Solve 4600*(1/0.92+1.7+1/0.92+0.62)

$$4600 \times ( \frac{ 1 }{ 0.92+1.7 } + \frac{ 1 }{ 0.92+0.62 } )$$

Evaluate

$$\frac{47840000}{10087}\approx 4742.738177853$$

Solution Steps

Add 0.92 and 1.7 to get 2.62.

$$4600\left(\frac{1}{2.62}+\frac{1}{0.92+0.62}\right)$$

Expand \frac{1}{2.62} by multiplying both numerator and the denominator by 100.

$$4600\left(\frac{100}{262}+\frac{1}{0.92+0.62}\right)$$

Reduce the fraction \frac{100}{262} to lowest terms by extracting and canceling out 2.

$$4600\left(\frac{50}{131}+\frac{1}{0.92+0.62}\right)$$

Add 0.92 and 0.62 to get 1.54.

$$4600\left(\frac{50}{131}+\frac{1}{1.54}\right)$$

Expand \frac{1}{1.54} by multiplying both numerator and the denominator by 100.

$$4600\left(\frac{50}{131}+\frac{100}{154}\right)$$

Reduce the fraction \frac{100}{154} to lowest terms by extracting and canceling out 2.

$$4600\left(\frac{50}{131}+\frac{50}{77}\right)$$

Least common multiple of 131 and 77 is 10087. Convert \frac{50}{131} and \frac{50}{77} to fractions with denominator 10087.

$$4600\left(\frac{3850}{10087}+\frac{6550}{10087}\right)$$

Since \frac{3850}{10087} and \frac{6550}{10087} have the same denominator, add them by adding their numerators.

$$4600\times \frac{3850+6550}{10087}$$

Add 3850 and 6550 to get 10400.

$$4600\times \frac{10400}{10087}$$

Express 4600\times \frac{10400}{10087} as a single fraction.

$$\frac{4600\times 10400}{10087}$$

Multiply 4600 and 10400 to get 47840000.

$$\frac{47840000}{10087}$$

Factor

$$\frac{13 \cdot 23 \cdot 2 ^ {8} \cdot 5 ^ {4}}{7 \cdot 11 \cdot 131} = 4742\frac{7446}{10087} = 4742.7381778526815$$