Solve (11/3+5/6)div4/9

$$( 1 \frac { 1 } { 3 } + \frac { 5 } { 6 } ) \div \frac { 4 } { 9 }$$

Evaluate

$$\frac{39}{8}=4.875$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\frac{3+1}{3}+\frac{5}{6}}{\frac{4}{9}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{4}{3}+\frac{5}{6}}{\frac{4}{9}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{\frac{8}{6}+\frac{5}{6}}{\frac{4}{9}}$$

Since \frac{8}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8+5}{6}}{\frac{4}{9}}$$

Add 8 and 5 to get 13.

$$\frac{\frac{13}{6}}{\frac{4}{9}}$$

Divide \frac{13}{6} by \frac{4}{9} by multiplying \frac{13}{6} by the reciprocal of \frac{4}{9}.

$$\frac{13}{6}\times \frac{9}{4}$$

Multiply \frac{13}{6} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 9}{6\times 4}$$

Do the multiplications in the fraction \frac{13\times 9}{6\times 4}.

$$\frac{117}{24}$$

Reduce the fraction \frac{117}{24} to lowest terms by extracting and canceling out 3.

$$\frac{39}{8}$$

Factor

$$\frac{3 \cdot 13}{2 ^ {3}} = 4\frac{7}{8} = 4.875$$