Solve {l}{14+2/7*1/4=1/8}{3/4:frac{2}{3}-frac{3}{8}=frac{1}{8}}

$$\left. \begin{array} { l } { 14 + \frac { 2 } { 7 } \cdot \frac { 1 } { 4 } = \frac { 1 } { 8 } } \\ { \frac { 3 } { 4 } : \frac { 2 } { 3 } - \frac { 3 } { 8 } = \frac { 1 } { 8 } } \end{array} \right.$$

Verify

Solution Steps

Multiply \frac{2}{7} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$14+\frac{2\times 1}{7\times 4}=\frac{1}{8}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Do the multiplications in the fraction \frac{2\times 1}{7\times 4}.

$$14+\frac{2}{28}=\frac{1}{8}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Reduce the fraction \frac{2}{28} to lowest terms by extracting and canceling out 2.

$$14+\frac{1}{14}=\frac{1}{8}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Convert 14 to fraction \frac{196}{14}.

$$\frac{196}{14}+\frac{1}{14}=\frac{1}{8}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Since \frac{196}{14} and \frac{1}{14} have the same denominator, add them by adding their numerators.

$$\frac{196+1}{14}=\frac{1}{8}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Add 196 and 1 to get 197.

$$\frac{197}{14}=\frac{1}{8}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Least common multiple of 14 and 8 is 56. Convert \frac{197}{14} and \frac{1}{8} to fractions with denominator 56.

$$\frac{788}{56}=\frac{7}{56}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Compare \frac{788}{56} and \frac{7}{56}.

$$\text{false}\text{ and }\frac{\frac{3}{4}}{\frac{2}{3}}-\frac{3}{8}=\frac{1}{8}$$

Divide \frac{3}{4} by \frac{2}{3} by multiplying \frac{3}{4} by the reciprocal of \frac{2}{3}.

$$\text{false}\text{ and }\frac{3}{4}\times \frac{3}{2}-\frac{3}{8}=\frac{1}{8}$$

Multiply \frac{3}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\text{false}\text{ and }\frac{3\times 3}{4\times 2}-\frac{3}{8}=\frac{1}{8}$$

Do the multiplications in the fraction \frac{3\times 3}{4\times 2}.

$$\text{false}\text{ and }\frac{9}{8}-\frac{3}{8}=\frac{1}{8}$$

Since \frac{9}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\text{false}\text{ and }\frac{9-3}{8}=\frac{1}{8}$$

Subtract 3 from 9 to get 6.

$$\text{false}\text{ and }\frac{6}{8}=\frac{1}{8}$$

Compare \frac{6}{8} and \frac{1}{8}.

$$\text{false}\text{ and }\text{false}$$

The conjunction of \text{false} and \text{false} is \text{false}.

$$\text{false}$$