Solve (0.92-0.14/1.01+1.11-0.12/1.38+0.8-0.11^2/0.96)div3=

$$( \frac { 0.92 - 0.14 } { 1.01 } + \frac { 1.11 - 0.12 } { 1.38 } + \frac { 0.8 - 0.11 ^ { 2 } } { 0.96 } ) \div 3 =$$

Evaluate

$$\frac{51523717}{66902400}\approx 0.770132566$$

Solution Steps

Subtract 0.14 from 0.92 to get 0.78.

$$\frac{\frac{0.78}{1.01}+\frac{1.11-0.12}{1.38}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

Expand \frac{0.78}{1.01} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{78}{101}+\frac{1.11-0.12}{1.38}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

Subtract 0.12 from 1.11 to get 0.99.

$$\frac{\frac{78}{101}+\frac{0.99}{1.38}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

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

$$\frac{\frac{78}{101}+\frac{99}{138}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

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

$$\frac{\frac{78}{101}+\frac{33}{46}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

Least common multiple of 101 and 46 is 4646. Convert \frac{78}{101} and \frac{33}{46} to fractions with denominator 4646.

$$\frac{\frac{3588}{4646}+\frac{3333}{4646}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

Since \frac{3588}{4646} and \frac{3333}{4646} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3588+3333}{4646}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

Add 3588 and 3333 to get 6921.

$$\frac{\frac{6921}{4646}+\frac{0.8-0.11^{2}}{0.96}}{3}$$

Calculate 0.11 to the power of 2 and get 0.0121.

$$\frac{\frac{6921}{4646}+\frac{0.8-0.0121}{0.96}}{3}$$

Subtract 0.0121 from 0.8 to get 0.7879.

$$\frac{\frac{6921}{4646}+\frac{0.7879}{0.96}}{3}$$

Expand \frac{0.7879}{0.96} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{6921}{4646}+\frac{7879}{9600}}{3}$$

Least common multiple of 4646 and 9600 is 22300800. Convert \frac{6921}{4646} and \frac{7879}{9600} to fractions with denominator 22300800.

$$\frac{\frac{33220800}{22300800}+\frac{18302917}{22300800}}{3}$$

Since \frac{33220800}{22300800} and \frac{18302917}{22300800} have the same denominator, add them by adding their numerators.

$$\frac{\frac{33220800+18302917}{22300800}}{3}$$

Add 33220800 and 18302917 to get 51523717.

$$\frac{\frac{51523717}{22300800}}{3}$$

Express \frac{\frac{51523717}{22300800}}{3} as a single fraction.

$$\frac{51523717}{22300800\times 3}$$

Multiply 22300800 and 3 to get 66902400.

$$\frac{51523717}{66902400}$$

Factor

$$\frac{7 \cdot 7360531}{23 \cdot 101 \cdot 2 ^ {7} \cdot 3 ^ {2} \cdot 5 ^ {2}} = 0.770132566245755$$