Solve 2*242.5left(1+0.114right)/frac{0.3{0.114}+0.114/0.3+2*0.114}

$$\frac{ 2 \cdot 242.5 \left( 1+0.114 \right) }{ \frac{ 0.3 }{ 0.114 } + \frac{ 0.114 }{ 0.3 } +2 \times 0.114 }$$

Evaluate

$$\frac{5132755}{30776}\approx 166.777846374$$

Solution Steps

Multiply 2 and 242.5 to get 485.

$$\frac{485\left(1+0.114\right)}{\frac{0.3}{0.114}+\frac{0.114}{0.3}+2\times 0.114}$$

Add 1 and 0.114 to get 1.114.

$$\frac{485\times 1.114}{\frac{0.3}{0.114}+\frac{0.114}{0.3}+2\times 0.114}$$

Multiply 485 and 1.114 to get 540.29.

$$\frac{540.29}{\frac{0.3}{0.114}+\frac{0.114}{0.3}+2\times 0.114}$$

Expand \frac{0.3}{0.114} by multiplying both numerator and the denominator by 1000.

$$\frac{540.29}{\frac{300}{114}+\frac{0.114}{0.3}+2\times 0.114}$$

Reduce the fraction \frac{300}{114} to lowest terms by extracting and canceling out 6.

$$\frac{540.29}{\frac{50}{19}+\frac{0.114}{0.3}+2\times 0.114}$$

Expand \frac{0.114}{0.3} by multiplying both numerator and the denominator by 1000.

$$\frac{540.29}{\frac{50}{19}+\frac{114}{300}+2\times 0.114}$$

Reduce the fraction \frac{114}{300} to lowest terms by extracting and canceling out 6.

$$\frac{540.29}{\frac{50}{19}+\frac{19}{50}+2\times 0.114}$$

Least common multiple of 19 and 50 is 950. Convert \frac{50}{19} and \frac{19}{50} to fractions with denominator 950.

$$\frac{540.29}{\frac{2500}{950}+\frac{361}{950}+2\times 0.114}$$

Since \frac{2500}{950} and \frac{361}{950} have the same denominator, add them by adding their numerators.

$$\frac{540.29}{\frac{2500+361}{950}+2\times 0.114}$$

Add 2500 and 361 to get 2861.

$$\frac{540.29}{\frac{2861}{950}+2\times 0.114}$$

Multiply 2 and 0.114 to get 0.228.

$$\frac{540.29}{\frac{2861}{950}+0.228}$$

Convert decimal number 0.228 to fraction \frac{228}{1000}. Reduce the fraction \frac{228}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{540.29}{\frac{2861}{950}+\frac{57}{250}}$$

Least common multiple of 950 and 250 is 4750. Convert \frac{2861}{950} and \frac{57}{250} to fractions with denominator 4750.

$$\frac{540.29}{\frac{14305}{4750}+\frac{1083}{4750}}$$

Since \frac{14305}{4750} and \frac{1083}{4750} have the same denominator, add them by adding their numerators.

$$\frac{540.29}{\frac{14305+1083}{4750}}$$

Add 14305 and 1083 to get 15388.

$$\frac{540.29}{\frac{15388}{4750}}$$

Reduce the fraction \frac{15388}{4750} to lowest terms by extracting and canceling out 2.

$$\frac{540.29}{\frac{7694}{2375}}$$

Divide 540.29 by \frac{7694}{2375} by multiplying 540.29 by the reciprocal of \frac{7694}{2375}.

$$540.29\times \frac{2375}{7694}$$

Convert decimal number 540.29 to fraction \frac{54029}{100}.

$$\frac{54029}{100}\times \frac{2375}{7694}$$

Multiply \frac{54029}{100} times \frac{2375}{7694} by multiplying numerator times numerator and denominator times denominator.

$$\frac{54029\times 2375}{100\times 7694}$$

Do the multiplications in the fraction \frac{54029\times 2375}{100\times 7694}.

$$\frac{128318875}{769400}$$

Reduce the fraction \frac{128318875}{769400} to lowest terms by extracting and canceling out 25.

$$\frac{5132755}{30776}$$

Factor

$$\frac{5 \cdot 19 \cdot 97 \cdot 557}{3847 \cdot 2 ^ {3}} = 166\frac{23939}{30776} = 166.77784637379776$$