Solve 1/2+7/9div[7/10*11/4]

$$\frac { 1 } { 2 } + \frac { 7 } { 9 } \div [ \frac { 7 } { 10 } \times 1 \frac { 1 } { 4 } ]$$

Evaluate

$$\frac{25}{18}\approx 1.388888889$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{1}{2}+\frac{\frac{7}{9}}{\frac{7}{10}\times \frac{4+1}{4}}$$

Add 4 and 1 to get 5.

$$\frac{1}{2}+\frac{\frac{7}{9}}{\frac{7}{10}\times \frac{5}{4}}$$

Multiply \frac{7}{10} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{\frac{7}{9}}{\frac{7\times 5}{10\times 4}}$$

Do the multiplications in the fraction \frac{7\times 5}{10\times 4}.

$$\frac{1}{2}+\frac{\frac{7}{9}}{\frac{35}{40}}$$

Reduce the fraction \frac{35}{40} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+\frac{\frac{7}{9}}{\frac{7}{8}}$$

Divide \frac{7}{9} by \frac{7}{8} by multiplying \frac{7}{9} by the reciprocal of \frac{7}{8}.

$$\frac{1}{2}+\frac{7}{9}\times \frac{8}{7}$$

Multiply \frac{7}{9} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{7\times 8}{9\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{1}{2}+\frac{8}{9}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{8}{9} to fractions with denominator 18.

$$\frac{9}{18}+\frac{16}{18}$$

Since \frac{9}{18} and \frac{16}{18} have the same denominator, add them by adding their numerators.

$$\frac{9+16}{18}$$

Add 9 and 16 to get 25.

$$\frac{25}{18}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3 ^ {2}} = 1\frac{7}{18} = 1.3888888888888888$$