Solve [(5-21/2)*20-41/2div99/100]*3.2+0.24div1/5

$$[ ( 5 - 2 \frac { 1 } { 2 } ) \times 20 - 4 \frac { 1 } { 2 } \div \frac { 99 } { 100 } ] \times 3.2 + 0.24 \div \frac { 1 } { 5 }$$

Evaluate

$$\frac{8066}{55}\approx 146.654545455$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\left(\left(5-\frac{4+1}{2}\right)\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Add 4 and 1 to get 5.

$$\left(\left(5-\frac{5}{2}\right)\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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

$$\left(\left(\frac{10}{2}-\frac{5}{2}\right)\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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

$$\left(\frac{10-5}{2}\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Subtract 5 from 10 to get 5.

$$\left(\frac{5}{2}\times 20-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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

$$\left(\frac{5\times 20}{2}-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Multiply 5 and 20 to get 100.

$$\left(\frac{100}{2}-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Divide 100 by 2 to get 50.

$$\left(50-\frac{\frac{4\times 2+1}{2}}{\frac{99}{100}}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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}.

$$\left(50-\frac{\left(4\times 2+1\right)\times 100}{2\times 99}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Cancel out 2 in both numerator and denominator.

$$\left(50-\frac{50\left(1+2\times 4\right)}{99}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Multiply 2 and 4 to get 8.

$$\left(50-\frac{50\left(1+8\right)}{99}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Add 1 and 8 to get 9.

$$\left(50-\frac{50\times 9}{99}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Multiply 50 and 9 to get 450.

$$\left(50-\frac{450}{99}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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

$$\left(50-\frac{50}{11}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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

$$\left(\frac{550}{11}-\frac{50}{11}\right)\times 3.2+\frac{0.24}{\frac{1}{5}}$$

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

$$\frac{550-50}{11}\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Subtract 50 from 550 to get 500.

$$\frac{500}{11}\times 3.2+\frac{0.24}{\frac{1}{5}}$$

Convert decimal number 3.2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{500}{11}\times \frac{16}{5}+\frac{0.24}{\frac{1}{5}}$$

Multiply \frac{500}{11} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{500\times 16}{11\times 5}+\frac{0.24}{\frac{1}{5}}$$

Do the multiplications in the fraction \frac{500\times 16}{11\times 5}.

$$\frac{8000}{55}+\frac{0.24}{\frac{1}{5}}$$

Reduce the fraction \frac{8000}{55} to lowest terms by extracting and canceling out 5.

$$\frac{1600}{11}+\frac{0.24}{\frac{1}{5}}$$

Divide 0.24 by \frac{1}{5} by multiplying 0.24 by the reciprocal of \frac{1}{5}.

$$\frac{1600}{11}+0.24\times 5$$

Multiply 0.24 and 5 to get 1.2.

$$\frac{1600}{11}+1.2$$

Convert decimal number 1.2 to fraction \frac{12}{10}. Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1600}{11}+\frac{6}{5}$$

Least common multiple of 11 and 5 is 55. Convert \frac{1600}{11} and \frac{6}{5} to fractions with denominator 55.

$$\frac{8000}{55}+\frac{66}{55}$$

Since \frac{8000}{55} and \frac{66}{55} have the same denominator, add them by adding their numerators.

$$\frac{8000+66}{55}$$

Add 8000 and 66 to get 8066.

$$\frac{8066}{55}$$

Factor

$$\frac{2 \cdot 37 \cdot 109}{5 \cdot 11} = 146\frac{36}{55} = 146.65454545454546$$