Solve [(5-21/2)*20-41/2div99/100]*32+024div1/5

$$[ ( 5 - 2 \frac { 1 } { 2 } ) \times 20 - 4 \frac { 1 } { 2 } \div \frac { 99 } { 100 } ] \times 32 + 024 \div \frac { 1 } { 5 }$$

Evaluate

$$\frac{16000}{11}\approx 1454.545454545$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\left(\left(5-\frac{4+1}{2}\right)\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Add 4 and 1 to get 5.

$$\left(\left(5-\frac{5}{2}\right)\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Convert 5 to fraction \frac{10}{2}.

$$\left(\left(\frac{10}{2}-\frac{5}{2}\right)\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Since \frac{10}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{10-5}{2}\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Subtract 5 from 10 to get 5.

$$\left(\frac{5}{2}\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Express \frac{5}{2}\times 20 as a single fraction.

$$\left(\frac{5\times 20}{2}-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Multiply 5 and 20 to get 100.

$$\left(\frac{100}{2}-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Divide 100 by 2 to get 50.

$$\left(50-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Divide \frac{4\times 2+1}{2} by \frac{99}{100} by multiplying \frac{4\times 2+1}{2} by the reciprocal of \frac{99}{100}.

$$\left(50-\frac{\left(4\times 2+1\right)\times 100}{2\times 99}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Cancel out 2 in both numerator and denominator.

$$\left(50-\frac{50\left(1+2\times 4\right)}{99}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Multiply 2 and 4 to get 8.

$$\left(50-\frac{50\left(1+8\right)}{99}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Add 1 and 8 to get 9.

$$\left(50-\frac{50\times 9}{99}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Multiply 50 and 9 to get 450.

$$\left(50-\frac{450}{99}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Reduce the fraction \frac{450}{99} to lowest terms by extracting and canceling out 9.

$$\left(50-\frac{50}{11}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Convert 50 to fraction \frac{550}{11}.

$$\left(\frac{550}{11}-\frac{50}{11}\right)\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Since \frac{550}{11} and \frac{50}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{550-50}{11}\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Subtract 50 from 550 to get 500.

$$\frac{500}{11}\times 32+\frac{0\times 24}{\frac{1}{5}}$$

Express \frac{500}{11}\times 32 as a single fraction.

$$\frac{500\times 32}{11}+\frac{0\times 24}{\frac{1}{5}}$$

Multiply 500 and 32 to get 16000.

$$\frac{16000}{11}+\frac{0\times 24}{\frac{1}{5}}$$

Multiply 0 and 24 to get 0.

$$\frac{16000}{11}+\frac{0}{\frac{1}{5}}$$

Zero divided by any non-zero number gives zero.

$$\frac{16000}{11}+0$$

Add \frac{16000}{11} and 0 to get \frac{16000}{11}.

$$\frac{16000}{11}$$

Factor

$$\frac{2 ^ {7} \cdot 5 ^ {3}}{11} = 1454\frac{6}{11} = 1454.5454545454545$$