Solve {4+7*(1/5-2/3)-5}

$$\{ 4 + 7 \times ( \frac { 1 } { 5 } - \frac { 2 } { 3 } ) - 5 \}$$

Evaluate

$$-\frac{64}{15}\approx -4.266666667$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$4+7\left(\frac{3}{15}-\frac{10}{15}\right)-5$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$4+7\times \frac{3-10}{15}-5$$

Subtract 10 from 3 to get -7.

$$4+7\left(-\frac{7}{15}\right)-5$$

Express 7\left(-\frac{7}{15}\right) as a single fraction.

$$4+\frac{7\left(-7\right)}{15}-5$$

Multiply 7 and -7 to get -49.

$$4+\frac{-49}{15}-5$$

Fraction \frac{-49}{15} can be rewritten as -\frac{49}{15} by extracting the negative sign.

$$4-\frac{49}{15}-5$$

Convert 4 to fraction \frac{60}{15}.

$$\frac{60}{15}-\frac{49}{15}-5$$

Since \frac{60}{15} and \frac{49}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{60-49}{15}-5$$

Subtract 49 from 60 to get 11.

$$\frac{11}{15}-5$$

Convert 5 to fraction \frac{75}{15}.

$$\frac{11}{15}-\frac{75}{15}$$

Since \frac{11}{15} and \frac{75}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-75}{15}$$

Subtract 75 from 11 to get -64.

$$-\frac{64}{15}$$

Factor

$$-\frac{64}{15} = -4\frac{4}{15} = -4.266666666666667$$