Solve 7*21/5+1/2-1/3-1/6

$$7 \cdot 2 \frac { 1 } { 5 } + \frac { 1 } { 2 } - \frac { 1 } { 3 } - \frac { 1 } { 6 }$$

Evaluate

$$\frac{77}{5}=15.4$$

Solution Steps

Multiply 2 and 5 to get 10.

$$7\times \frac{10+1}{5}+\frac{1}{2}-\frac{1}{3}-\frac{1}{6}$$

Add 10 and 1 to get 11.

$$7\times \frac{11}{5}+\frac{1}{2}-\frac{1}{3}-\frac{1}{6}$$

Express 7\times \frac{11}{5} as a single fraction.

$$\frac{7\times 11}{5}+\frac{1}{2}-\frac{1}{3}-\frac{1}{6}$$

Multiply 7 and 11 to get 77.

$$\frac{77}{5}+\frac{1}{2}-\frac{1}{3}-\frac{1}{6}$$

Least common multiple of 5 and 2 is 10. Convert \frac{77}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{154}{10}+\frac{5}{10}-\frac{1}{3}-\frac{1}{6}$$

Since \frac{154}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{154+5}{10}-\frac{1}{3}-\frac{1}{6}$$

Add 154 and 5 to get 159.

$$\frac{159}{10}-\frac{1}{3}-\frac{1}{6}$$

Least common multiple of 10 and 3 is 30. Convert \frac{159}{10} and \frac{1}{3} to fractions with denominator 30.

$$\frac{477}{30}-\frac{10}{30}-\frac{1}{6}$$

Since \frac{477}{30} and \frac{10}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{477-10}{30}-\frac{1}{6}$$

Subtract 10 from 477 to get 467.

$$\frac{467}{30}-\frac{1}{6}$$

Least common multiple of 30 and 6 is 30. Convert \frac{467}{30} and \frac{1}{6} to fractions with denominator 30.

$$\frac{467}{30}-\frac{5}{30}$$

Since \frac{467}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{467-5}{30}$$

Subtract 5 from 467 to get 462.

$$\frac{462}{30}$$

Reduce the fraction \frac{462}{30} to lowest terms by extracting and canceling out 6.

$$\frac{77}{5}$$

Factor

$$\frac{7 \cdot 11}{5} = 15\frac{2}{5} = 15.4$$