Solve 4/3-(1/2+1/4)-(1/8+frac{1}{16})

$$\frac { 4 } { 3 } - ( \frac { 1 } { 2 } + \frac { 1 } { 4 } ) - ( \frac { 1 } { 8 } + \frac { 1 } { 16 } )$$

Evaluate

$$\frac{19}{48}\approx 0.395833333$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{4}{3}-\left(\frac{2}{4}+\frac{1}{4}\right)-\left(\frac{1}{8}+\frac{1}{16}\right)$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}-\frac{2+1}{4}-\left(\frac{1}{8}+\frac{1}{16}\right)$$

Add 2 and 1 to get 3.

$$\frac{4}{3}-\frac{3}{4}-\left(\frac{1}{8}+\frac{1}{16}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{16}{12}-\frac{9}{12}-\left(\frac{1}{8}+\frac{1}{16}\right)$$

Since \frac{16}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-9}{12}-\left(\frac{1}{8}+\frac{1}{16}\right)$$

Subtract 9 from 16 to get 7.

$$\frac{7}{12}-\left(\frac{1}{8}+\frac{1}{16}\right)$$

Least common multiple of 8 and 16 is 16. Convert \frac{1}{8} and \frac{1}{16} to fractions with denominator 16.

$$\frac{7}{12}-\left(\frac{2}{16}+\frac{1}{16}\right)$$

Since \frac{2}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}-\frac{2+1}{16}$$

Add 2 and 1 to get 3.

$$\frac{7}{12}-\frac{3}{16}$$

Least common multiple of 12 and 16 is 48. Convert \frac{7}{12} and \frac{3}{16} to fractions with denominator 48.

$$\frac{28}{48}-\frac{9}{48}$$

Since \frac{28}{48} and \frac{9}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-9}{48}$$

Subtract 9 from 28 to get 19.

$$\frac{19}{48}$$

Factor

$$\frac{19}{2 ^ {4} \cdot 3} = 0.3958333333333333$$