Solve -(-86/7)-(-75/14)+(-64/7)+1-53/14

$$- ( - 8 \frac { 6 } { 7 } ) - ( - 7 \frac { 5 } { 14 } ) + ( - 6 \frac { 4 } { 7 } ) + 1 - 5 \frac { 3 } { 14 }$$

Evaluate

$$\frac{38}{7}\approx 5.428571429$$

Solution Steps

Multiply 8 and 7 to get 56.

$$-\left(-\frac{56+6}{7}\right)-\left(-\frac{7\times 14+5}{14}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 56 and 6 to get 62.

$$-\left(-\frac{62}{7}\right)-\left(-\frac{7\times 14+5}{14}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

The opposite of -\frac{62}{7} is \frac{62}{7}.

$$\frac{62}{7}-\left(-\frac{7\times 14+5}{14}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Multiply 7 and 14 to get 98.

$$\frac{62}{7}-\left(-\frac{98+5}{14}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 98 and 5 to get 103.

$$\frac{62}{7}-\left(-\frac{103}{14}\right)-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

The opposite of -\frac{103}{14} is \frac{103}{14}.

$$\frac{62}{7}+\frac{103}{14}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{62}{7} and \frac{103}{14} to fractions with denominator 14.

$$\frac{124}{14}+\frac{103}{14}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Since \frac{124}{14} and \frac{103}{14} have the same denominator, add them by adding their numerators.

$$\frac{124+103}{14}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 124 and 103 to get 227.

$$\frac{227}{14}-\frac{6\times 7+4}{7}+1-\frac{5\times 14+3}{14}$$

Multiply 6 and 7 to get 42.

$$\frac{227}{14}-\frac{42+4}{7}+1-\frac{5\times 14+3}{14}$$

Add 42 and 4 to get 46.

$$\frac{227}{14}-\frac{46}{7}+1-\frac{5\times 14+3}{14}$$

Least common multiple of 14 and 7 is 14. Convert \frac{227}{14} and \frac{46}{7} to fractions with denominator 14.

$$\frac{227}{14}-\frac{92}{14}+1-\frac{5\times 14+3}{14}$$

Since \frac{227}{14} and \frac{92}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{227-92}{14}+1-\frac{5\times 14+3}{14}$$

Subtract 92 from 227 to get 135.

$$\frac{135}{14}+1-\frac{5\times 14+3}{14}$$

Convert 1 to fraction \frac{14}{14}.

$$\frac{135}{14}+\frac{14}{14}-\frac{5\times 14+3}{14}$$

Since \frac{135}{14} and \frac{14}{14} have the same denominator, add them by adding their numerators.

$$\frac{135+14}{14}-\frac{5\times 14+3}{14}$$

Add 135 and 14 to get 149.

$$\frac{149}{14}-\frac{5\times 14+3}{14}$$

Multiply 5 and 14 to get 70.

$$\frac{149}{14}-\frac{70+3}{14}$$

Add 70 and 3 to get 73.

$$\frac{149}{14}-\frac{73}{14}$$

Since \frac{149}{14} and \frac{73}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{149-73}{14}$$

Subtract 73 from 149 to get 76.

$$\frac{76}{14}$$

Reduce the fraction \frac{76}{14} to lowest terms by extracting and canceling out 2.

$$\frac{38}{7}$$

Factor

$$\frac{2 \cdot 19}{7} = 5\frac{3}{7} = 5.428571428571429$$