Solve 0.233+(0.233+0.77)*0.222/0.775

$$0.233 + ( 0.233 + 0.77 ) \times \frac { 0.222 } { 0.775 }$$

Evaluate

$$\frac{403241}{775000}\approx 0.520310968$$

Solution Steps

Add 0.233 and 0.77 to get 1.003.

$$0.233+1.003\times \frac{0.222}{0.775}$$

Expand \frac{0.222}{0.775} by multiplying both numerator and the denominator by 1000.

$$0.233+1.003\times \frac{222}{775}$$

Convert decimal number 1.003 to fraction \frac{1003}{1000}.

$$0.233+\frac{1003}{1000}\times \frac{222}{775}$$

Multiply \frac{1003}{1000} times \frac{222}{775} by multiplying numerator times numerator and denominator times denominator.

$$0.233+\frac{1003\times 222}{1000\times 775}$$

Do the multiplications in the fraction \frac{1003\times 222}{1000\times 775}.

$$0.233+\frac{222666}{775000}$$

Reduce the fraction \frac{222666}{775000} to lowest terms by extracting and canceling out 2.

$$0.233+\frac{111333}{387500}$$

Convert decimal number 0.233 to fraction \frac{233}{1000}.

$$\frac{233}{1000}+\frac{111333}{387500}$$

Least common multiple of 1000 and 387500 is 775000. Convert \frac{233}{1000} and \frac{111333}{387500} to fractions with denominator 775000.

$$\frac{180575}{775000}+\frac{222666}{775000}$$

Since \frac{180575}{775000} and \frac{222666}{775000} have the same denominator, add them by adding their numerators.

$$\frac{180575+222666}{775000}$$

Add 180575 and 222666 to get 403241.

$$\frac{403241}{775000}$$

Factor

$$\frac{403241}{31 \cdot 2 ^ {3} \cdot 5 ^ {5}} = 0.5203109677419355$$