04

Simplify the Numerator

We can simplify the numerator by performing the subtraction: $$-\frac{6-1}{21} = -\frac{5}{21}$$
05

Check for Lowest Terms

Our result is \(-\frac{5}{21}\). Since the numerator and the denominator have no common factors (other than \(1\)), the result is already in the lowest terms. So the operation is: $$-\frac{2}{7}-\frac{1}{21}=-\frac{5}{21}$$

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