Solve 42/3-63/7-(-12/9)+5frac{10/21}{5}

$$\frac { 4 \frac { 2 } { 3 } - 6 \frac { 3 } { 7 } - ( - 1 \frac { 2 } { 9 } ) + 5 \frac { 10 } { 21 } } { 5 }$$

Evaluate

$$\frac{311}{315}\approx 0.987301587$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\frac{\frac{12+2}{3}-\frac{6\times 7+3}{7}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Add 12 and 2 to get 14.

$$\frac{\frac{14}{3}-\frac{6\times 7+3}{7}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Multiply 6 and 7 to get 42.

$$\frac{\frac{14}{3}-\frac{42+3}{7}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Add 42 and 3 to get 45.

$$\frac{\frac{14}{3}-\frac{45}{7}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Least common multiple of 3 and 7 is 21. Convert \frac{14}{3} and \frac{45}{7} to fractions with denominator 21.

$$\frac{\frac{98}{21}-\frac{135}{21}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Since \frac{98}{21} and \frac{135}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{98-135}{21}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Subtract 135 from 98 to get -37.

$$\frac{-\frac{37}{21}-\left(-\frac{1\times 9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Multiply 1 and 9 to get 9.

$$\frac{-\frac{37}{21}-\left(-\frac{9+2}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

Add 9 and 2 to get 11.

$$\frac{-\frac{37}{21}-\left(-\frac{11}{9}\right)+\frac{5\times 21+10}{21}}{5}$$

The opposite of -\frac{11}{9} is \frac{11}{9}.

$$\frac{-\frac{37}{21}+\frac{11}{9}+\frac{5\times 21+10}{21}}{5}$$

Least common multiple of 21 and 9 is 63. Convert -\frac{37}{21} and \frac{11}{9} to fractions with denominator 63.

$$\frac{-\frac{111}{63}+\frac{77}{63}+\frac{5\times 21+10}{21}}{5}$$

Since -\frac{111}{63} and \frac{77}{63} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-111+77}{63}+\frac{5\times 21+10}{21}}{5}$$

Add -111 and 77 to get -34.

$$\frac{-\frac{34}{63}+\frac{5\times 21+10}{21}}{5}$$

Multiply 5 and 21 to get 105.

$$\frac{-\frac{34}{63}+\frac{105+10}{21}}{5}$$

Add 105 and 10 to get 115.

$$\frac{-\frac{34}{63}+\frac{115}{21}}{5}$$

Least common multiple of 63 and 21 is 63. Convert -\frac{34}{63} and \frac{115}{21} to fractions with denominator 63.

$$\frac{-\frac{34}{63}+\frac{345}{63}}{5}$$

Since -\frac{34}{63} and \frac{345}{63} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-34+345}{63}}{5}$$

Add -34 and 345 to get 311.

$$\frac{\frac{311}{63}}{5}$$

Express \frac{\frac{311}{63}}{5} as a single fraction.

$$\frac{311}{63\times 5}$$

Multiply 63 and 5 to get 315.

$$\frac{311}{315}$$

Factor

$$\frac{311}{3 ^ {2} \cdot 5 \cdot 7} = 0.9873015873015873$$