Solve 1.002/1.002+frac{1.958*1.978{1.958+1.978}}

$$\frac { 1.002 } { 1.002 + \frac { 1.958 \times 1.978 } { 1.958 + 1.978 } }$$

Evaluate

$$\frac{985968}{1954199}\approx 0.504538177$$

Solution Steps

Multiply 1.958 and 1.978 to get 3.872924.

$$\frac{1.002}{1.002+\frac{3.872924}{1.958+1.978}}$$

Add 1.958 and 1.978 to get 3.936.

$$\frac{1.002}{1.002+\frac{3.872924}{3.936}}$$

Expand \frac{3.872924}{3.936} by multiplying both numerator and the denominator by 1000000.

$$\frac{1.002}{1.002+\frac{3872924}{3936000}}$$

Reduce the fraction \frac{3872924}{3936000} to lowest terms by extracting and canceling out 4.

$$\frac{1.002}{1.002+\frac{968231}{984000}}$$

Convert decimal number 1.002 to fraction \frac{1002}{1000}. Reduce the fraction \frac{1002}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{1.002}{\frac{501}{500}+\frac{968231}{984000}}$$

Least common multiple of 500 and 984000 is 984000. Convert \frac{501}{500} and \frac{968231}{984000} to fractions with denominator 984000.

$$\frac{1.002}{\frac{985968}{984000}+\frac{968231}{984000}}$$

Since \frac{985968}{984000} and \frac{968231}{984000} have the same denominator, add them by adding their numerators.

$$\frac{1.002}{\frac{985968+968231}{984000}}$$

Add 985968 and 968231 to get 1954199.

$$\frac{1.002}{\frac{1954199}{984000}}$$

Divide 1.002 by \frac{1954199}{984000} by multiplying 1.002 by the reciprocal of \frac{1954199}{984000}.

$$1.002\times \frac{984000}{1954199}$$

Convert decimal number 1.002 to fraction \frac{1002}{1000}. Reduce the fraction \frac{1002}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{501}{500}\times \frac{984000}{1954199}$$

Multiply \frac{501}{500} times \frac{984000}{1954199} by multiplying numerator times numerator and denominator times denominator.

$$\frac{501\times 984000}{500\times 1954199}$$

Do the multiplications in the fraction \frac{501\times 984000}{500\times 1954199}.

$$\frac{492984000}{977099500}$$

Reduce the fraction \frac{492984000}{977099500} to lowest terms by extracting and canceling out 500.

$$\frac{985968}{1954199}$$

Factor

$$\frac{41 \cdot 167 \cdot 2 ^ {4} \cdot 3 ^ {2}}{13 \cdot 150323} = 0.5045381765111946$$