Solve 0.4^2*2/0.0864-0.35^2*2/0.0864

$${ 0.4 }^{ 2 } \times \frac{ 2 }{ 0.0864 } - { 0.35 }^{ 2 } \times \frac{ 2 }{ 0.0864 }$$

Evaluate

$$\frac{125}{144}\approx 0.868055556$$

Solution Steps

Calculate 0.4 to the power of 2 and get 0.16.

$$0.16\times \frac{2}{0.0864}-0.35^{2}\times \frac{2}{0.0864}$$

Expand \frac{2}{0.0864} by multiplying both numerator and the denominator by 10000.

$$0.16\times \frac{20000}{864}-0.35^{2}\times \frac{2}{0.0864}$$

Reduce the fraction \frac{20000}{864} to lowest terms by extracting and canceling out 32.

$$0.16\times \frac{625}{27}-0.35^{2}\times \frac{2}{0.0864}$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{4}{25}\times \frac{625}{27}-0.35^{2}\times \frac{2}{0.0864}$$

Multiply \frac{4}{25} times \frac{625}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 625}{25\times 27}-0.35^{2}\times \frac{2}{0.0864}$$

Do the multiplications in the fraction \frac{4\times 625}{25\times 27}.

$$\frac{2500}{675}-0.35^{2}\times \frac{2}{0.0864}$$

Reduce the fraction \frac{2500}{675} to lowest terms by extracting and canceling out 25.

$$\frac{100}{27}-0.35^{2}\times \frac{2}{0.0864}$$

Calculate 0.35 to the power of 2 and get 0.1225.

$$\frac{100}{27}-0.1225\times \frac{2}{0.0864}$$

Expand \frac{2}{0.0864} by multiplying both numerator and the denominator by 10000.

$$\frac{100}{27}-0.1225\times \frac{20000}{864}$$

Reduce the fraction \frac{20000}{864} to lowest terms by extracting and canceling out 32.

$$\frac{100}{27}-0.1225\times \frac{625}{27}$$

Convert decimal number 0.1225 to fraction \frac{1225}{10000}. Reduce the fraction \frac{1225}{10000} to lowest terms by extracting and canceling out 25.

$$\frac{100}{27}-\frac{49}{400}\times \frac{625}{27}$$

Multiply \frac{49}{400} times \frac{625}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{100}{27}-\frac{49\times 625}{400\times 27}$$

Do the multiplications in the fraction \frac{49\times 625}{400\times 27}.

$$\frac{100}{27}-\frac{30625}{10800}$$

Reduce the fraction \frac{30625}{10800} to lowest terms by extracting and canceling out 25.

$$\frac{100}{27}-\frac{1225}{432}$$

Least common multiple of 27 and 432 is 432. Convert \frac{100}{27} and \frac{1225}{432} to fractions with denominator 432.

$$\frac{1600}{432}-\frac{1225}{432}$$

Since \frac{1600}{432} and \frac{1225}{432} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1600-1225}{432}$$

Subtract 1225 from 1600 to get 375.

$$\frac{375}{432}$$

Reduce the fraction \frac{375}{432} to lowest terms by extracting and canceling out 3.

$$\frac{125}{144}$$

Factor

$$\frac{5 ^ {3}}{2 ^ {4} \cdot 3 ^ {2}} = 0.8680555555555556$$