Solve 14*(-1/2)^2-43*(1/7)^2

$$14 \times ( - \frac { 1 } { 2 } ) ^ { 2 } - 43 \times ( \frac { 1 } { 7 } ) ^ { 2 }$$

Evaluate

$$\frac{257}{98}\approx 2.62244898$$

Solution Steps

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

$$14\times \frac{1}{4}-43\times \left(\frac{1}{7}\right)^{2}$$

Multiply 14 and \frac{1}{4} to get \frac{14}{4}.

$$\frac{14}{4}-43\times \left(\frac{1}{7}\right)^{2}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}-43\times \left(\frac{1}{7}\right)^{2}$$

Calculate \frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$\frac{7}{2}-43\times \frac{1}{49}$$

Multiply 43 and \frac{1}{49} to get \frac{43}{49}.

$$\frac{7}{2}-\frac{43}{49}$$

Least common multiple of 2 and 49 is 98. Convert \frac{7}{2} and \frac{43}{49} to fractions with denominator 98.

$$\frac{343}{98}-\frac{86}{98}$$

Since \frac{343}{98} and \frac{86}{98} have the same denominator, subtract them by subtracting their numerators.

$$\frac{343-86}{98}$$

Subtract 86 from 343 to get 257.

$$\frac{257}{98}$$

Factor

$$\frac{257}{2 \cdot 7 ^ {2}} = 2\frac{61}{98} = 2.622448979591837$$