Solve 24.57div31/2+(3.35-5/8)-(-225)div121/2=

$$24.57 \div 3 \frac { 1 } { 2 } +(3.35- \frac{ 5 }{ 8 } )-(-225) \div 12 \frac { 1 } { 2 } =$$

Evaluate

$$27.745$$

Solution Steps

Divide 24.57 by \frac{3\times 2+1}{2} by multiplying 24.57 by the reciprocal of \frac{3\times 2+1}{2}.

$$\frac{24.57\times 2}{3\times 2+1}+3.35-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Multiply 24.57 and 2 to get 49.14.

$$\frac{49.14}{3\times 2+1}+3.35-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{49.14}{6+1}+3.35-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{49.14}{7}+3.35-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Expand \frac{49.14}{7} by multiplying both numerator and the denominator by 100.

$$\frac{4914}{700}+3.35-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Reduce the fraction \frac{4914}{700} to lowest terms by extracting and canceling out 14.

$$\frac{351}{50}+3.35-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Convert decimal number 3.35 to fraction \frac{335}{100}. Reduce the fraction \frac{335}{100} to lowest terms by extracting and canceling out 5.

$$\frac{351}{50}+\frac{67}{20}-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Least common multiple of 50 and 20 is 100. Convert \frac{351}{50} and \frac{67}{20} to fractions with denominator 100.

$$\frac{702}{100}+\frac{335}{100}-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Since \frac{702}{100} and \frac{335}{100} have the same denominator, add them by adding their numerators.

$$\frac{702+335}{100}-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Add 702 and 335 to get 1037.

$$\frac{1037}{100}-\frac{5}{8}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Least common multiple of 100 and 8 is 200. Convert \frac{1037}{100} and \frac{5}{8} to fractions with denominator 200.

$$\frac{2074}{200}-\frac{125}{200}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Since \frac{2074}{200} and \frac{125}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2074-125}{200}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Subtract 125 from 2074 to get 1949.

$$\frac{1949}{200}-\frac{-225}{\frac{12\times 2+1}{2}}$$

Divide -225 by \frac{12\times 2+1}{2} by multiplying -225 by the reciprocal of \frac{12\times 2+1}{2}.

$$\frac{1949}{200}-\frac{-225\times 2}{12\times 2+1}$$

Multiply -225 and 2 to get -450.

$$\frac{1949}{200}-\frac{-450}{12\times 2+1}$$

Multiply 12 and 2 to get 24.

$$\frac{1949}{200}-\frac{-450}{24+1}$$

Add 24 and 1 to get 25.

$$\frac{1949}{200}-\frac{-450}{25}$$

Divide -450 by 25 to get -18.

$$\frac{1949}{200}-\left(-18\right)$$

The opposite of -18 is 18.

$$\frac{1949}{200}+18$$

Convert 18 to fraction \frac{3600}{200}.

$$\frac{1949}{200}+\frac{3600}{200}$$

Since \frac{1949}{200} and \frac{3600}{200} have the same denominator, add them by adding their numerators.

$$\frac{1949+3600}{200}$$

Add 1949 and 3600 to get 5549.

$$\frac{5549}{200}$$

Factor

$$\frac{31 \cdot 179}{2 ^ {3} \cdot 5 ^ {2}} = 27\frac{149}{200} = 27.745$$