Solve (13/5-7/5)-(3/4+1/7)

$$( \frac { 13 } { 5 } - \frac { 7 } { 5 } ) - ( \frac { 3 } { 4 } + \frac { 1 } { 7 } )$$

Evaluate

$$\frac{43}{140}\approx 0.307142857$$

Solution Steps

Since \frac{13}{5} and \frac{7}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-7}{5}-\left(\frac{3}{4}+\frac{1}{7}\right)$$

Subtract 7 from 13 to get 6.

$$\frac{6}{5}-\left(\frac{3}{4}+\frac{1}{7}\right)$$

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{1}{7} to fractions with denominator 28.

$$\frac{6}{5}-\left(\frac{21}{28}+\frac{4}{28}\right)$$

Since \frac{21}{28} and \frac{4}{28} have the same denominator, add them by adding their numerators.

$$\frac{6}{5}-\frac{21+4}{28}$$

Add 21 and 4 to get 25.

$$\frac{6}{5}-\frac{25}{28}$$

Least common multiple of 5 and 28 is 140. Convert \frac{6}{5} and \frac{25}{28} to fractions with denominator 140.

$$\frac{168}{140}-\frac{125}{140}$$

Since \frac{168}{140} and \frac{125}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{168-125}{140}$$

Subtract 125 from 168 to get 43.

$$\frac{43}{140}$$

Factor

$$\frac{43}{2 ^ {2} \cdot 5 \cdot 7} = 0.30714285714285716$$