Solve 44/5div3/5text{of}5+4/5*3/10-frac{1}{5}

$$4 \frac { 4 } { 5 } \div \frac { 3 } { 5 } \text { of } 5 + \frac { 4 } { 5 } \times \frac { 3 } { 10 } - \frac { 1 } { 5 }$$

Evaluate

$$\frac{1001}{25}=40.04$$

Solution Steps

Divide \frac{4\times 5+4}{5} by \frac{3}{5} by multiplying \frac{4\times 5+4}{5} by the reciprocal of \frac{3}{5}.

$$\frac{\left(4\times 5+4\right)\times 5}{5\times 3}\times 5+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4+4\times 5}{3}\times 5+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$$

Multiply 4 and 5 to get 20.

$$\frac{4+20}{3}\times 5+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$$

Add 4 and 20 to get 24.

$$\frac{24}{3}\times 5+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$$

Divide 24 by 3 to get 8.

$$8\times 5+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$$

Multiply 8 and 5 to get 40.

$$40+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$$

Multiply \frac{4}{5} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$40+\frac{4\times 3}{5\times 10}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{4\times 3}{5\times 10}.

$$40+\frac{12}{50}-\frac{1}{5}$$

Reduce the fraction \frac{12}{50} to lowest terms by extracting and canceling out 2.

$$40+\frac{6}{25}-\frac{1}{5}$$

Convert 40 to fraction \frac{1000}{25}.

$$\frac{1000}{25}+\frac{6}{25}-\frac{1}{5}$$

Since \frac{1000}{25} and \frac{6}{25} have the same denominator, add them by adding their numerators.

$$\frac{1000+6}{25}-\frac{1}{5}$$

Add 1000 and 6 to get 1006.

$$\frac{1006}{25}-\frac{1}{5}$$

Least common multiple of 25 and 5 is 25. Convert \frac{1006}{25} and \frac{1}{5} to fractions with denominator 25.

$$\frac{1006}{25}-\frac{5}{25}$$

Since \frac{1006}{25} and \frac{5}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1006-5}{25}$$

Subtract 5 from 1006 to get 1001.

$$\frac{1001}{25}$$

Factor

$$\frac{7 \cdot 11 \cdot 13}{5 ^ {2}} = 40\frac{1}{25} = 40.04$$