Solve 1+1/5(-1/5+1/3)+[1/10+(-frac{1}{5})]+(-frac{1}{25})

$$1 + \frac { 1 } { 5 } ( - \frac { 1 } { 5 } + \frac { 1 } { 3 } ) + [ \frac { 1 } { 10 } + ( - \frac { 1 } { 5 } ) ] + ( - \frac { 1 } { 25 } )$$

Evaluate

$$\frac{133}{150}\approx 0.886666667$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert -\frac{1}{5} and \frac{1}{3} to fractions with denominator 15.

$$1+\frac{1}{5}\left(-\frac{3}{15}+\frac{5}{15}\right)+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Since -\frac{3}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{5}\times \frac{-3+5}{15}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Add -3 and 5 to get 2.

$$1+\frac{1}{5}\times \frac{2}{15}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Multiply \frac{1}{5} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{1\times 2}{5\times 15}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Do the multiplications in the fraction \frac{1\times 2}{5\times 15}.

$$1+\frac{2}{75}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Convert 1 to fraction \frac{75}{75}.

$$\frac{75}{75}+\frac{2}{75}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Since \frac{75}{75} and \frac{2}{75} have the same denominator, add them by adding their numerators.

$$\frac{75+2}{75}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Add 75 and 2 to get 77.

$$\frac{77}{75}+\frac{1}{10}-\frac{1}{5}-\frac{1}{25}$$

Least common multiple of 75 and 10 is 150. Convert \frac{77}{75} and \frac{1}{10} to fractions with denominator 150.

$$\frac{154}{150}+\frac{15}{150}-\frac{1}{5}-\frac{1}{25}$$

Since \frac{154}{150} and \frac{15}{150} have the same denominator, add them by adding their numerators.

$$\frac{154+15}{150}-\frac{1}{5}-\frac{1}{25}$$

Add 154 and 15 to get 169.

$$\frac{169}{150}-\frac{1}{5}-\frac{1}{25}$$

Least common multiple of 150 and 5 is 150. Convert \frac{169}{150} and \frac{1}{5} to fractions with denominator 150.

$$\frac{169}{150}-\frac{30}{150}-\frac{1}{25}$$

Since \frac{169}{150} and \frac{30}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{169-30}{150}-\frac{1}{25}$$

Subtract 30 from 169 to get 139.

$$\frac{139}{150}-\frac{1}{25}$$

Least common multiple of 150 and 25 is 150. Convert \frac{139}{150} and \frac{1}{25} to fractions with denominator 150.

$$\frac{139}{150}-\frac{6}{150}$$

Since \frac{139}{150} and \frac{6}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{139-6}{150}$$

Subtract 6 from 139 to get 133.

$$\frac{133}{150}$$

Factor

$$\frac{7 \cdot 19}{2 \cdot 3 \cdot 5 ^ {2}} = 0.8866666666666667$$