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

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

Evaluate

$$\frac{20}{21}\approx 0.952380952$$

Solution Steps

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

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

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

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

Subtract 1 from 2 to get 1.

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

Divide \frac{1}{2} by \frac{3}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{4}.

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

Multiply \frac{1}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 4}{2\times 3}.

$$\frac{4}{6}+\frac{\frac{3}{2}-1}{2-\frac{1}{4}}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Subtract 2 from 3 to get 1.

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

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

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

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

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

Subtract 1 from 8 to get 7.

$$\frac{2}{3}+\frac{\frac{1}{2}}{\frac{7}{4}}$$

Divide \frac{1}{2} by \frac{7}{4} by multiplying \frac{1}{2} by the reciprocal of \frac{7}{4}.

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

Multiply \frac{1}{2} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 4}{2\times 7}.

$$\frac{2}{3}+\frac{4}{14}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 3 and 7 is 21. Convert \frac{2}{3} and \frac{2}{7} to fractions with denominator 21.

$$\frac{14}{21}+\frac{6}{21}$$

Since \frac{14}{21} and \frac{6}{21} have the same denominator, add them by adding their numerators.

$$\frac{14+6}{21}$$

Add 14 and 6 to get 20.

$$\frac{20}{21}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3 \cdot 7} = 0.9523809523809523$$