Solve [45/12+(-1/7)]+[(-12/7)+61/12]

$$[ 4 \frac { 5 } { 12 } + ( - \frac { 1 } { 7 } ) ] + [ ( - 1 \frac { 2 } { 7 } ) + 6 \frac { 1 } { 12 } ]$$

Evaluate

$$\frac{127}{14}\approx 9.071428571$$

Solution Steps

Multiply 4 and 12 to get 48.

$$\frac{48+5}{12}-\frac{1}{7}-\frac{1\times 7+2}{7}+\frac{6\times 12+1}{12}$$

Add 48 and 5 to get 53.

$$\frac{53}{12}-\frac{1}{7}-\frac{1\times 7+2}{7}+\frac{6\times 12+1}{12}$$

Least common multiple of 12 and 7 is 84. Convert \frac{53}{12} and \frac{1}{7} to fractions with denominator 84.

$$\frac{371}{84}-\frac{12}{84}-\frac{1\times 7+2}{7}+\frac{6\times 12+1}{12}$$

Since \frac{371}{84} and \frac{12}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{371-12}{84}-\frac{1\times 7+2}{7}+\frac{6\times 12+1}{12}$$

Subtract 12 from 371 to get 359.

$$\frac{359}{84}-\frac{1\times 7+2}{7}+\frac{6\times 12+1}{12}$$

Multiply 1 and 7 to get 7.

$$\frac{359}{84}-\frac{7+2}{7}+\frac{6\times 12+1}{12}$$

Add 7 and 2 to get 9.

$$\frac{359}{84}-\frac{9}{7}+\frac{6\times 12+1}{12}$$

Least common multiple of 84 and 7 is 84. Convert \frac{359}{84} and \frac{9}{7} to fractions with denominator 84.

$$\frac{359}{84}-\frac{108}{84}+\frac{6\times 12+1}{12}$$

Since \frac{359}{84} and \frac{108}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{359-108}{84}+\frac{6\times 12+1}{12}$$

Subtract 108 from 359 to get 251.

$$\frac{251}{84}+\frac{6\times 12+1}{12}$$

Multiply 6 and 12 to get 72.

$$\frac{251}{84}+\frac{72+1}{12}$$

Add 72 and 1 to get 73.

$$\frac{251}{84}+\frac{73}{12}$$

Least common multiple of 84 and 12 is 84. Convert \frac{251}{84} and \frac{73}{12} to fractions with denominator 84.

$$\frac{251}{84}+\frac{511}{84}$$

Since \frac{251}{84} and \frac{511}{84} have the same denominator, add them by adding their numerators.

$$\frac{251+511}{84}$$

Add 251 and 511 to get 762.

$$\frac{762}{84}$$

Reduce the fraction \frac{762}{84} to lowest terms by extracting and canceling out 6.

$$\frac{127}{14}$$

Factor

$$\frac{127}{2 \cdot 7} = 9\frac{1}{14} = 9.071428571428571$$