Solve 7/8div11/8-1/3text{of}12div(1+7/9)

$$\frac { 7 } { 8 } \div 1 \frac { 1 } { 8 } - \frac { 1 } { 3 } \text { of } 12 \div ( 1 + \frac { 7 } { 9 } )$$

Evaluate

$$-\frac{53}{36}\approx -1.472222222$$

Solution Steps

Divide \frac{7}{8} by \frac{1\times 8+1}{8} by multiplying \frac{7}{8} by the reciprocal of \frac{1\times 8+1}{8}.

$$\frac{7\times 8}{8\left(1\times 8+1\right)}-\frac{\frac{1}{3}\times 12}{1+\frac{7}{9}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{7}{1+8}-\frac{\frac{1}{3}\times 12}{1+\frac{7}{9}}$$

Add 1 and 8 to get 9.

$$\frac{7}{9}-\frac{\frac{1}{3}\times 12}{1+\frac{7}{9}}$$

Multiply \frac{1}{3} and 12 to get \frac{12}{3}.

$$\frac{7}{9}-\frac{\frac{12}{3}}{1+\frac{7}{9}}$$

Divide 12 by 3 to get 4.

$$\frac{7}{9}-\frac{4}{1+\frac{7}{9}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{7}{9}-\frac{4}{\frac{9}{9}+\frac{7}{9}}$$

Since \frac{9}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$\frac{7}{9}-\frac{4}{\frac{9+7}{9}}$$

Add 9 and 7 to get 16.

$$\frac{7}{9}-\frac{4}{\frac{16}{9}}$$

Divide 4 by \frac{16}{9} by multiplying 4 by the reciprocal of \frac{16}{9}.

$$\frac{7}{9}-4\times \frac{9}{16}$$

Express 4\times \frac{9}{16} as a single fraction.

$$\frac{7}{9}-\frac{4\times 9}{16}$$

Multiply 4 and 9 to get 36.

$$\frac{7}{9}-\frac{36}{16}$$

Reduce the fraction \frac{36}{16} to lowest terms by extracting and canceling out 4.

$$\frac{7}{9}-\frac{9}{4}$$

Least common multiple of 9 and 4 is 36. Convert \frac{7}{9} and \frac{9}{4} to fractions with denominator 36.

$$\frac{28}{36}-\frac{81}{36}$$

Since \frac{28}{36} and \frac{81}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-81}{36}$$

Subtract 81 from 28 to get -53.

$$-\frac{53}{36}$$

Factor

$$-\frac{53}{36} = -1\frac{17}{36} = -1.4722222222222223$$