Solve 1/8.7+0.12/0.81+0.15/0.064+0.2/0.47+frac{0.02}{0.81}+frac{1}{23}

$$\frac{ 1 }{ 8.7 } + \frac{ 0.12 }{ 0.81 } + \frac{ 0.15 }{ 0.064 } + \frac{ 0.2 }{ 0.47 } + \frac{ 0.02 }{ 0.81 } + \frac{ 1 }{ 23 }$$

Evaluate

$$\frac{251939543}{81256608}\approx 3.100542211$$

Solution Steps

Expand \frac{1}{8.7} by multiplying both numerator and the denominator by 10.

$$\frac{10}{87}+\frac{0.12}{0.81}+\frac{0.15}{0.064}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Expand \frac{0.12}{0.81} by multiplying both numerator and the denominator by 100.

$$\frac{10}{87}+\frac{12}{81}+\frac{0.15}{0.064}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Reduce the fraction \frac{12}{81} to lowest terms by extracting and canceling out 3.

$$\frac{10}{87}+\frac{4}{27}+\frac{0.15}{0.064}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Least common multiple of 87 and 27 is 783. Convert \frac{10}{87} and \frac{4}{27} to fractions with denominator 783.

$$\frac{90}{783}+\frac{116}{783}+\frac{0.15}{0.064}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Since \frac{90}{783} and \frac{116}{783} have the same denominator, add them by adding their numerators.

$$\frac{90+116}{783}+\frac{0.15}{0.064}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Add 90 and 116 to get 206.

$$\frac{206}{783}+\frac{0.15}{0.064}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Expand \frac{0.15}{0.064} by multiplying both numerator and the denominator by 1000.

$$\frac{206}{783}+\frac{150}{64}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Reduce the fraction \frac{150}{64} to lowest terms by extracting and canceling out 2.

$$\frac{206}{783}+\frac{75}{32}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Least common multiple of 783 and 32 is 25056. Convert \frac{206}{783} and \frac{75}{32} to fractions with denominator 25056.

$$\frac{6592}{25056}+\frac{58725}{25056}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Since \frac{6592}{25056} and \frac{58725}{25056} have the same denominator, add them by adding their numerators.

$$\frac{6592+58725}{25056}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Add 6592 and 58725 to get 65317.

$$\frac{65317}{25056}+\frac{0.2}{0.47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Expand \frac{0.2}{0.47} by multiplying both numerator and the denominator by 100.

$$\frac{65317}{25056}+\frac{20}{47}+\frac{0.02}{0.81}+\frac{1}{23}$$

Least common multiple of 25056 and 47 is 1177632. Convert \frac{65317}{25056} and \frac{20}{47} to fractions with denominator 1177632.

$$\frac{3069899}{1177632}+\frac{501120}{1177632}+\frac{0.02}{0.81}+\frac{1}{23}$$

Since \frac{3069899}{1177632} and \frac{501120}{1177632} have the same denominator, add them by adding their numerators.

$$\frac{3069899+501120}{1177632}+\frac{0.02}{0.81}+\frac{1}{23}$$

Add 3069899 and 501120 to get 3571019.

$$\frac{3571019}{1177632}+\frac{0.02}{0.81}+\frac{1}{23}$$

Expand \frac{0.02}{0.81} by multiplying both numerator and the denominator by 100.

$$\frac{3571019}{1177632}+\frac{2}{81}+\frac{1}{23}$$

Least common multiple of 1177632 and 81 is 3532896. Convert \frac{3571019}{1177632} and \frac{2}{81} to fractions with denominator 3532896.

$$\frac{10713057}{3532896}+\frac{87232}{3532896}+\frac{1}{23}$$

Since \frac{10713057}{3532896} and \frac{87232}{3532896} have the same denominator, add them by adding their numerators.

$$\frac{10713057+87232}{3532896}+\frac{1}{23}$$

Add 10713057 and 87232 to get 10800289.

$$\frac{10800289}{3532896}+\frac{1}{23}$$

Least common multiple of 3532896 and 23 is 81256608. Convert \frac{10800289}{3532896} and \frac{1}{23} to fractions with denominator 81256608.

$$\frac{248406647}{81256608}+\frac{3532896}{81256608}$$

Since \frac{248406647}{81256608} and \frac{3532896}{81256608} have the same denominator, add them by adding their numerators.

$$\frac{248406647+3532896}{81256608}$$

Add 248406647 and 3532896 to get 251939543.

$$\frac{251939543}{81256608}$$

Factor

$$\frac{6833 \cdot 36871}{23 \cdot 29 \cdot 47 \cdot 2 ^ {5} \cdot 3 ^ {4}} = 3\frac{8169719}{81256608} = 3.100542210671654$$