Solve 7/13+2/3-(1/2)^2

$$\frac { 7 } { 13 } + \frac { 2 } { 3 } - ( \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{149}{156}\approx 0.955128205$$

Solution Steps

Least common multiple of 13 and 3 is 39. Convert \frac{7}{13} and \frac{2}{3} to fractions with denominator 39.

$$\frac{21}{39}+\frac{26}{39}-\left(\frac{1}{2}\right)^{2}$$

Since \frac{21}{39} and \frac{26}{39} have the same denominator, add them by adding their numerators.

$$\frac{21+26}{39}-\left(\frac{1}{2}\right)^{2}$$

Add 21 and 26 to get 47.

$$\frac{47}{39}-\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{47}{39}-\frac{1}{4}$$

Least common multiple of 39 and 4 is 156. Convert \frac{47}{39} and \frac{1}{4} to fractions with denominator 156.

$$\frac{188}{156}-\frac{39}{156}$$

Since \frac{188}{156} and \frac{39}{156} have the same denominator, subtract them by subtracting their numerators.

$$\frac{188-39}{156}$$

Subtract 39 from 188 to get 149.

$$\frac{149}{156}$$

Factor

$$\frac{149}{2 ^ {2} \cdot 3 \cdot 13} = 0.9551282051282052$$