Solve [3/2*(4-1/2)+1/2*(2-3/4)]div(frac{2}{3}+frac{1}{2})=

$$[ \frac { 3 } { 2 } \cdot ( 4 - \frac { 1 } { 2 } ) + \frac { 1 } { 2 } \cdot ( 2 - \frac { 3 } { 4 } ) ] \div ( \frac { 2 } { 3 } + \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{141}{28}\approx 5.035714286$$

Solution Steps

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

$$\frac{\frac{3}{2}\left(\frac{8}{2}-\frac{1}{2}\right)+\frac{1}{2}\left(2-\frac{3}{4}\right)}{\frac{2}{3}+\frac{1}{2}}$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}\times \frac{8-1}{2}+\frac{1}{2}\left(2-\frac{3}{4}\right)}{\frac{2}{3}+\frac{1}{2}}$$

Subtract 1 from 8 to get 7.

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

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

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

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

$$\frac{\frac{21}{4}+\frac{1}{2}\left(2-\frac{3}{4}\right)}{\frac{2}{3}+\frac{1}{2}}$$

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

$$\frac{\frac{21}{4}+\frac{1}{2}\left(\frac{8}{4}-\frac{3}{4}\right)}{\frac{2}{3}+\frac{1}{2}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21}{4}+\frac{1}{2}\times \frac{8-3}{4}}{\frac{2}{3}+\frac{1}{2}}$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{21}{4}+\frac{1}{2}\times \frac{5}{4}}{\frac{2}{3}+\frac{1}{2}}$$

Multiply \frac{1}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{21}{4}+\frac{1\times 5}{2\times 4}}{\frac{2}{3}+\frac{1}{2}}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 4}.

$$\frac{\frac{21}{4}+\frac{5}{8}}{\frac{2}{3}+\frac{1}{2}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{21}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{\frac{42}{8}+\frac{5}{8}}{\frac{2}{3}+\frac{1}{2}}$$

Since \frac{42}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{42+5}{8}}{\frac{2}{3}+\frac{1}{2}}$$

Add 42 and 5 to get 47.

$$\frac{\frac{47}{8}}{\frac{2}{3}+\frac{1}{2}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{47}{8}}{\frac{4}{6}+\frac{3}{6}}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{47}{8}}{\frac{4+3}{6}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{47}{8}}{\frac{7}{6}}$$

Divide \frac{47}{8} by \frac{7}{6} by multiplying \frac{47}{8} by the reciprocal of \frac{7}{6}.

$$\frac{47}{8}\times \frac{6}{7}$$

Multiply \frac{47}{8} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{47\times 6}{8\times 7}$$

Do the multiplications in the fraction \frac{47\times 6}{8\times 7}.

$$\frac{282}{56}$$

Reduce the fraction \frac{282}{56} to lowest terms by extracting and canceling out 2.

$$\frac{141}{28}$$

Factor

$$\frac{3 \cdot 47}{2 ^ {2} \cdot 7} = 5\frac{1}{28} = 5.035714285714286$$