Solve (10)/(3)\div(2)/(5)=(10)/(3)\times(5)/(2)=

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Question

$$\frac{ 10 }{ 3 } \div \frac{ 2 }{ 5 } = \frac{ 10 }{ 3 } \times \frac{ 5 }{ 2 } =$$

$\text{true}$

Divide $\frac{10}{3}$ by $\frac{2}{5}$ by multiplying $\frac{10}{3}$ by the reciprocal of $\frac{2}{5}$.

$$\frac{10}{3}\times \frac{5}{2}=\frac{10}{3}\times \frac{5}{2}$$

Multiply $\frac{10}{3}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 5}{3\times 2}=\frac{10}{3}\times \frac{5}{2}$$

Do the multiplications in the fraction $\frac{10\times 5}{3\times 2}$.

$$\frac{50}{6}=\frac{10}{3}\times \frac{5}{2}$$

Reduce the fraction $\frac{50}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{25}{3}=\frac{10}{3}\times \frac{5}{2}$$

Multiply $\frac{10}{3}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{3}=\frac{10\times 5}{3\times 2}$$

Do the multiplications in the fraction $\frac{10\times 5}{3\times 2}$.

$$\frac{25}{3}=\frac{50}{6}$$

Reduce the fraction $\frac{50}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{25}{3}=\frac{25}{3}$$

Compare $\frac{25}{3}$ and $\frac{25}{3}$.

$$\text{true}$$