Solve 1/frac{5-1{4+1}}{3-1/2}

$$\frac { 1 } { \frac { 5 - 1 } { 4 + 1 } } { 3 - \frac { 1 } { 2 } }$$

Evaluate

$$\frac{25}{8}=3.125$$

Solution Steps

Divide 1 by \frac{5-1}{4+1} by multiplying 1 by the reciprocal of \frac{5-1}{4+1}.

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

Add 4 and 1 to get 5.

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

Subtract 1 from 5 to get 4.

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

Convert 3 to fraction \frac{6}{2}.

$$\frac{5}{4}\left(\frac{6}{2}-\frac{1}{2}\right)$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}\times \frac{6-1}{2}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{4}\times \frac{5}{2}$$

Multiply \frac{5}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5}{4\times 2}$$

Do the multiplications in the fraction \frac{5\times 5}{4\times 2}.

$$\frac{25}{8}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3}} = 3\frac{1}{8} = 3.125$$