Solve 1/32+1/16+1/8+1/42

$$\frac { 1 } { 32 } + \frac { 1 } { 16 } + \frac { 1 } { 8 } + \frac { 1 } { 42 }$$

Evaluate

$$\frac{163}{672}\approx 0.242559524$$

Solution Steps

Least common multiple of 32 and 16 is 32. Convert \frac{1}{32} and \frac{1}{16} to fractions with denominator 32.

$$\frac{1}{32}+\frac{2}{32}+\frac{1}{8}+\frac{1}{42}$$

Since \frac{1}{32} and \frac{2}{32} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{32}+\frac{1}{8}+\frac{1}{42}$$

Add 1 and 2 to get 3.

$$\frac{3}{32}+\frac{1}{8}+\frac{1}{42}$$

Least common multiple of 32 and 8 is 32. Convert \frac{3}{32} and \frac{1}{8} to fractions with denominator 32.

$$\frac{3}{32}+\frac{4}{32}+\frac{1}{42}$$

Since \frac{3}{32} and \frac{4}{32} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{32}+\frac{1}{42}$$

Add 3 and 4 to get 7.

$$\frac{7}{32}+\frac{1}{42}$$

Least common multiple of 32 and 42 is 672. Convert \frac{7}{32} and \frac{1}{42} to fractions with denominator 672.

$$\frac{147}{672}+\frac{16}{672}$$

Since \frac{147}{672} and \frac{16}{672} have the same denominator, add them by adding their numerators.

$$\frac{147+16}{672}$$

Add 147 and 16 to get 163.

$$\frac{163}{672}$$

Factor

$$\frac{163}{2 ^ {5} \cdot 3 \cdot 7} = 0.2425595238095238$$