Solve 3-1/2[2-1/4(2/5+1)]=?

$$3 - \frac { 1 } { 2 } [ 2 - \frac { 1 } { 4 } ( \frac { 2 } { 5 } + 1 ) ] = ?$$

Evaluate

$$\frac{87}{40}=2.175$$

Solution Steps

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

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

Since \frac{2}{5} and \frac{5}{5} have the same denominator, add them by adding their numerators.

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

Add 2 and 5 to get 7.

$$3-\frac{1}{2}\left(2-\frac{1}{4}\times \frac{7}{5}\right)$$

Multiply \frac{1}{4} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$3-\frac{1}{2}\left(2-\frac{1\times 7}{4\times 5}\right)$$

Do the multiplications in the fraction \frac{1\times 7}{4\times 5}.

$$3-\frac{1}{2}\left(2-\frac{7}{20}\right)$$

Convert 2 to fraction \frac{40}{20}.

$$3-\frac{1}{2}\left(\frac{40}{20}-\frac{7}{20}\right)$$

Since \frac{40}{20} and \frac{7}{20} have the same denominator, subtract them by subtracting their numerators.

$$3-\frac{1}{2}\times \frac{40-7}{20}$$

Subtract 7 from 40 to get 33.

$$3-\frac{1}{2}\times \frac{33}{20}$$

Multiply \frac{1}{2} times \frac{33}{20} by multiplying numerator times numerator and denominator times denominator.

$$3-\frac{1\times 33}{2\times 20}$$

Do the multiplications in the fraction \frac{1\times 33}{2\times 20}.

$$3-\frac{33}{40}$$

Convert 3 to fraction \frac{120}{40}.

$$\frac{120}{40}-\frac{33}{40}$$

Since \frac{120}{40} and \frac{33}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{120-33}{40}$$

Subtract 33 from 120 to get 87.

$$\frac{87}{40}$$

Factor

$$\frac{3 \cdot 29}{2 ^ {3} \cdot 5} = 2\frac{7}{40} = 2.175$$