Solve 1-1/2/frac{frac{3{4}}{2-1/4}}+frac{3/2-1}{(1,3)^2}

$$\frac { 1 - \frac { 1 } { 2 } } { \frac { \frac { 3 } { 4 } } { 2 - \frac { 1 } { 4 } } } + \frac { \frac { 3 } { 2 } - 1 } { ( 1,3 ) ^ { 2 } }$$

Evaluate

$$\frac{1483}{1014}\approx 1,462524655$$

Solution Steps

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

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

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

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

Subtract 1 from 2 to get 1.

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

Convert 2 to fraction \frac{8}{4}.

$$\frac{\frac{1}{2}}{\frac{\frac{3}{4}}{\frac{8}{4}-\frac{1}{4}}}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{2}}{\frac{\frac{3}{4}}{\frac{8-1}{4}}}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

Subtract 1 from 8 to get 7.

$$\frac{\frac{1}{2}}{\frac{\frac{3}{4}}{\frac{7}{4}}}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

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

$$\frac{\frac{1}{2}}{\frac{3}{4}\times \frac{4}{7}}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

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

$$\frac{\frac{1}{2}}{\frac{3\times 4}{4\times 7}}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{1}{2}}{\frac{3}{7}}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

Divide \frac{1}{2} by \frac{3}{7} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{7}.

$$\frac{1}{2}\times \frac{7}{3}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

Multiply \frac{1}{2} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{2\times 3}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 3}.

$$\frac{7}{6}+\frac{\frac{3}{2}-1}{1,3^{2}}$$

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

$$\frac{7}{6}+\frac{\frac{3}{2}-\frac{2}{2}}{1,3^{2}}$$

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

$$\frac{7}{6}+\frac{\frac{3-2}{2}}{1,3^{2}}$$

Subtract 2 from 3 to get 1.

$$\frac{7}{6}+\frac{\frac{1}{2}}{1,3^{2}}$$

Calculate 1,3 to the power of 2 and get 1,69.

$$\frac{7}{6}+\frac{\frac{1}{2}}{1,69}$$

Express \frac{\frac{1}{2}}{1,69} as a single fraction.

$$\frac{7}{6}+\frac{1}{2\times 1,69}$$

Multiply 2 and 1,69 to get 3,38.

$$\frac{7}{6}+\frac{1}{3,38}$$

Expand \frac{1}{3,38} by multiplying both numerator and the denominator by 100.

$$\frac{7}{6}+\frac{100}{338}$$

Reduce the fraction \frac{100}{338} to lowest terms by extracting and canceling out 2.

$$\frac{7}{6}+\frac{50}{169}$$

Least common multiple of 6 and 169 is 1014. Convert \frac{7}{6} and \frac{50}{169} to fractions with denominator 1014.

$$\frac{1183}{1014}+\frac{300}{1014}$$

Since \frac{1183}{1014} and \frac{300}{1014} have the same denominator, add them by adding their numerators.

$$\frac{1183+300}{1014}$$

Add 1183 and 300 to get 1483.

$$\frac{1483}{1014}$$

Factor

$$\frac{1483}{2 \cdot 3 \cdot 13 ^ {2}} = 1\frac{469}{1014} = 1.4625246548323472$$