Solve ((3/4-1/2)div4/3+1))(-3/4+frac{1}{3})*frac{3}{2}

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

Evaluate

$$\frac{19}{16}=1.1875$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{4}}{\frac{4}{3}}+1$$

Divide \frac{1}{4} by \frac{4}{3} by multiplying \frac{1}{4} by the reciprocal of \frac{4}{3}.

$$\frac{1}{4}\times \frac{3}{4}+1$$

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

$$\frac{1\times 3}{4\times 4}+1$$

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

$$\frac{3}{16}+1$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{3}{16}+\frac{16}{16}$$

Since \frac{3}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$\frac{3+16}{16}$$

Add 3 and 16 to get 19.

$$\frac{19}{16}$$

Factor

$$\frac{19}{2 ^ {4}} = 1\frac{3}{16} = 1.1875$$