Solve 9/4*(4/3-4/6)+(4/6divfrac{8}{3})

$$\frac { 9 } { 4 } \times ( \frac { 4 } { 3 } - \frac { 4 } { 6 } ) + ( \frac { 4 } { 6 } \div \frac { 8 } { 3 } )$$

Evaluate

$$\frac{7}{4}=1.75$$

Solution Steps

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

$$\frac{9}{4}\left(\frac{4}{3}-\frac{2}{3}\right)+\frac{\frac{4}{6}}{\frac{8}{3}}$$

Since \frac{4}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{4}\times \frac{4-2}{3}+\frac{\frac{4}{6}}{\frac{8}{3}}$$

Subtract 2 from 4 to get 2.

$$\frac{9}{4}\times \frac{2}{3}+\frac{\frac{4}{6}}{\frac{8}{3}}$$

Multiply \frac{9}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 2}{4\times 3}+\frac{\frac{4}{6}}{\frac{8}{3}}$$

Do the multiplications in the fraction \frac{9\times 2}{4\times 3}.

$$\frac{18}{12}+\frac{\frac{4}{6}}{\frac{8}{3}}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$\frac{3}{2}+\frac{\frac{4}{6}}{\frac{8}{3}}$$

Divide \frac{4}{6} by \frac{8}{3} by multiplying \frac{4}{6} by the reciprocal of \frac{8}{3}.

$$\frac{3}{2}+\frac{4\times 3}{6\times 8}$$

Cancel out 2\times 2\times 3 in both numerator and denominator.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{6}{4}+\frac{1}{4}$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{4}$$

Add 6 and 1 to get 7.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$