Solve 1/1-1/7-6/21=7-18/7=frac{-12}{7}

$$\frac { 1 } { 1 } - \frac { 1 } { 7 } - \frac { 6 } { 21 } = \frac { 7 - 18 } { 7 } = \frac { - 12 } { 7 }$$

Verify

Solution Steps

Divide 1 by 1 to get 1.

$$1-\frac{1}{7}-\frac{6}{21}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{7}{7}-\frac{1}{7}-\frac{6}{21}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Since \frac{7}{7} and \frac{1}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-1}{7}-\frac{6}{21}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Subtract 1 from 7 to get 6.

$$\frac{6}{7}-\frac{6}{21}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

$$\frac{6}{7}-\frac{2}{7}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Since \frac{6}{7} and \frac{2}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-2}{7}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Subtract 2 from 6 to get 4.

$$\frac{4}{7}=\frac{7-18}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Subtract 18 from 7 to get -11.

$$\frac{4}{7}=\frac{-11}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Fraction \frac{-11}{7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$\frac{4}{7}=-\frac{11}{7}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Compare \frac{4}{7} and -\frac{11}{7}.

$$\text{false}\text{ and }\frac{7-18}{7}=\frac{-12}{7}$$

Subtract 18 from 7 to get -11.

$$\text{false}\text{ and }\frac{-11}{7}=\frac{-12}{7}$$

Fraction \frac{-11}{7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$\text{false}\text{ and }-\frac{11}{7}=\frac{-12}{7}$$

Fraction \frac{-12}{7} can be rewritten as -\frac{12}{7} by extracting the negative sign.

$$\text{false}\text{ and }-\frac{11}{7}=-\frac{12}{7}$$

Compare -\frac{11}{7} and -\frac{12}{7}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$