Solve 1/2+1/2*3/13-3/16+frac{1}{2}text{of}frac{3}{2}

$$\frac { 1 } { 2 } + \frac { 1 } { 2 } \times \frac { 3 } { 13 } - \frac { 3 } { 16 } + \frac { 1 } { 2 } \text { of } \frac { 3 } { 2 }$$

Evaluate

$$\frac{245}{208}\approx 1.177884615$$

Solution Steps

Multiply \frac{1}{2} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{1\times 3}{2\times 13}-\frac{3}{16}+\frac{1}{2}\times \frac{3}{2}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 13}.

$$\frac{1}{2}+\frac{3}{26}-\frac{3}{16}+\frac{1}{2}\times \frac{3}{2}$$

Least common multiple of 2 and 26 is 26. Convert \frac{1}{2} and \frac{3}{26} to fractions with denominator 26.

$$\frac{13}{26}+\frac{3}{26}-\frac{3}{16}+\frac{1}{2}\times \frac{3}{2}$$

Since \frac{13}{26} and \frac{3}{26} have the same denominator, add them by adding their numerators.

$$\frac{13+3}{26}-\frac{3}{16}+\frac{1}{2}\times \frac{3}{2}$$

Add 13 and 3 to get 16.

$$\frac{16}{26}-\frac{3}{16}+\frac{1}{2}\times \frac{3}{2}$$

Reduce the fraction \frac{16}{26} to lowest terms by extracting and canceling out 2.

$$\frac{8}{13}-\frac{3}{16}+\frac{1}{2}\times \frac{3}{2}$$

Least common multiple of 13 and 16 is 208. Convert \frac{8}{13} and \frac{3}{16} to fractions with denominator 208.

$$\frac{128}{208}-\frac{39}{208}+\frac{1}{2}\times \frac{3}{2}$$

Since \frac{128}{208} and \frac{39}{208} have the same denominator, subtract them by subtracting their numerators.

$$\frac{128-39}{208}+\frac{1}{2}\times \frac{3}{2}$$

Subtract 39 from 128 to get 89.

$$\frac{89}{208}+\frac{1}{2}\times \frac{3}{2}$$

Multiply \frac{1}{2} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{89}{208}+\frac{1\times 3}{2\times 2}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 2}.

$$\frac{89}{208}+\frac{3}{4}$$

Least common multiple of 208 and 4 is 208. Convert \frac{89}{208} and \frac{3}{4} to fractions with denominator 208.

$$\frac{89}{208}+\frac{156}{208}$$

Since \frac{89}{208} and \frac{156}{208} have the same denominator, add them by adding their numerators.

$$\frac{89+156}{208}$$

Add 89 and 156 to get 245.

$$\frac{245}{208}$$

Factor

$$\frac{5 \cdot 7 ^ {2}}{2 ^ {4} \cdot 13} = 1\frac{37}{208} = 1.1778846153846154$$