Solve 152/5-(24/7+63/4)

$$15 \frac{ 2 }{ 5 } -(2 \frac{ 4 }{ 7 } +6 \frac{ 3 }{ 4 } )$$

Evaluate

$$\frac{851}{140}\approx 6.078571429$$

Solution Steps

Multiply 15 and 5 to get 75.

$$\frac{75+2}{5}-\left(\frac{2\times 7+4}{7}+\frac{6\times 4+3}{4}\right)$$

Add 75 and 2 to get 77.

$$\frac{77}{5}-\left(\frac{2\times 7+4}{7}+\frac{6\times 4+3}{4}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{77}{5}-\left(\frac{14+4}{7}+\frac{6\times 4+3}{4}\right)$$

Add 14 and 4 to get 18.

$$\frac{77}{5}-\left(\frac{18}{7}+\frac{6\times 4+3}{4}\right)$$

Multiply 6 and 4 to get 24.

$$\frac{77}{5}-\left(\frac{18}{7}+\frac{24+3}{4}\right)$$

Add 24 and 3 to get 27.

$$\frac{77}{5}-\left(\frac{18}{7}+\frac{27}{4}\right)$$

Least common multiple of 7 and 4 is 28. Convert \frac{18}{7} and \frac{27}{4} to fractions with denominator 28.

$$\frac{77}{5}-\left(\frac{72}{28}+\frac{189}{28}\right)$$

Since \frac{72}{28} and \frac{189}{28} have the same denominator, add them by adding their numerators.

$$\frac{77}{5}-\frac{72+189}{28}$$

Add 72 and 189 to get 261.

$$\frac{77}{5}-\frac{261}{28}$$

Least common multiple of 5 and 28 is 140. Convert \frac{77}{5} and \frac{261}{28} to fractions with denominator 140.

$$\frac{2156}{140}-\frac{1305}{140}$$

Since \frac{2156}{140} and \frac{1305}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2156-1305}{140}$$

Subtract 1305 from 2156 to get 851.

$$\frac{851}{140}$$

Factor

$$\frac{23 \cdot 37}{2 ^ {2} \cdot 5 \cdot 7} = 6\frac{11}{140} = 6.078571428571428$$