Solve 21/8+1/6text{of}3/2-12/3

$$2 \frac { 1 } { 8 } + \frac { 1 } { 6 } \text { of } \frac { 3 } { 2 } - 1 \frac { 2 } { 3 }$$

Evaluate

$$\frac{17}{24}\approx 0.708333333$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{16+1}{8}+\frac{1}{6}\times \frac{3}{2}-\frac{1\times 3+2}{3}$$

Add 16 and 1 to get 17.

$$\frac{17}{8}+\frac{1}{6}\times \frac{3}{2}-\frac{1\times 3+2}{3}$$

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17}{8}+\frac{1\times 3}{6\times 2}-\frac{1\times 3+2}{3}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$\frac{17}{8}+\frac{3}{12}-\frac{1\times 3+2}{3}$$

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

$$\frac{17}{8}+\frac{1}{4}-\frac{1\times 3+2}{3}$$

Least common multiple of 8 and 4 is 8. Convert \frac{17}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{17}{8}+\frac{2}{8}-\frac{1\times 3+2}{3}$$

Since \frac{17}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{17+2}{8}-\frac{1\times 3+2}{3}$$

Add 17 and 2 to get 19.

$$\frac{19}{8}-\frac{1\times 3+2}{3}$$

Multiply 1 and 3 to get 3.

$$\frac{19}{8}-\frac{3+2}{3}$$

Add 3 and 2 to get 5.

$$\frac{19}{8}-\frac{5}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{19}{8} and \frac{5}{3} to fractions with denominator 24.

$$\frac{57}{24}-\frac{40}{24}$$

Since \frac{57}{24} and \frac{40}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{57-40}{24}$$

Subtract 40 from 57 to get 17.

$$\frac{17}{24}$$

Factor

$$\frac{17}{2 ^ {3} \cdot 3} = 0.7083333333333334$$