Solve {l}{7/19-5/9=5-0}{8/21+7/9=6-0}

$$\left. \begin{array} { l } { \frac { 7 } { 19 } - \frac { 5 } { 9 } = 5 - 0 } \\ { \frac { 8 } { 21 } + \frac { 7 } { 9 } = 6 - 0 } \end{array} \right.$$

Verify

Solution Steps

Least common multiple of 19 and 9 is 171. Convert \frac{7}{19} and \frac{5}{9} to fractions with denominator 171.

$$\frac{63}{171}-\frac{95}{171}=5-0\text{ and }\frac{8}{21}+\frac{7}{9}=6-0$$

Since \frac{63}{171} and \frac{95}{171} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-95}{171}=5-0\text{ and }\frac{8}{21}+\frac{7}{9}=6-0$$

Subtract 95 from 63 to get -32.

$$-\frac{32}{171}=5-0\text{ and }\frac{8}{21}+\frac{7}{9}=6-0$$

Subtract 0 from 5 to get 5.

$$-\frac{32}{171}=5\text{ and }\frac{8}{21}+\frac{7}{9}=6-0$$

Convert 5 to fraction \frac{855}{171}.

$$-\frac{32}{171}=\frac{855}{171}\text{ and }\frac{8}{21}+\frac{7}{9}=6-0$$

Compare -\frac{32}{171} and \frac{855}{171}.

$$\text{false}\text{ and }\frac{8}{21}+\frac{7}{9}=6-0$$

Least common multiple of 21 and 9 is 63. Convert \frac{8}{21} and \frac{7}{9} to fractions with denominator 63.

$$\text{false}\text{ and }\frac{24}{63}+\frac{49}{63}=6-0$$

Since \frac{24}{63} and \frac{49}{63} have the same denominator, add them by adding their numerators.

$$\text{false}\text{ and }\frac{24+49}{63}=6-0$$

Add 24 and 49 to get 73.

$$\text{false}\text{ and }\frac{73}{63}=6-0$$

Subtract 0 from 6 to get 6.

$$\text{false}\text{ and }\frac{73}{63}=6$$

Convert 6 to fraction \frac{378}{63}.

$$\text{false}\text{ and }\frac{73}{63}=\frac{378}{63}$$

Compare \frac{73}{63} and \frac{378}{63}.

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

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

$$\text{false}$$