Solve 36/1000*18/43/frac{1{6}*(1-18/43)+frac{36}{100}*frac{18}{43}}

$$\frac { \frac { 36 } { 1000 } \times \frac { 18 } { 43 } } { \frac { 1 } { 6 } \times ( 1 - \frac { 18 } { 43 } ) + \frac { 36 } { 100 } \times \frac { 18 } { 43 } }$$

Evaluate

$$\frac{486}{7985}\approx 0.06086412$$

Solution Steps

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

$$\frac{\frac{9}{250}\times \frac{18}{43}}{\frac{1}{6}\left(1-\frac{18}{43}\right)+\frac{36}{100}\times \frac{18}{43}}$$

Multiply \frac{9}{250} times \frac{18}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9\times 18}{250\times 43}}{\frac{1}{6}\left(1-\frac{18}{43}\right)+\frac{36}{100}\times \frac{18}{43}}$$

Do the multiplications in the fraction \frac{9\times 18}{250\times 43}.

$$\frac{\frac{162}{10750}}{\frac{1}{6}\left(1-\frac{18}{43}\right)+\frac{36}{100}\times \frac{18}{43}}$$

Reduce the fraction \frac{162}{10750} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{81}{5375}}{\frac{1}{6}\left(1-\frac{18}{43}\right)+\frac{36}{100}\times \frac{18}{43}}$$

Convert 1 to fraction \frac{43}{43}.

$$\frac{\frac{81}{5375}}{\frac{1}{6}\left(\frac{43}{43}-\frac{18}{43}\right)+\frac{36}{100}\times \frac{18}{43}}$$

Since \frac{43}{43} and \frac{18}{43} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{81}{5375}}{\frac{1}{6}\times \frac{43-18}{43}+\frac{36}{100}\times \frac{18}{43}}$$

Subtract 18 from 43 to get 25.

$$\frac{\frac{81}{5375}}{\frac{1}{6}\times \frac{25}{43}+\frac{36}{100}\times \frac{18}{43}}$$

Multiply \frac{1}{6} times \frac{25}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{81}{5375}}{\frac{1\times 25}{6\times 43}+\frac{36}{100}\times \frac{18}{43}}$$

Do the multiplications in the fraction \frac{1\times 25}{6\times 43}.

$$\frac{\frac{81}{5375}}{\frac{25}{258}+\frac{36}{100}\times \frac{18}{43}}$$

Reduce the fraction \frac{36}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{81}{5375}}{\frac{25}{258}+\frac{9}{25}\times \frac{18}{43}}$$

Multiply \frac{9}{25} times \frac{18}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{81}{5375}}{\frac{25}{258}+\frac{9\times 18}{25\times 43}}$$

Do the multiplications in the fraction \frac{9\times 18}{25\times 43}.

$$\frac{\frac{81}{5375}}{\frac{25}{258}+\frac{162}{1075}}$$

Least common multiple of 258 and 1075 is 6450. Convert \frac{25}{258} and \frac{162}{1075} to fractions with denominator 6450.

$$\frac{\frac{81}{5375}}{\frac{625}{6450}+\frac{972}{6450}}$$

Since \frac{625}{6450} and \frac{972}{6450} have the same denominator, add them by adding their numerators.

$$\frac{\frac{81}{5375}}{\frac{625+972}{6450}}$$

Add 625 and 972 to get 1597.

$$\frac{\frac{81}{5375}}{\frac{1597}{6450}}$$

Divide \frac{81}{5375} by \frac{1597}{6450} by multiplying \frac{81}{5375} by the reciprocal of \frac{1597}{6450}.

$$\frac{81}{5375}\times \frac{6450}{1597}$$

Multiply \frac{81}{5375} times \frac{6450}{1597} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 6450}{5375\times 1597}$$

Do the multiplications in the fraction \frac{81\times 6450}{5375\times 1597}.

$$\frac{522450}{8583875}$$

Reduce the fraction \frac{522450}{8583875} to lowest terms by extracting and canceling out 1075.

$$\frac{486}{7985}$$

Factor

$$\frac{2 \cdot 3 ^ {5}}{5 \cdot 1597} = 0.06086412022542267$$