Solve (25*9.09%+50*5.05%+100*3.03%+300*1.01%+500*1.01%)*77

$$( 25 \times 9.09 \% + 50 \times 5.05 \% + 100 \times 3.03 \% + 300 \times 1.01 \% + 500 \times 1.01 \% ) \times 77$$

Evaluate

$$1224.8775$$

Solution Steps

Expand \frac{9.09}{100} by multiplying both numerator and the denominator by 100.

$$\left(25\times \frac{909}{10000}+50\times \frac{5.05}{100}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Express 25\times \frac{909}{10000} as a single fraction.

$$\left(\frac{25\times 909}{10000}+50\times \frac{5.05}{100}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Multiply 25 and 909 to get 22725.

$$\left(\frac{22725}{10000}+50\times \frac{5.05}{100}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Reduce the fraction \frac{22725}{10000} to lowest terms by extracting and canceling out 25.

$$\left(\frac{909}{400}+50\times \frac{5.05}{100}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Expand \frac{5.05}{100} by multiplying both numerator and the denominator by 100.

$$\left(\frac{909}{400}+50\times \frac{505}{10000}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Reduce the fraction \frac{505}{10000} to lowest terms by extracting and canceling out 5.

$$\left(\frac{909}{400}+50\times \frac{101}{2000}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Express 50\times \frac{101}{2000} as a single fraction.

$$\left(\frac{909}{400}+\frac{50\times 101}{2000}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Multiply 50 and 101 to get 5050.

$$\left(\frac{909}{400}+\frac{5050}{2000}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Reduce the fraction \frac{5050}{2000} to lowest terms by extracting and canceling out 50.

$$\left(\frac{909}{400}+\frac{101}{40}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Least common multiple of 400 and 40 is 400. Convert \frac{909}{400} and \frac{101}{40} to fractions with denominator 400.

$$\left(\frac{909}{400}+\frac{1010}{400}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Since \frac{909}{400} and \frac{1010}{400} have the same denominator, add them by adding their numerators.

$$\left(\frac{909+1010}{400}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Add 909 and 1010 to get 1919.

$$\left(\frac{1919}{400}+100\times \frac{3.03}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Expand \frac{3.03}{100} by multiplying both numerator and the denominator by 100.

$$\left(\frac{1919}{400}+100\times \frac{303}{10000}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Express 100\times \frac{303}{10000} as a single fraction.

$$\left(\frac{1919}{400}+\frac{100\times 303}{10000}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Multiply 100 and 303 to get 30300.

$$\left(\frac{1919}{400}+\frac{30300}{10000}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Reduce the fraction \frac{30300}{10000} to lowest terms by extracting and canceling out 100.

$$\left(\frac{1919}{400}+\frac{303}{100}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Least common multiple of 400 and 100 is 400. Convert \frac{1919}{400} and \frac{303}{100} to fractions with denominator 400.

$$\left(\frac{1919}{400}+\frac{1212}{400}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Since \frac{1919}{400} and \frac{1212}{400} have the same denominator, add them by adding their numerators.

$$\left(\frac{1919+1212}{400}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Add 1919 and 1212 to get 3131.

$$\left(\frac{3131}{400}+300\times \frac{1.01}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Expand \frac{1.01}{100} by multiplying both numerator and the denominator by 100.

$$\left(\frac{3131}{400}+300\times \frac{101}{10000}+500\times \frac{1.01}{100}\right)\times 77$$

Express 300\times \frac{101}{10000} as a single fraction.

$$\left(\frac{3131}{400}+\frac{300\times 101}{10000}+500\times \frac{1.01}{100}\right)\times 77$$

Multiply 300 and 101 to get 30300.

$$\left(\frac{3131}{400}+\frac{30300}{10000}+500\times \frac{1.01}{100}\right)\times 77$$

Reduce the fraction \frac{30300}{10000} to lowest terms by extracting and canceling out 100.

$$\left(\frac{3131}{400}+\frac{303}{100}+500\times \frac{1.01}{100}\right)\times 77$$

Least common multiple of 400 and 100 is 400. Convert \frac{3131}{400} and \frac{303}{100} to fractions with denominator 400.

$$\left(\frac{3131}{400}+\frac{1212}{400}+500\times \frac{1.01}{100}\right)\times 77$$

Since \frac{3131}{400} and \frac{1212}{400} have the same denominator, add them by adding their numerators.

$$\left(\frac{3131+1212}{400}+500\times \frac{1.01}{100}\right)\times 77$$

Add 3131 and 1212 to get 4343.

$$\left(\frac{4343}{400}+500\times \frac{1.01}{100}\right)\times 77$$

Expand \frac{1.01}{100} by multiplying both numerator and the denominator by 100.

$$\left(\frac{4343}{400}+500\times \frac{101}{10000}\right)\times 77$$

Express 500\times \frac{101}{10000} as a single fraction.

$$\left(\frac{4343}{400}+\frac{500\times 101}{10000}\right)\times 77$$

Multiply 500 and 101 to get 50500.

$$\left(\frac{4343}{400}+\frac{50500}{10000}\right)\times 77$$

Reduce the fraction \frac{50500}{10000} to lowest terms by extracting and canceling out 500.

$$\left(\frac{4343}{400}+\frac{101}{20}\right)\times 77$$

Least common multiple of 400 and 20 is 400. Convert \frac{4343}{400} and \frac{101}{20} to fractions with denominator 400.

$$\left(\frac{4343}{400}+\frac{2020}{400}\right)\times 77$$

Since \frac{4343}{400} and \frac{2020}{400} have the same denominator, add them by adding their numerators.

$$\frac{4343+2020}{400}\times 77$$

Add 4343 and 2020 to get 6363.

$$\frac{6363}{400}\times 77$$

Express \frac{6363}{400}\times 77 as a single fraction.

$$\frac{6363\times 77}{400}$$

Multiply 6363 and 77 to get 489951.

$$\frac{489951}{400}$$

Factor

$$\frac{11 \cdot 101 \cdot 3 ^ {2} \cdot 7 ^ {2}}{2 ^ {4} \cdot 5 ^ {2}} = 1224\frac{351}{400} = 1224.8775$$