Solve 4600*(1/0.92*0.656+1.7+1/0.92*0.656+0.62)

$$4600 \times ( \frac{ 1 }{ 0.92 \times 0.656+1.7 } + \frac{ 1 }{ 0.92 \times 0.656+0.62 } )$$

Evaluate

$$\frac{211255000000}{36697953}\approx 5756.588112694$$

Solution Steps

Multiply 0.92 and 0.656 to get 0.60352.

$$4600\left(\frac{1}{0.60352+1.7}+\frac{1}{0.92\times 0.656+0.62}\right)$$

Add 0.60352 and 1.7 to get 2.30352.

$$4600\left(\frac{1}{2.30352}+\frac{1}{0.92\times 0.656+0.62}\right)$$

Expand \frac{1}{2.30352} by multiplying both numerator and the denominator by 100000.

$$4600\left(\frac{100000}{230352}+\frac{1}{0.92\times 0.656+0.62}\right)$$

Reduce the fraction \frac{100000}{230352} to lowest terms by extracting and canceling out 16.

$$4600\left(\frac{6250}{14397}+\frac{1}{0.92\times 0.656+0.62}\right)$$

Multiply 0.92 and 0.656 to get 0.60352.

$$4600\left(\frac{6250}{14397}+\frac{1}{0.60352+0.62}\right)$$

Add 0.60352 and 0.62 to get 1.22352.

$$4600\left(\frac{6250}{14397}+\frac{1}{1.22352}\right)$$

Expand \frac{1}{1.22352} by multiplying both numerator and the denominator by 100000.

$$4600\left(\frac{6250}{14397}+\frac{100000}{122352}\right)$$

Reduce the fraction \frac{100000}{122352} to lowest terms by extracting and canceling out 16.

$$4600\left(\frac{6250}{14397}+\frac{6250}{7647}\right)$$

Least common multiple of 14397 and 7647 is 36697953. Convert \frac{6250}{14397} and \frac{6250}{7647} to fractions with denominator 36697953.

$$4600\left(\frac{15931250}{36697953}+\frac{29993750}{36697953}\right)$$

Since \frac{15931250}{36697953} and \frac{29993750}{36697953} have the same denominator, add them by adding their numerators.

$$4600\times \frac{15931250+29993750}{36697953}$$

Add 15931250 and 29993750 to get 45925000.

$$4600\times \frac{45925000}{36697953}$$

Express 4600\times \frac{45925000}{36697953} as a single fraction.

$$\frac{4600\times 45925000}{36697953}$$

Multiply 4600 and 45925000 to get 211255000000.

$$\frac{211255000000}{36697953}$$

Factor

$$\frac{11 \cdot 23 \cdot 167 \cdot 2 ^ {6} \cdot 5 ^ {7}}{3 \cdot 2549 \cdot 4799} = 5756\frac{21582532}{36697953} = 5756.588112693915$$