Solve 45/8-62/9+(-51/6)-(-33/4)

$$4 \frac { 5 } { 8 } - 6 \frac { 2 } { 9 } + ( - 5 \frac { 1 } { 6 } ) - ( - 3 \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{217}{72}\approx -3.013888889$$

Solution Steps

Multiply 4 and 8 to get 32.

$$\frac{32+5}{8}-\frac{6\times 9+2}{9}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Add 32 and 5 to get 37.

$$\frac{37}{8}-\frac{6\times 9+2}{9}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Multiply 6 and 9 to get 54.

$$\frac{37}{8}-\frac{54+2}{9}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Add 54 and 2 to get 56.

$$\frac{37}{8}-\frac{56}{9}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Least common multiple of 8 and 9 is 72. Convert \frac{37}{8} and \frac{56}{9} to fractions with denominator 72.

$$\frac{333}{72}-\frac{448}{72}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Since \frac{333}{72} and \frac{448}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{333-448}{72}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Subtract 448 from 333 to get -115.

$$-\frac{115}{72}-\frac{5\times 6+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Multiply 5 and 6 to get 30.

$$-\frac{115}{72}-\frac{30+1}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Add 30 and 1 to get 31.

$$-\frac{115}{72}-\frac{31}{6}-\left(-\frac{3\times 4+3}{4}\right)$$

Least common multiple of 72 and 6 is 72. Convert -\frac{115}{72} and \frac{31}{6} to fractions with denominator 72.

$$-\frac{115}{72}-\frac{372}{72}-\left(-\frac{3\times 4+3}{4}\right)$$

Since -\frac{115}{72} and \frac{372}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-115-372}{72}-\left(-\frac{3\times 4+3}{4}\right)$$

Subtract 372 from -115 to get -487.

$$-\frac{487}{72}-\left(-\frac{3\times 4+3}{4}\right)$$

Multiply 3 and 4 to get 12.

$$-\frac{487}{72}-\left(-\frac{12+3}{4}\right)$$

Add 12 and 3 to get 15.

$$-\frac{487}{72}-\left(-\frac{15}{4}\right)$$

The opposite of -\frac{15}{4} is \frac{15}{4}.

$$-\frac{487}{72}+\frac{15}{4}$$

Least common multiple of 72 and 4 is 72. Convert -\frac{487}{72} and \frac{15}{4} to fractions with denominator 72.

$$-\frac{487}{72}+\frac{270}{72}$$

Since -\frac{487}{72} and \frac{270}{72} have the same denominator, add them by adding their numerators.

$$\frac{-487+270}{72}$$

Add -487 and 270 to get -217.

$$-\frac{217}{72}$$

Factor

$$-\frac{217}{72} = -3\frac{1}{72} = -3.013888888888889$$