Solve (1/7-1/8div7)*8/19+1div11/18=

$$( \frac { 1 } { 7 } - \frac { 1 } { 8 } \div 7 ) \times \frac { 8 } { 19 } + 1 \div 1 \frac { 1 } { 18 } =$$

Evaluate

$$1$$

Solution Steps

Express \frac{\frac{1}{8}}{7} as a single fraction.

$$\left(\frac{1}{7}-\frac{1}{8\times 7}\right)\times \frac{8}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Multiply 8 and 7 to get 56.

$$\left(\frac{1}{7}-\frac{1}{56}\right)\times \frac{8}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Least common multiple of 7 and 56 is 56. Convert \frac{1}{7} and \frac{1}{56} to fractions with denominator 56.

$$\left(\frac{8}{56}-\frac{1}{56}\right)\times \frac{8}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Since \frac{8}{56} and \frac{1}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-1}{56}\times \frac{8}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Subtract 1 from 8 to get 7.

$$\frac{7}{56}\times \frac{8}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Reduce the fraction \frac{7}{56} to lowest terms by extracting and canceling out 7.

$$\frac{1}{8}\times \frac{8}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Multiply \frac{1}{8} times \frac{8}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 8}{8\times 19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{1}{19}+\frac{1}{\frac{1\times 18+1}{18}}$$

Divide 1 by \frac{1\times 18+1}{18} by multiplying 1 by the reciprocal of \frac{1\times 18+1}{18}.

$$\frac{1}{19}+\frac{18}{1\times 18+1}$$

Multiply 1 and 18 to get 18.

$$\frac{1}{19}+\frac{18}{18+1}$$

Add 18 and 1 to get 19.

$$\frac{1}{19}+\frac{18}{19}$$

Since \frac{1}{19} and \frac{18}{19} have the same denominator, add them by adding their numerators.

$$\frac{1+18}{19}$$

Add 1 and 18 to get 19.

$$\frac{19}{19}$$

Divide 19 by 19 to get 1.

$$1$$

Factor

$$1$$