Solve 41/8-62/9+(-31/6)-(-53/4)

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

Evaluate

$$\frac{35}{72}\approx 0.486111111$$

Solution Steps

Multiply 4 and 8 to get 32.

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

Add 32 and 1 to get 33.

$$\frac{33}{8}-\frac{6\times 9+2}{9}-\frac{3\times 6+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Multiply 6 and 9 to get 54.

$$\frac{33}{8}-\frac{54+2}{9}-\frac{3\times 6+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Add 54 and 2 to get 56.

$$\frac{33}{8}-\frac{56}{9}-\frac{3\times 6+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Least common multiple of 8 and 9 is 72. Convert \frac{33}{8} and \frac{56}{9} to fractions with denominator 72.

$$\frac{297}{72}-\frac{448}{72}-\frac{3\times 6+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Since \frac{297}{72} and \frac{448}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{297-448}{72}-\frac{3\times 6+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Subtract 448 from 297 to get -151.

$$-\frac{151}{72}-\frac{3\times 6+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Multiply 3 and 6 to get 18.

$$-\frac{151}{72}-\frac{18+1}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Add 18 and 1 to get 19.

$$-\frac{151}{72}-\frac{19}{6}-\left(-\frac{5\times 4+3}{4}\right)$$

Least common multiple of 72 and 6 is 72. Convert -\frac{151}{72} and \frac{19}{6} to fractions with denominator 72.

$$-\frac{151}{72}-\frac{228}{72}-\left(-\frac{5\times 4+3}{4}\right)$$

Since -\frac{151}{72} and \frac{228}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-151-228}{72}-\left(-\frac{5\times 4+3}{4}\right)$$

Subtract 228 from -151 to get -379.

$$-\frac{379}{72}-\left(-\frac{5\times 4+3}{4}\right)$$

Multiply 5 and 4 to get 20.

$$-\frac{379}{72}-\left(-\frac{20+3}{4}\right)$$

Add 20 and 3 to get 23.

$$-\frac{379}{72}-\left(-\frac{23}{4}\right)$$

The opposite of -\frac{23}{4} is \frac{23}{4}.

$$-\frac{379}{72}+\frac{23}{4}$$

Least common multiple of 72 and 4 is 72. Convert -\frac{379}{72} and \frac{23}{4} to fractions with denominator 72.

$$-\frac{379}{72}+\frac{414}{72}$$

Since -\frac{379}{72} and \frac{414}{72} have the same denominator, add them by adding their numerators.

$$\frac{-379+414}{72}$$

Add -379 and 414 to get 35.

$$\frac{35}{72}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {3} \cdot 3 ^ {2}} = 0.4861111111111111$$