Solve 1-1/21+1/2*1/2^2

$$1 - \frac { 1 } { 21 } + \frac { 1 } { 2 } \times \frac { 1 } { 2 ^ { 2 } }$$

Evaluate

$$\frac{181}{168}\approx 1.077380952$$

Solution Steps

Convert 1 to fraction \frac{21}{21}.

$$\frac{21}{21}-\frac{1}{21}+\frac{1}{2}\times \frac{1}{2^{2}}$$

Since \frac{21}{21} and \frac{1}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-1}{21}+\frac{1}{2}\times \frac{1}{2^{2}}$$

Subtract 1 from 21 to get 20.

$$\frac{20}{21}+\frac{1}{2}\times \frac{1}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{20}{21}+\frac{1}{2}\times \frac{1}{4}$$

Multiply \frac{1}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20}{21}+\frac{1\times 1}{2\times 4}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 4}.

$$\frac{20}{21}+\frac{1}{8}$$

Least common multiple of 21 and 8 is 168. Convert \frac{20}{21} and \frac{1}{8} to fractions with denominator 168.

$$\frac{160}{168}+\frac{21}{168}$$

Since \frac{160}{168} and \frac{21}{168} have the same denominator, add them by adding their numerators.

$$\frac{160+21}{168}$$

Add 160 and 21 to get 181.

$$\frac{181}{168}$$

Factor

$$\frac{181}{2 ^ {3} \cdot 3 \cdot 7} = 1\frac{13}{168} = 1.0773809523809523$$