Solve 3-1/2[1-1/3(1-1/5)]

$$3 - \frac { 1 } { 2 } [ 1 - \frac { 1 } { 3 } ( 1 - \frac { 1 } { 5 } ) ]$$

Evaluate

$$\frac{79}{30}\approx 2.633333333$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$3-\frac{1}{2}\left(1-\frac{1}{3}\left(\frac{5}{5}-\frac{1}{5}\right)\right)$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$3-\frac{1}{2}\left(1-\frac{1}{3}\times \frac{5-1}{5}\right)$$

Subtract 1 from 5 to get 4.

$$3-\frac{1}{2}\left(1-\frac{1}{3}\times \frac{4}{5}\right)$$

Multiply \frac{1}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$3-\frac{1}{2}\left(1-\frac{1\times 4}{3\times 5}\right)$$

Do the multiplications in the fraction \frac{1\times 4}{3\times 5}.

$$3-\frac{1}{2}\left(1-\frac{4}{15}\right)$$

Convert 1 to fraction \frac{15}{15}.

$$3-\frac{1}{2}\left(\frac{15}{15}-\frac{4}{15}\right)$$

Since \frac{15}{15} and \frac{4}{15} have the same denominator, subtract them by subtracting their numerators.

$$3-\frac{1}{2}\times \frac{15-4}{15}$$

Subtract 4 from 15 to get 11.

$$3-\frac{1}{2}\times \frac{11}{15}$$

Multiply \frac{1}{2} times \frac{11}{15} by multiplying numerator times numerator and denominator times denominator.

$$3-\frac{1\times 11}{2\times 15}$$

Do the multiplications in the fraction \frac{1\times 11}{2\times 15}.

$$3-\frac{11}{30}$$

Convert 3 to fraction \frac{90}{30}.

$$\frac{90}{30}-\frac{11}{30}$$

Since \frac{90}{30} and \frac{11}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{90-11}{30}$$

Subtract 11 from 90 to get 79.

$$\frac{79}{30}$$

Factor

$$\frac{79}{2 \cdot 3 \cdot 5} = 2\frac{19}{30} = 2.6333333333333333$$