Solve (1/4/frac{1{2}}-3/4/frac{3{1}})*frac{1}{2}+frac{7}{5}

$$( \frac{ \frac{ 1 }{ 4 } }{ \frac{ 1 }{ 2 } } - \frac{ \frac{ 3 }{ 4 } }{ \frac{ 3 }{ 1 } } ) \times \frac{ 1 }{ 2 } + \frac{ 7 }{ 5 }$$

Evaluate

$$\frac{61}{40}=1.525$$

Solution Steps

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

$$\left(\frac{1}{4}\times 2-\frac{\frac{3}{4}}{\frac{3}{1}}\right)\times \frac{1}{2}+\frac{7}{5}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\left(\frac{2}{4}-\frac{\frac{3}{4}}{\frac{3}{1}}\right)\times \frac{1}{2}+\frac{7}{5}$$

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

$$\left(\frac{1}{2}-\frac{\frac{3}{4}}{\frac{3}{1}}\right)\times \frac{1}{2}+\frac{7}{5}$$

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

$$\left(\frac{1}{2}-\frac{3}{4\times 3}\right)\times \frac{1}{2}+\frac{7}{5}$$

Multiply 4 and 3 to get 12.

$$\left(\frac{1}{2}-\frac{3}{12}\right)\times \frac{1}{2}+\frac{7}{5}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\left(\frac{1}{2}-\frac{1}{4}\right)\times \frac{1}{2}+\frac{7}{5}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\left(\frac{2}{4}-\frac{1}{4}\right)\times \frac{1}{2}+\frac{7}{5}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-1}{4}\times \frac{1}{2}+\frac{7}{5}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{4}\times \frac{1}{2}+\frac{7}{5}$$

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

$$\frac{1\times 1}{4\times 2}+\frac{7}{5}$$

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

$$\frac{1}{8}+\frac{7}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{1}{8} and \frac{7}{5} to fractions with denominator 40.

$$\frac{5}{40}+\frac{56}{40}$$

Since \frac{5}{40} and \frac{56}{40} have the same denominator, add them by adding their numerators.

$$\frac{5+56}{40}$$

Add 5 and 56 to get 61.

$$\frac{61}{40}$$

Factor

$$\frac{61}{2 ^ {3} \cdot 5} = 1\frac{21}{40} = 1.525$$