Solve 1+{15/4*[6/8:1/2+3/4]}}

$$1 + \{ \frac { 15 } { 4 } \cdot [ \frac { 6 } { 8 } : \frac { 1 } { 2 } + \frac { 3 } { 4 } ] \} \}$$

Evaluate

$$\frac{151}{16}=9.4375$$

Solution Steps

Divide \frac{6}{8} by \frac{1}{2} by multiplying \frac{6}{8} by the reciprocal of \frac{1}{2}.

$$1+\frac{15}{4}\left(\frac{6\times 2}{8}+\frac{3}{4}\right)$$

Multiply 6 and 2 to get 12.

$$1+\frac{15}{4}\left(\frac{12}{8}+\frac{3}{4}\right)$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$1+\frac{15}{4}\left(\frac{3}{2}+\frac{3}{4}\right)$$

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

$$1+\frac{15}{4}\left(\frac{6}{4}+\frac{3}{4}\right)$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$1+\frac{15}{4}\times \frac{6+3}{4}$$

Add 6 and 3 to get 9.

$$1+\frac{15}{4}\times \frac{9}{4}$$

Multiply \frac{15}{4} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{15\times 9}{4\times 4}$$

Do the multiplications in the fraction \frac{15\times 9}{4\times 4}.

$$1+\frac{135}{16}$$

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

$$\frac{16}{16}+\frac{135}{16}$$

Since \frac{16}{16} and \frac{135}{16} have the same denominator, add them by adding their numerators.

$$\frac{16+135}{16}$$

Add 16 and 135 to get 151.

$$\frac{151}{16}$$

Factor

$$\frac{151}{2 ^ {4}} = 9\frac{7}{16} = 9.4375$$