Solve 0.71-1/4/0.71+frac{1{4}}

$$\frac{ 0.71- \frac{ 1 }{ 4 } }{ 0.71+ \frac{ 1 }{ 4 } }$$

Evaluate

$$\frac{23}{48}\approx 0.479166667$$

Solution Steps

Convert decimal number 0.71 to fraction \frac{71}{100}.

$$\frac{\frac{71}{100}-\frac{1}{4}}{0.71+\frac{1}{4}}$$

Least common multiple of 100 and 4 is 100. Convert \frac{71}{100} and \frac{1}{4} to fractions with denominator 100.

$$\frac{\frac{71}{100}-\frac{25}{100}}{0.71+\frac{1}{4}}$$

Since \frac{71}{100} and \frac{25}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{71-25}{100}}{0.71+\frac{1}{4}}$$

Subtract 25 from 71 to get 46.

$$\frac{\frac{46}{100}}{0.71+\frac{1}{4}}$$

Reduce the fraction \frac{46}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{23}{50}}{0.71+\frac{1}{4}}$$

Convert decimal number 0.71 to fraction \frac{71}{100}.

$$\frac{\frac{23}{50}}{\frac{71}{100}+\frac{1}{4}}$$

Least common multiple of 100 and 4 is 100. Convert \frac{71}{100} and \frac{1}{4} to fractions with denominator 100.

$$\frac{\frac{23}{50}}{\frac{71}{100}+\frac{25}{100}}$$

Since \frac{71}{100} and \frac{25}{100} have the same denominator, add them by adding their numerators.

$$\frac{\frac{23}{50}}{\frac{71+25}{100}}$$

Add 71 and 25 to get 96.

$$\frac{\frac{23}{50}}{\frac{96}{100}}$$

Reduce the fraction \frac{96}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{23}{50}}{\frac{24}{25}}$$

Divide \frac{23}{50} by \frac{24}{25} by multiplying \frac{23}{50} by the reciprocal of \frac{24}{25}.

$$\frac{23}{50}\times \frac{25}{24}$$

Multiply \frac{23}{50} times \frac{25}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 25}{50\times 24}$$

Do the multiplications in the fraction \frac{23\times 25}{50\times 24}.

$$\frac{575}{1200}$$

Reduce the fraction \frac{575}{1200} to lowest terms by extracting and canceling out 25.

$$\frac{23}{48}$$

Factor

$$\frac{23}{3 \cdot 2 ^ {4}} = 0.4791666666666667$$