Solve 30/30+8/9+9/10+4/4+frac{9}{10}div5

$$\frac{ 30 }{ 30 } + \frac{ 8 }{ 9 } + \frac{ 9 }{ 10 } + \frac{ 4 }{ 4 } + \frac{ 9 }{ 10 } \div 5$$

Evaluate

$$\frac{893}{225}\approx 3.968888889$$

Solution Steps

Divide 30 by 30 to get 1.

$$1+\frac{8}{9}+\frac{9}{10}+\frac{4}{4}+\frac{\frac{9}{10}}{5}$$

Divide 4 by 4 to get 1.

$$1+\frac{8}{9}+\frac{9}{10}+1+\frac{\frac{9}{10}}{5}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{9}{9}+\frac{8}{9}+\frac{9}{10}+1+\frac{\frac{9}{10}}{5}$$

Since \frac{9}{9} and \frac{8}{9} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{9}+\frac{9}{10}+1+\frac{\frac{9}{10}}{5}$$

Add 9 and 8 to get 17.

$$\frac{17}{9}+\frac{9}{10}+1+\frac{\frac{9}{10}}{5}$$

Least common multiple of 9 and 10 is 90. Convert \frac{17}{9} and \frac{9}{10} to fractions with denominator 90.

$$\frac{170}{90}+\frac{81}{90}+1+\frac{\frac{9}{10}}{5}$$

Since \frac{170}{90} and \frac{81}{90} have the same denominator, add them by adding their numerators.

$$\frac{170+81}{90}+1+\frac{\frac{9}{10}}{5}$$

Add 170 and 81 to get 251.

$$\frac{251}{90}+1+\frac{\frac{9}{10}}{5}$$

Convert 1 to fraction \frac{90}{90}.

$$\frac{251}{90}+\frac{90}{90}+\frac{\frac{9}{10}}{5}$$

Since \frac{251}{90} and \frac{90}{90} have the same denominator, add them by adding their numerators.

$$\frac{251+90}{90}+\frac{\frac{9}{10}}{5}$$

Add 251 and 90 to get 341.

$$\frac{341}{90}+\frac{\frac{9}{10}}{5}$$

Express \frac{\frac{9}{10}}{5} as a single fraction.

$$\frac{341}{90}+\frac{9}{10\times 5}$$

Multiply 10 and 5 to get 50.

$$\frac{341}{90}+\frac{9}{50}$$

Least common multiple of 90 and 50 is 450. Convert \frac{341}{90} and \frac{9}{50} to fractions with denominator 450.

$$\frac{1705}{450}+\frac{81}{450}$$

Since \frac{1705}{450} and \frac{81}{450} have the same denominator, add them by adding their numerators.

$$\frac{1705+81}{450}$$

Add 1705 and 81 to get 1786.

$$\frac{1786}{450}$$

Reduce the fraction \frac{1786}{450} to lowest terms by extracting and canceling out 2.

$$\frac{893}{225}$$

Factor

$$\frac{19 \cdot 47}{3 ^ {2} \cdot 5 ^ {2}} = 3\frac{218}{225} = 3.968888888888889$$