Solve 1+1/2/1+frac{3{4}}

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

Evaluate

$$\frac{6}{7}\approx 0.857142857$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

Add 4 and 3 to get 7.

$$\frac{\frac{3}{2}}{\frac{7}{4}}$$

Divide \frac{3}{2} by \frac{7}{4} by multiplying \frac{3}{2} by the reciprocal of \frac{7}{4}.

$$\frac{3}{2}\times \frac{4}{7}$$

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

$$\frac{3\times 4}{2\times 7}$$

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

$$\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{6}{7}$$

Factor

$$\frac{2 \cdot 3}{7} = 0.8571428571428571$$