Solve 18-33-45:375/56:2frac{1{3}+25}

$$18 - \frac { 33 - 45 : 375 } { 56 : 2 \frac { 1 } { 3 } + 25 }$$

Evaluate

$$\frac{21228}{1225}\approx 17.328979592$$

Solution Steps

Reduce the fraction \frac{45}{375} to lowest terms by extracting and canceling out 15.

$$18-\frac{33-\frac{3}{25}}{\frac{56}{\frac{2\times 3+1}{3}}+25}$$

Convert 33 to fraction \frac{825}{25}.

$$18-\frac{\frac{825}{25}-\frac{3}{25}}{\frac{56}{\frac{2\times 3+1}{3}}+25}$$

Since \frac{825}{25} and \frac{3}{25} have the same denominator, subtract them by subtracting their numerators.

$$18-\frac{\frac{825-3}{25}}{\frac{56}{\frac{2\times 3+1}{3}}+25}$$

Subtract 3 from 825 to get 822.

$$18-\frac{\frac{822}{25}}{\frac{56}{\frac{2\times 3+1}{3}}+25}$$

Divide 56 by \frac{2\times 3+1}{3} by multiplying 56 by the reciprocal of \frac{2\times 3+1}{3}.

$$18-\frac{\frac{822}{25}}{\frac{56\times 3}{2\times 3+1}+25}$$

Multiply 56 and 3 to get 168.

$$18-\frac{\frac{822}{25}}{\frac{168}{2\times 3+1}+25}$$

Multiply 2 and 3 to get 6.

$$18-\frac{\frac{822}{25}}{\frac{168}{6+1}+25}$$

Add 6 and 1 to get 7.

$$18-\frac{\frac{822}{25}}{\frac{168}{7}+25}$$

Divide 168 by 7 to get 24.

$$18-\frac{\frac{822}{25}}{24+25}$$

Add 24 and 25 to get 49.

$$18-\frac{\frac{822}{25}}{49}$$

Express \frac{\frac{822}{25}}{49} as a single fraction.

$$18-\frac{822}{25\times 49}$$

Multiply 25 and 49 to get 1225.

$$18-\frac{822}{1225}$$

Convert 18 to fraction \frac{22050}{1225}.

$$\frac{22050}{1225}-\frac{822}{1225}$$

Since \frac{22050}{1225} and \frac{822}{1225} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22050-822}{1225}$$

Subtract 822 from 22050 to get 21228.

$$\frac{21228}{1225}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 29 \cdot 61}{5 ^ {2} \cdot 7 ^ {2}} = 17\frac{403}{1225} = 17.328979591836735$$