Solve 2*242.5left(1+0.018right)/frac{0.3{0.018}+0.018/0.3+2*0.018}

$$\frac{ 2 \cdot 242.5 \left( 1+0.018 \right) }{ \frac{ 0.3 }{ 0.018 } + \frac{ 0.018 }{ 0.3 } +2 \times 0.018 }$$

Evaluate

$$\frac{740595}{25144}\approx 29.45414413$$

Solution Steps

Multiply 2 and 242.5 to get 485.

$$\frac{485\left(1+0.018\right)}{\frac{0.3}{0.018}+\frac{0.018}{0.3}+2\times 0.018}$$

Add 1 and 0.018 to get 1.018.

$$\frac{485\times 1.018}{\frac{0.3}{0.018}+\frac{0.018}{0.3}+2\times 0.018}$$

Multiply 485 and 1.018 to get 493.73.

$$\frac{493.73}{\frac{0.3}{0.018}+\frac{0.018}{0.3}+2\times 0.018}$$

Expand \frac{0.3}{0.018} by multiplying both numerator and the denominator by 1000.

$$\frac{493.73}{\frac{300}{18}+\frac{0.018}{0.3}+2\times 0.018}$$

Reduce the fraction \frac{300}{18} to lowest terms by extracting and canceling out 6.

$$\frac{493.73}{\frac{50}{3}+\frac{0.018}{0.3}+2\times 0.018}$$

Expand \frac{0.018}{0.3} by multiplying both numerator and the denominator by 1000.

$$\frac{493.73}{\frac{50}{3}+\frac{18}{300}+2\times 0.018}$$

Reduce the fraction \frac{18}{300} to lowest terms by extracting and canceling out 6.

$$\frac{493.73}{\frac{50}{3}+\frac{3}{50}+2\times 0.018}$$

Least common multiple of 3 and 50 is 150. Convert \frac{50}{3} and \frac{3}{50} to fractions with denominator 150.

$$\frac{493.73}{\frac{2500}{150}+\frac{9}{150}+2\times 0.018}$$

Since \frac{2500}{150} and \frac{9}{150} have the same denominator, add them by adding their numerators.

$$\frac{493.73}{\frac{2500+9}{150}+2\times 0.018}$$

Add 2500 and 9 to get 2509.

$$\frac{493.73}{\frac{2509}{150}+2\times 0.018}$$

Multiply 2 and 0.018 to get 0.036.

$$\frac{493.73}{\frac{2509}{150}+0.036}$$

Convert decimal number 0.036 to fraction \frac{36}{1000}. Reduce the fraction \frac{36}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{493.73}{\frac{2509}{150}+\frac{9}{250}}$$

Least common multiple of 150 and 250 is 750. Convert \frac{2509}{150} and \frac{9}{250} to fractions with denominator 750.

$$\frac{493.73}{\frac{12545}{750}+\frac{27}{750}}$$

Since \frac{12545}{750} and \frac{27}{750} have the same denominator, add them by adding their numerators.

$$\frac{493.73}{\frac{12545+27}{750}}$$

Add 12545 and 27 to get 12572.

$$\frac{493.73}{\frac{12572}{750}}$$

Reduce the fraction \frac{12572}{750} to lowest terms by extracting and canceling out 2.

$$\frac{493.73}{\frac{6286}{375}}$$

Divide 493.73 by \frac{6286}{375} by multiplying 493.73 by the reciprocal of \frac{6286}{375}.

$$493.73\times \frac{375}{6286}$$

Convert decimal number 493.73 to fraction \frac{49373}{100}.

$$\frac{49373}{100}\times \frac{375}{6286}$$

Multiply \frac{49373}{100} times \frac{375}{6286} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49373\times 375}{100\times 6286}$$

Do the multiplications in the fraction \frac{49373\times 375}{100\times 6286}.

$$\frac{18514875}{628600}$$

Reduce the fraction \frac{18514875}{628600} to lowest terms by extracting and canceling out 25.

$$\frac{740595}{25144}$$

Factor

$$\frac{3 \cdot 5 \cdot 97 \cdot 509}{7 \cdot 449 \cdot 2 ^ {3}} = 29\frac{11419}{25144} = 29.45414412981228$$