Solve 51/2:8/9-21/6

$$5 \frac { 1 } { 2 } : \frac { 8 } { 9 } - 2 \frac { 1 } { 6 }$$

Evaluate

$$\frac{193}{48}\approx 4.020833333$$

Solution Steps

Divide \frac{5\times 2+1}{2} by \frac{8}{9} by multiplying \frac{5\times 2+1}{2} by the reciprocal of \frac{8}{9}.

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

Multiply 5 and 2 to get 10.

$$\frac{\left(10+1\right)\times 9}{2\times 8}-\frac{2\times 6+1}{6}$$

Add 10 and 1 to get 11.

$$\frac{11\times 9}{2\times 8}-\frac{2\times 6+1}{6}$$

Multiply 11 and 9 to get 99.

$$\frac{99}{2\times 8}-\frac{2\times 6+1}{6}$$

Multiply 2 and 8 to get 16.

$$\frac{99}{16}-\frac{2\times 6+1}{6}$$

Multiply 2 and 6 to get 12.

$$\frac{99}{16}-\frac{12+1}{6}$$

Add 12 and 1 to get 13.

$$\frac{99}{16}-\frac{13}{6}$$

Least common multiple of 16 and 6 is 48. Convert \frac{99}{16} and \frac{13}{6} to fractions with denominator 48.

$$\frac{297}{48}-\frac{104}{48}$$

Since \frac{297}{48} and \frac{104}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{297-104}{48}$$

Subtract 104 from 297 to get 193.

$$\frac{193}{48}$$

Factor

$$\frac{193}{2 ^ {4} \cdot 3} = 4\frac{1}{48} = 4.020833333333333$$