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

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

Evaluate

$$\frac{1}{7}\approx 0.142857143$$

Solution Steps

Multiply 8 and 7 to get 56.

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

Add 56 and 6 to get 62.

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

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

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

Multiply 7 and 14 to get 98.

$$\frac{62}{7}-|-\frac{98+5}{14}|-\frac{6\times 7+4}{7}+|-\frac{5\times 14+3}{14}|$$

Add 98 and 5 to get 103.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{103}{14} is \frac{103}{14}.

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

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

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

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

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

Subtract 103 from 124 to get 21.

$$\frac{21}{14}-\frac{6\times 7+4}{7}+|-\frac{5\times 14+3}{14}|$$

Reduce the fraction \frac{21}{14} to lowest terms by extracting and canceling out 7.

$$\frac{3}{2}-\frac{6\times 7+4}{7}+|-\frac{5\times 14+3}{14}|$$

Multiply 6 and 7 to get 42.

$$\frac{3}{2}-\frac{42+4}{7}+|-\frac{5\times 14+3}{14}|$$

Add 42 and 4 to get 46.

$$\frac{3}{2}-\frac{46}{7}+|-\frac{5\times 14+3}{14}|$$

Least common multiple of 2 and 7 is 14. Convert \frac{3}{2} and \frac{46}{7} to fractions with denominator 14.

$$\frac{21}{14}-\frac{92}{14}+|-\frac{5\times 14+3}{14}|$$

Since \frac{21}{14} and \frac{92}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-92}{14}+|-\frac{5\times 14+3}{14}|$$

Subtract 92 from 21 to get -71.

$$-\frac{71}{14}+|-\frac{5\times 14+3}{14}|$$

Multiply 5 and 14 to get 70.

$$-\frac{71}{14}+|-\frac{70+3}{14}|$$

Add 70 and 3 to get 73.

$$-\frac{71}{14}+|-\frac{73}{14}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{73}{14} is \frac{73}{14}.

$$-\frac{71}{14}+\frac{73}{14}$$

Since -\frac{71}{14} and \frac{73}{14} have the same denominator, add them by adding their numerators.

$$\frac{-71+73}{14}$$

Add -71 and 73 to get 2.

$$\frac{2}{14}$$

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

$$\frac{1}{7}$$

Factor

$$\frac{1}{7} = 0.14285714285714285$$