Solve 0.92-0.14/1.09+1.11-0.12/1.38+0.8-0.12/0.96/3

$$\frac{ \frac{ 0.92-0.14 }{ 1.09 } + \frac{ 1.11-0.12 }{ 1.38 } + \frac{ 0.8-0.12 }{ 0.96 } }{ 3 }$$

Evaluate

$$\frac{128839}{180504}\approx 0.713773656$$

Solution Steps

Subtract 0.14 from 0.92 to get 0.78.

$$\frac{\frac{0.78}{1.09}+\frac{1.11-0.12}{1.38}+\frac{0.8-0.12}{0.96}}{3}$$

Expand \frac{0.78}{1.09} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{78}{109}+\frac{1.11-0.12}{1.38}+\frac{0.8-0.12}{0.96}}{3}$$

Subtract 0.12 from 1.11 to get 0.99.

$$\frac{\frac{78}{109}+\frac{0.99}{1.38}+\frac{0.8-0.12}{0.96}}{3}$$

Expand \frac{0.99}{1.38} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{78}{109}+\frac{99}{138}+\frac{0.8-0.12}{0.96}}{3}$$

Reduce the fraction \frac{99}{138} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{78}{109}+\frac{33}{46}+\frac{0.8-0.12}{0.96}}{3}$$

Least common multiple of 109 and 46 is 5014. Convert \frac{78}{109} and \frac{33}{46} to fractions with denominator 5014.

$$\frac{\frac{3588}{5014}+\frac{3597}{5014}+\frac{0.8-0.12}{0.96}}{3}$$

Since \frac{3588}{5014} and \frac{3597}{5014} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3588+3597}{5014}+\frac{0.8-0.12}{0.96}}{3}$$

Add 3588 and 3597 to get 7185.

$$\frac{\frac{7185}{5014}+\frac{0.8-0.12}{0.96}}{3}$$

Subtract 0.12 from 0.8 to get 0.68.

$$\frac{\frac{7185}{5014}+\frac{0.68}{0.96}}{3}$$

Expand \frac{0.68}{0.96} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{7185}{5014}+\frac{68}{96}}{3}$$

Reduce the fraction \frac{68}{96} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7185}{5014}+\frac{17}{24}}{3}$$

Least common multiple of 5014 and 24 is 60168. Convert \frac{7185}{5014} and \frac{17}{24} to fractions with denominator 60168.

$$\frac{\frac{86220}{60168}+\frac{42619}{60168}}{3}$$

Since \frac{86220}{60168} and \frac{42619}{60168} have the same denominator, add them by adding their numerators.

$$\frac{\frac{86220+42619}{60168}}{3}$$

Add 86220 and 42619 to get 128839.

$$\frac{\frac{128839}{60168}}{3}$$

Express \frac{\frac{128839}{60168}}{3} as a single fraction.

$$\frac{128839}{60168\times 3}$$

Multiply 60168 and 3 to get 180504.

$$\frac{128839}{180504}$$

Factor

$$\frac{19 \cdot 6781}{23 \cdot 109 \cdot 2 ^ {3} \cdot 3 ^ {2}} = 0.7137736559854629$$