Solve 2+(3div3/4+1/2)*(5/4-1)

$$2 + ( 3 \div \frac { 3 } { 4 } + \frac { 1 } { 2 } ) \cdot ( \frac { 5 } { 4 } - 1 )$$

Evaluate

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

Solution Steps

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

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

Cancel out 3 and 3.

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

Convert 4 to fraction \frac{8}{2}.

$$2+\left(\frac{8}{2}+\frac{1}{2}\right)\left(\frac{5}{4}-1\right)$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$2+\frac{8+1}{2}\left(\frac{5}{4}-1\right)$$

Add 8 and 1 to get 9.

$$2+\frac{9}{2}\left(\frac{5}{4}-1\right)$$

Convert 1 to fraction \frac{4}{4}.

$$2+\frac{9}{2}\left(\frac{5}{4}-\frac{4}{4}\right)$$

Since \frac{5}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{9}{2}\times \frac{5-4}{4}$$

Subtract 4 from 5 to get 1.

$$2+\frac{9}{2}\times \frac{1}{4}$$

Multiply \frac{9}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{9\times 1}{2\times 4}$$

Do the multiplications in the fraction \frac{9\times 1}{2\times 4}.

$$2+\frac{9}{8}$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{16}{8}+\frac{9}{8}$$

Since \frac{16}{8} and \frac{9}{8} have the same denominator, add them by adding their numerators.

$$\frac{16+9}{8}$$

Add 16 and 9 to get 25.

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

Factor

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