Solve 6/3*3/7=6/5*7/3=frac{42}{13}

$$\frac { 6 } { 3 } \cdot \frac { 3 } { 7 } = \frac { 6 } { 5 } \cdot \frac { 7 } { 3 } = \frac { 42 } { 13 }$$

Verify

Solution Steps

Divide 6 by 3 to get 2.

$$2\times \frac{3}{7}=\frac{6}{5}\times \frac{7}{3}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Express 2\times \frac{3}{7} as a single fraction.

$$\frac{2\times 3}{7}=\frac{6}{5}\times \frac{7}{3}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{7}=\frac{6}{5}\times \frac{7}{3}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Multiply \frac{6}{5} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{7}=\frac{6\times 7}{5\times 3}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Do the multiplications in the fraction \frac{6\times 7}{5\times 3}.

$$\frac{6}{7}=\frac{42}{15}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Reduce the fraction \frac{42}{15} to lowest terms by extracting and canceling out 3.

$$\frac{6}{7}=\frac{14}{5}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Least common multiple of 7 and 5 is 35. Convert \frac{6}{7} and \frac{14}{5} to fractions with denominator 35.

$$\frac{30}{35}=\frac{98}{35}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Compare \frac{30}{35} and \frac{98}{35}.

$$\text{false}\text{ and }\frac{6}{5}\times \frac{7}{3}=\frac{42}{13}$$

Multiply \frac{6}{5} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\text{false}\text{ and }\frac{6\times 7}{5\times 3}=\frac{42}{13}$$

Do the multiplications in the fraction \frac{6\times 7}{5\times 3}.

$$\text{false}\text{ and }\frac{42}{15}=\frac{42}{13}$$

Reduce the fraction \frac{42}{15} to lowest terms by extracting and canceling out 3.

$$\text{false}\text{ and }\frac{14}{5}=\frac{42}{13}$$

Least common multiple of 5 and 13 is 65. Convert \frac{14}{5} and \frac{42}{13} to fractions with denominator 65.

$$\text{false}\text{ and }\frac{182}{65}=\frac{210}{65}$$

Compare \frac{182}{65} and \frac{210}{65}.

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

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

$$\text{false}$$