Solve 22*5%/22*5%+21*0.25%*22+21/22*5%+21*0.25^2

$$\frac { 22 \times 5 \% } { 22 \times 5 \% + 21 \times 0.25 \% } \times \frac { 22 + 21 } { 22 \times 5 \% + 21 \times 0.25 ^ { 2 } }$$

Evaluate

$$\frac{1513600}{88973}\approx 17.011902487$$

Solution Steps

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{22\times \frac{1}{20}}{22\times \frac{5}{100}+21\times \frac{0.25}{100}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Multiply 22 and \frac{1}{20} to get \frac{22}{20}.

$$\frac{\frac{22}{20}}{22\times \frac{5}{100}+21\times \frac{0.25}{100}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Reduce the fraction \frac{22}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{10}}{22\times \frac{5}{100}+21\times \frac{0.25}{100}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{11}{10}}{22\times \frac{1}{20}+21\times \frac{0.25}{100}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Multiply 22 and \frac{1}{20} to get \frac{22}{20}.

$$\frac{\frac{11}{10}}{\frac{22}{20}+21\times \frac{0.25}{100}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Reduce the fraction \frac{22}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{10}}{\frac{11}{10}+21\times \frac{0.25}{100}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Expand \frac{0.25}{100} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{11}{10}}{\frac{11}{10}+21\times \frac{25}{10000}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Reduce the fraction \frac{25}{10000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{11}{10}}{\frac{11}{10}+21\times \frac{1}{400}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Multiply 21 and \frac{1}{400} to get \frac{21}{400}.

$$\frac{\frac{11}{10}}{\frac{11}{10}+\frac{21}{400}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Least common multiple of 10 and 400 is 400. Convert \frac{11}{10} and \frac{21}{400} to fractions with denominator 400.

$$\frac{\frac{11}{10}}{\frac{440}{400}+\frac{21}{400}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Since \frac{440}{400} and \frac{21}{400} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{10}}{\frac{440+21}{400}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Add 440 and 21 to get 461.

$$\frac{\frac{11}{10}}{\frac{461}{400}}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Divide \frac{11}{10} by \frac{461}{400} by multiplying \frac{11}{10} by the reciprocal of \frac{461}{400}.

$$\frac{11}{10}\times \frac{400}{461}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Multiply \frac{11}{10} times \frac{400}{461} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 400}{10\times 461}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Do the multiplications in the fraction \frac{11\times 400}{10\times 461}.

$$\frac{4400}{4610}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Reduce the fraction \frac{4400}{4610} to lowest terms by extracting and canceling out 10.

$$\frac{440}{461}\times \frac{22+21}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Add 22 and 21 to get 43.

$$\frac{440}{461}\times \frac{43}{22\times \frac{5}{100}+21\times 0.25^{2}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{440}{461}\times \frac{43}{22\times \frac{1}{20}+21\times 0.25^{2}}$$

Multiply 22 and \frac{1}{20} to get \frac{22}{20}.

$$\frac{440}{461}\times \frac{43}{\frac{22}{20}+21\times 0.25^{2}}$$

Reduce the fraction \frac{22}{20} to lowest terms by extracting and canceling out 2.

$$\frac{440}{461}\times \frac{43}{\frac{11}{10}+21\times 0.25^{2}}$$

Calculate 0.25 to the power of 2 and get 0.0625.

$$\frac{440}{461}\times \frac{43}{\frac{11}{10}+21\times 0.0625}$$

Multiply 21 and 0.0625 to get 1.3125.

$$\frac{440}{461}\times \frac{43}{\frac{11}{10}+1.3125}$$

Convert decimal number 1.3125 to fraction \frac{13125}{10000}. Reduce the fraction \frac{13125}{10000} to lowest terms by extracting and canceling out 625.

$$\frac{440}{461}\times \frac{43}{\frac{11}{10}+\frac{21}{16}}$$

Least common multiple of 10 and 16 is 80. Convert \frac{11}{10} and \frac{21}{16} to fractions with denominator 80.

$$\frac{440}{461}\times \frac{43}{\frac{88}{80}+\frac{105}{80}}$$

Since \frac{88}{80} and \frac{105}{80} have the same denominator, add them by adding their numerators.

$$\frac{440}{461}\times \frac{43}{\frac{88+105}{80}}$$

Add 88 and 105 to get 193.

$$\frac{440}{461}\times \frac{43}{\frac{193}{80}}$$

Divide 43 by \frac{193}{80} by multiplying 43 by the reciprocal of \frac{193}{80}.

$$\frac{440}{461}\times 43\times \frac{80}{193}$$

Express 43\times \frac{80}{193} as a single fraction.

$$\frac{440}{461}\times \frac{43\times 80}{193}$$

Multiply 43 and 80 to get 3440.

$$\frac{440}{461}\times \frac{3440}{193}$$

Multiply \frac{440}{461} times \frac{3440}{193} by multiplying numerator times numerator and denominator times denominator.

$$\frac{440\times 3440}{461\times 193}$$

Do the multiplications in the fraction \frac{440\times 3440}{461\times 193}.

$$\frac{1513600}{88973}$$

Factor

$$\frac{11 \cdot 43 \cdot 2 ^ {7} \cdot 5 ^ {2}}{193 \cdot 461} = 17\frac{1059}{88973} = 17.01190248727142$$