Solve 1/7div2=1/14quadquad1/3div5=1/15

$$\frac { 1 } { 7 } \div 2 = \frac { 1 } { 14 } \quad \quad \frac { 1 } { 3 } \div 5 = \frac { 1 } { 15 }$$

Verify

Solution Steps

Express \frac{\frac{1}{7}}{2} as a single fraction.

$$\frac{1}{7\times 2}=\frac{\frac{1}{14}\times \frac{1}{3}}{5}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Multiply 7 and 2 to get 14.

$$\frac{1}{14}=\frac{\frac{1}{14}\times \frac{1}{3}}{5}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Multiply \frac{1}{14} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{14}=\frac{\frac{1\times 1}{14\times 3}}{5}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Do the multiplications in the fraction \frac{1\times 1}{14\times 3}.

$$\frac{1}{14}=\frac{\frac{1}{42}}{5}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Express \frac{\frac{1}{42}}{5} as a single fraction.

$$\frac{1}{14}=\frac{1}{42\times 5}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Multiply 42 and 5 to get 210.

$$\frac{1}{14}=\frac{1}{210}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Least common multiple of 14 and 210 is 210. Convert \frac{1}{14} and \frac{1}{210} to fractions with denominator 210.

$$\frac{15}{210}=\frac{1}{210}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Compare \frac{15}{210} and \frac{1}{210}.

$$\text{false}\text{ and }\frac{\frac{1}{14}\times \frac{1}{3}}{5}=\frac{1}{15}$$

Multiply \frac{1}{14} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\text{false}\text{ and }\frac{\frac{1\times 1}{14\times 3}}{5}=\frac{1}{15}$$

Do the multiplications in the fraction \frac{1\times 1}{14\times 3}.

$$\text{false}\text{ and }\frac{\frac{1}{42}}{5}=\frac{1}{15}$$

Express \frac{\frac{1}{42}}{5} as a single fraction.

$$\text{false}\text{ and }\frac{1}{42\times 5}=\frac{1}{15}$$

Multiply 42 and 5 to get 210.

$$\text{false}\text{ and }\frac{1}{210}=\frac{1}{15}$$

Least common multiple of 210 and 15 is 210. Convert \frac{1}{210} and \frac{1}{15} to fractions with denominator 210.

$$\text{false}\text{ and }\frac{1}{210}=\frac{14}{210}$$

Compare \frac{1}{210} and \frac{14}{210}.

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

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

$$\text{false}$$