Solve (55/6+63/4)+(102/3-55/8)

$$( 5 \frac { 5 } { 6 } + 6 \frac { 3 } { 4 } ) + ( 10 \frac { 2 } { 3 } - 5 \frac { 5 } { 8 } )$$

Evaluate

$$\frac{141}{8}=17.625$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{30+5}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Add 30 and 5 to get 35.

$$\frac{35}{6}+\frac{6\times 4+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Multiply 6 and 4 to get 24.

$$\frac{35}{6}+\frac{24+3}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Add 24 and 3 to get 27.

$$\frac{35}{6}+\frac{27}{4}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Least common multiple of 6 and 4 is 12. Convert \frac{35}{6} and \frac{27}{4} to fractions with denominator 12.

$$\frac{70}{12}+\frac{81}{12}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Since \frac{70}{12} and \frac{81}{12} have the same denominator, add them by adding their numerators.

$$\frac{70+81}{12}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Add 70 and 81 to get 151.

$$\frac{151}{12}+\frac{10\times 3+2}{3}-\frac{5\times 8+5}{8}$$

Multiply 10 and 3 to get 30.

$$\frac{151}{12}+\frac{30+2}{3}-\frac{5\times 8+5}{8}$$

Add 30 and 2 to get 32.

$$\frac{151}{12}+\frac{32}{3}-\frac{5\times 8+5}{8}$$

Least common multiple of 12 and 3 is 12. Convert \frac{151}{12} and \frac{32}{3} to fractions with denominator 12.

$$\frac{151}{12}+\frac{128}{12}-\frac{5\times 8+5}{8}$$

Since \frac{151}{12} and \frac{128}{12} have the same denominator, add them by adding their numerators.

$$\frac{151+128}{12}-\frac{5\times 8+5}{8}$$

Add 151 and 128 to get 279.

$$\frac{279}{12}-\frac{5\times 8+5}{8}$$

Reduce the fraction \frac{279}{12} to lowest terms by extracting and canceling out 3.

$$\frac{93}{4}-\frac{5\times 8+5}{8}$$

Multiply 5 and 8 to get 40.

$$\frac{93}{4}-\frac{40+5}{8}$$

Add 40 and 5 to get 45.

$$\frac{93}{4}-\frac{45}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{93}{4} and \frac{45}{8} to fractions with denominator 8.

$$\frac{186}{8}-\frac{45}{8}$$

Since \frac{186}{8} and \frac{45}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{186-45}{8}$$

Subtract 45 from 186 to get 141.

$$\frac{141}{8}$$

Factor

$$\frac{3 \cdot 47}{2 ^ {3}} = 17\frac{5}{8} = 17.625$$