Solve 1/8x3.14x100-1/4*3.14*25-1/2*5*5

$$\frac { 1 } { 8 } x 3.14 x 100 - \frac { 1 } { 4 } \times 3.14 \times 25 - \frac { 1 } { 2 } \times 5 \times 5$$

Evaluate

$$\frac{7x_{3}x_{100}}{400}-32.125$$

Solution Steps

Convert decimal number 0.14 to fraction \frac{14}{100}. Reduce the fraction \frac{14}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{8}x_{3}\times \frac{7}{50}x_{100}-\frac{1}{4}\times 3.14\times 25-\frac{1}{2}\times 5\times 5$$

Multiply \frac{1}{8} times \frac{7}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{8\times 50}x_{3}x_{100}-\frac{1}{4}\times 3.14\times 25-\frac{1}{2}\times 5\times 5$$

Do the multiplications in the fraction \frac{1\times 7}{8\times 50}.

$$\frac{7}{400}x_{3}x_{100}-\frac{1}{4}\times 3.14\times 25-\frac{1}{2}\times 5\times 5$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\frac{7}{400}x_{3}x_{100}-\frac{1}{4}\times \frac{157}{50}\times 25-\frac{1}{2}\times 5\times 5$$

Multiply \frac{1}{4} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{400}x_{3}x_{100}-\frac{1\times 157}{4\times 50}\times 25-\frac{1}{2}\times 5\times 5$$

Do the multiplications in the fraction \frac{1\times 157}{4\times 50}.

$$\frac{7}{400}x_{3}x_{100}-\frac{157}{200}\times 25-\frac{1}{2}\times 5\times 5$$

Express \frac{157}{200}\times 25 as a single fraction.

$$\frac{7}{400}x_{3}x_{100}-\frac{157\times 25}{200}-\frac{1}{2}\times 5\times 5$$

Multiply 157 and 25 to get 3925.

$$\frac{7}{400}x_{3}x_{100}-\frac{3925}{200}-\frac{1}{2}\times 5\times 5$$

Reduce the fraction \frac{3925}{200} to lowest terms by extracting and canceling out 25.

$$\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{1}{2}\times 5\times 5$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{5}{2}\times 5$$

Express \frac{5}{2}\times 5 as a single fraction.

$$\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{5\times 5}{2}$$

Multiply 5 and 5 to get 25.

$$\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{25}{2}$$

Least common multiple of 8 and 2 is 8. Convert -\frac{157}{8} and \frac{25}{2} to fractions with denominator 8.

$$\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{100}{8}$$

Since -\frac{157}{8} and \frac{100}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{400}x_{3}x_{100}+\frac{-157-100}{8}$$

Subtract 100 from -157 to get -257.

$$\frac{7}{400}x_{3}x_{100}-\frac{257}{8}$$

Factor

$$\frac{7x_{3}x_{100}-12850}{400}$$

Solution Steps

Convert decimal number 0.14 to fraction \frac{14}{100}. Reduce the fraction \frac{14}{100} to lowest terms by extracting and canceling out 2.

$$factor(\frac{1}{8}x_{3}\times \frac{7}{50}x_{100}-\frac{1}{4}\times 3.14\times 25-\frac{1}{2}\times 5\times 5)$$

Multiply \frac{1}{8} times \frac{7}{50} by multiplying numerator times numerator and denominator times denominator.

$$factor(\frac{1\times 7}{8\times 50}x_{3}x_{100}-\frac{1}{4}\times 3.14\times 25-\frac{1}{2}\times 5\times 5)$$

Do the multiplications in the fraction \frac{1\times 7}{8\times 50}.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{1}{4}\times 3.14\times 25-\frac{1}{2}\times 5\times 5)$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{1}{4}\times \frac{157}{50}\times 25-\frac{1}{2}\times 5\times 5)$$

Multiply \frac{1}{4} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{1\times 157}{4\times 50}\times 25-\frac{1}{2}\times 5\times 5)$$

Do the multiplications in the fraction \frac{1\times 157}{4\times 50}.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157}{200}\times 25-\frac{1}{2}\times 5\times 5)$$

Express \frac{157}{200}\times 25 as a single fraction.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157\times 25}{200}-\frac{1}{2}\times 5\times 5)$$

Multiply 157 and 25 to get 3925.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{3925}{200}-\frac{1}{2}\times 5\times 5)$$

Reduce the fraction \frac{3925}{200} to lowest terms by extracting and canceling out 25.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{1}{2}\times 5\times 5)$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{5}{2}\times 5)$$

Express \frac{5}{2}\times 5 as a single fraction.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{5\times 5}{2})$$

Multiply 5 and 5 to get 25.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{25}{2})$$

Least common multiple of 8 and 2 is 8. Convert -\frac{157}{8} and \frac{25}{2} to fractions with denominator 8.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{157}{8}-\frac{100}{8})$$

Since -\frac{157}{8} and \frac{100}{8} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{7}{400}x_{3}x_{100}+\frac{-157-100}{8})$$

Subtract 100 from -157 to get -257.

$$factor(\frac{7}{400}x_{3}x_{100}-\frac{257}{8})$$

Factor out \frac{1}{400}.

$$\frac{7x_{3}x_{100}-12850}{400}$$