Solve (1+5/42)+(-3/21)+(+4/28)+(-2/63)=

$$( 1 + \frac { 5 } { 42 } ) + ( - \frac { 3 } { 21 } ) + ( + \frac { 4 } { 28 } ) + ( - \frac { 2 } { 63 } ) =$$

Evaluate

$$\frac{137}{126}\approx 1.087301587$$

Solution Steps

Convert 1 to fraction \frac{42}{42}.

$$\frac{42}{42}+\frac{5}{42}-\frac{3}{21}+\frac{4}{28}-\frac{2}{63}$$

Since \frac{42}{42} and \frac{5}{42} have the same denominator, add them by adding their numerators.

$$\frac{42+5}{42}-\frac{3}{21}+\frac{4}{28}-\frac{2}{63}$$

Add 42 and 5 to get 47.

$$\frac{47}{42}-\frac{3}{21}+\frac{4}{28}-\frac{2}{63}$$

Reduce the fraction \frac{3}{21} to lowest terms by extracting and canceling out 3.

$$\frac{47}{42}-\frac{1}{7}+\frac{4}{28}-\frac{2}{63}$$

Least common multiple of 42 and 7 is 42. Convert \frac{47}{42} and \frac{1}{7} to fractions with denominator 42.

$$\frac{47}{42}-\frac{6}{42}+\frac{4}{28}-\frac{2}{63}$$

Since \frac{47}{42} and \frac{6}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{47-6}{42}+\frac{4}{28}-\frac{2}{63}$$

Subtract 6 from 47 to get 41.

$$\frac{41}{42}+\frac{4}{28}-\frac{2}{63}$$

Reduce the fraction \frac{4}{28} to lowest terms by extracting and canceling out 4.

$$\frac{41}{42}+\frac{1}{7}-\frac{2}{63}$$

Least common multiple of 42 and 7 is 42. Convert \frac{41}{42} and \frac{1}{7} to fractions with denominator 42.

$$\frac{41}{42}+\frac{6}{42}-\frac{2}{63}$$

Since \frac{41}{42} and \frac{6}{42} have the same denominator, add them by adding their numerators.

$$\frac{41+6}{42}-\frac{2}{63}$$

Add 41 and 6 to get 47.

$$\frac{47}{42}-\frac{2}{63}$$

Least common multiple of 42 and 63 is 126. Convert \frac{47}{42} and \frac{2}{63} to fractions with denominator 126.

$$\frac{141}{126}-\frac{4}{126}$$

Since \frac{141}{126} and \frac{4}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{141-4}{126}$$

Subtract 4 from 141 to get 137.

$$\frac{137}{126}$$

Factor

$$\frac{137}{2 \cdot 3 ^ {2} \cdot 7} = 1\frac{11}{126} = 1.0873015873015872$$