Solve 3/4*22/3+5/9*6/5+frac{2}{23}*frac{23}{6}divfrac{2}{7}*frac{7}{3}

$$\frac{ 3 }{ 4 } \times 2 \frac{ 2 }{ 3 } + \frac{ 5 }{ 9 } \times \frac{ 6 }{ 5 } + \frac{ 2 }{ 23 } \times \frac{ 23 }{ 6 } \div \frac{ 2 }{ 7 } \times \frac{ 7 }{ 3 }$$

Evaluate

$$\frac{97}{18}\approx 5.388888889$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{3}{4}\times \frac{6+2}{3}+\frac{5}{9}\times \frac{6}{5}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Add 6 and 2 to get 8.

$$\frac{3}{4}\times \frac{8}{3}+\frac{5}{9}\times \frac{6}{5}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Multiply \frac{3}{4} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 8}{4\times 3}+\frac{5}{9}\times \frac{6}{5}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{4}+\frac{5}{9}\times \frac{6}{5}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Divide 8 by 4 to get 2.

$$2+\frac{5}{9}\times \frac{6}{5}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Multiply \frac{5}{9} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{5\times 6}{9\times 5}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Cancel out 5 in both numerator and denominator.

$$2+\frac{6}{9}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$2+\frac{2}{3}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}+\frac{2}{3}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+2}{3}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Add 6 and 2 to get 8.

$$\frac{8}{3}+\frac{\frac{2}{23}\times \frac{23}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

Multiply \frac{2}{23} times \frac{23}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}+\frac{\frac{2\times 23}{23\times 6}}{\frac{2}{7}}\times \frac{7}{3}$$

Cancel out 23 in both numerator and denominator.

$$\frac{8}{3}+\frac{\frac{2}{6}}{\frac{2}{7}}\times \frac{7}{3}$$

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

$$\frac{8}{3}+\frac{\frac{1}{3}}{\frac{2}{7}}\times \frac{7}{3}$$

Divide \frac{1}{3} by \frac{2}{7} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{7}.

$$\frac{8}{3}+\frac{1}{3}\times \frac{7}{2}\times \frac{7}{3}$$

Multiply \frac{1}{3} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}+\frac{1\times 7}{3\times 2}\times \frac{7}{3}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 2}.

$$\frac{8}{3}+\frac{7}{6}\times \frac{7}{3}$$

Multiply \frac{7}{6} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}+\frac{7\times 7}{6\times 3}$$

Do the multiplications in the fraction \frac{7\times 7}{6\times 3}.

$$\frac{8}{3}+\frac{49}{18}$$

Least common multiple of 3 and 18 is 18. Convert \frac{8}{3} and \frac{49}{18} to fractions with denominator 18.

$$\frac{48}{18}+\frac{49}{18}$$

Since \frac{48}{18} and \frac{49}{18} have the same denominator, add them by adding their numerators.

$$\frac{48+49}{18}$$

Add 48 and 49 to get 97.

$$\frac{97}{18}$$

Factor

$$\frac{97}{2 \cdot 3 ^ {2}} = 5\frac{7}{18} = 5.388888888888889$$