Solve (2/5-31/3-1/7)*14/5+frac{1}{40}=

$$( \frac { 2 } { 5 } - 3 \frac { 1 } { 3 } - \frac { 1 } { 7 } ) \cdot 1 \frac { 4 } { 5 } + \frac { 1 } { 40 } =$$

Evaluate

$$-\frac{7717}{1400}\approx -5.512142857$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\left(\frac{2}{5}-\frac{9+1}{3}-\frac{1}{7}\right)\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Add 9 and 1 to get 10.

$$\left(\frac{2}{5}-\frac{10}{3}-\frac{1}{7}\right)\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{10}{3} to fractions with denominator 15.

$$\left(\frac{6}{15}-\frac{50}{15}-\frac{1}{7}\right)\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Since \frac{6}{15} and \frac{50}{15} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{6-50}{15}-\frac{1}{7}\right)\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Subtract 50 from 6 to get -44.

$$\left(-\frac{44}{15}-\frac{1}{7}\right)\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Least common multiple of 15 and 7 is 105. Convert -\frac{44}{15} and \frac{1}{7} to fractions with denominator 105.

$$\left(-\frac{308}{105}-\frac{15}{105}\right)\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Since -\frac{308}{105} and \frac{15}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-308-15}{105}\times \frac{1\times 5+4}{5}+\frac{1}{40}$$

Subtract 15 from -308 to get -323.

$$-\frac{323}{105}\times \frac{5+4}{5}+\frac{1}{40}$$

Add 5 and 4 to get 9.

$$-\frac{323}{105}\times \frac{9}{5}+\frac{1}{40}$$

Multiply -\frac{323}{105} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-323\times 9}{105\times 5}+\frac{1}{40}$$

Do the multiplications in the fraction \frac{-323\times 9}{105\times 5}.

$$\frac{-2907}{525}+\frac{1}{40}$$

Reduce the fraction \frac{-2907}{525} to lowest terms by extracting and canceling out 3.

$$-\frac{969}{175}+\frac{1}{40}$$

Least common multiple of 175 and 40 is 1400. Convert -\frac{969}{175} and \frac{1}{40} to fractions with denominator 1400.

$$-\frac{7752}{1400}+\frac{35}{1400}$$

Since -\frac{7752}{1400} and \frac{35}{1400} have the same denominator, add them by adding their numerators.

$$\frac{-7752+35}{1400}$$

Add -7752 and 35 to get -7717.

$$-\frac{7717}{1400}$$

Factor

$$-\frac{7717}{1400} = -5\frac{717}{1400} = -5.512142857142857$$