Solve 1/2text{of}(4/3*31/2div7/4-frac{1}{2})=?

$$\frac { 1 } { 2 } \text { of } ( \frac { 4 } { 3 } \times 3 \frac { 1 } { 2 } \div \frac { 7 } { 4 } - \frac { 1 } { 2 } ) = ?$$

Evaluate

$$\frac{13}{12}\approx 1.083333333$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{1}{2}\left(\frac{\frac{4}{3}\times \frac{6+1}{2}}{\frac{7}{4}}-\frac{1}{2}\right)$$

Add 6 and 1 to get 7.

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

Multiply \frac{4}{3} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\times 7}{3\times 2}.

$$\frac{1}{2}\left(\frac{\frac{28}{6}}{\frac{7}{4}}-\frac{1}{2}\right)$$

Reduce the fraction \frac{28}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\left(\frac{\frac{14}{3}}{\frac{7}{4}}-\frac{1}{2}\right)$$

Divide \frac{14}{3} by \frac{7}{4} by multiplying \frac{14}{3} by the reciprocal of \frac{7}{4}.

$$\frac{1}{2}\left(\frac{14}{3}\times \frac{4}{7}-\frac{1}{2}\right)$$

Multiply \frac{14}{3} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}\left(\frac{14\times 4}{3\times 7}-\frac{1}{2}\right)$$

Do the multiplications in the fraction \frac{14\times 4}{3\times 7}.

$$\frac{1}{2}\left(\frac{56}{21}-\frac{1}{2}\right)$$

Reduce the fraction \frac{56}{21} to lowest terms by extracting and canceling out 7.

$$\frac{1}{2}\left(\frac{8}{3}-\frac{1}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{1}{2}\left(\frac{16}{6}-\frac{3}{6}\right)$$

Since \frac{16}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{16-3}{6}$$

Subtract 3 from 16 to get 13.

$$\frac{1}{2}\times \frac{13}{6}$$

Multiply \frac{1}{2} times \frac{13}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 13}{2\times 6}$$

Do the multiplications in the fraction \frac{1\times 13}{2\times 6}.

$$\frac{13}{12}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 3} = 1\frac{1}{12} = 1.0833333333333333$$