Solve 1/0.12*0.41^2-1/0.12*0.39^2

$$\frac{ 1 }{ 0.12 } \times { 0.41 }^{ 2 } - \frac{ 1 }{ 0.12 } \times { 0.39 }^{ 2 }$$

Evaluate

$$\frac{2}{15}\approx 0.133333333$$

Solution Steps

Expand \frac{1}{0.12} by multiplying both numerator and the denominator by 100.

$$\frac{100}{12}\times 0.41^{2}-\frac{1}{0.12}\times 0.39^{2}$$

Reduce the fraction \frac{100}{12} to lowest terms by extracting and canceling out 4.

$$\frac{25}{3}\times 0.41^{2}-\frac{1}{0.12}\times 0.39^{2}$$

Calculate 0.41 to the power of 2 and get 0.1681.

$$\frac{25}{3}\times 0.1681-\frac{1}{0.12}\times 0.39^{2}$$

Convert decimal number 0.1681 to fraction \frac{1681}{10000}.

$$\frac{25}{3}\times \frac{1681}{10000}-\frac{1}{0.12}\times 0.39^{2}$$

Multiply \frac{25}{3} times \frac{1681}{10000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 1681}{3\times 10000}-\frac{1}{0.12}\times 0.39^{2}$$

Do the multiplications in the fraction \frac{25\times 1681}{3\times 10000}.

$$\frac{42025}{30000}-\frac{1}{0.12}\times 0.39^{2}$$

Reduce the fraction \frac{42025}{30000} to lowest terms by extracting and canceling out 25.

$$\frac{1681}{1200}-\frac{1}{0.12}\times 0.39^{2}$$

Expand \frac{1}{0.12} by multiplying both numerator and the denominator by 100.

$$\frac{1681}{1200}-\frac{100}{12}\times 0.39^{2}$$

Reduce the fraction \frac{100}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1681}{1200}-\frac{25}{3}\times 0.39^{2}$$

Calculate 0.39 to the power of 2 and get 0.1521.

$$\frac{1681}{1200}-\frac{25}{3}\times 0.1521$$

Convert decimal number 0.1521 to fraction \frac{1521}{10000}.

$$\frac{1681}{1200}-\frac{25}{3}\times \frac{1521}{10000}$$

Multiply \frac{25}{3} times \frac{1521}{10000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1681}{1200}-\frac{25\times 1521}{3\times 10000}$$

Do the multiplications in the fraction \frac{25\times 1521}{3\times 10000}.

$$\frac{1681}{1200}-\frac{38025}{30000}$$

Reduce the fraction \frac{38025}{30000} to lowest terms by extracting and canceling out 75.

$$\frac{1681}{1200}-\frac{507}{400}$$

Least common multiple of 1200 and 400 is 1200. Convert \frac{1681}{1200} and \frac{507}{400} to fractions with denominator 1200.

$$\frac{1681}{1200}-\frac{1521}{1200}$$

Since \frac{1681}{1200} and \frac{1521}{1200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1681-1521}{1200}$$

Subtract 1521 from 1681 to get 160.

$$\frac{160}{1200}$$

Reduce the fraction \frac{160}{1200} to lowest terms by extracting and canceling out 80.

$$\frac{2}{15}$$

Factor

$$\frac{2}{3 \cdot 5} = 0.13333333333333333$$