Solve 1/10:1/5+1/4(3/2-frac{7}{4})

$$\frac { 1 } { 10 } : \frac { 1 } { 5 } + \frac { 1 } { 4 } ( \frac { 3 } { 2 } - \frac { 7 } { 4 } )$$

Evaluate

$$\frac{7}{16}=0.4375$$

Solution Steps

Divide \frac{1}{10} by \frac{1}{5} by multiplying \frac{1}{10} by the reciprocal of \frac{1}{5}.

$$\frac{1}{10}\times 5+\frac{1}{4}\left(\frac{3}{2}-\frac{7}{4}\right)$$

Multiply \frac{1}{10} and 5 to get \frac{5}{10}.

$$\frac{5}{10}+\frac{1}{4}\left(\frac{3}{2}-\frac{7}{4}\right)$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{1}{2}+\frac{1}{4}\left(\frac{6}{4}-\frac{7}{4}\right)$$

Since \frac{6}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}+\frac{1}{4}\times \frac{6-7}{4}$$

Subtract 7 from 6 to get -1.

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

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

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 4}.

$$\frac{1}{2}+\frac{-1}{16}$$

Fraction \frac{-1}{16} can be rewritten as -\frac{1}{16} by extracting the negative sign.

$$\frac{1}{2}-\frac{1}{16}$$

Least common multiple of 2 and 16 is 16. Convert \frac{1}{2} and \frac{1}{16} to fractions with denominator 16.

$$\frac{8}{16}-\frac{1}{16}$$

Since \frac{8}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-1}{16}$$

Subtract 1 from 8 to get 7.

$$\frac{7}{16}$$

Factor

$$\frac{7}{2 ^ {4}} = 0.4375$$