Question

1. $\frac{2}{5} div \frac{3}{6} =$ 2. $\frac{3}{8} div \frac{2}{5} =$

Explanation:

Problem 1: $\boldsymbol{\frac{2}{5} \div \frac{3}{6}}$

Step1: Recall fraction division rule

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{6}$ is $\frac{6}{3}$. So, $\frac{2}{5} \div \frac{3}{6} = \frac{2}{5} \times \frac{6}{3}$.

Step2: Simplify and multiply

Simplify $\frac{6}{3}$ to $2$. Then multiply: $\frac{2}{5} \times 2 = \frac{4}{5}$. Wait, no, wait, original second fraction is $\frac{3}{6}$, reciprocal is $\frac{6}{3}=2$. Wait, no, let's do it correctly. $\frac{2}{5} \times \frac{6}{3}=\frac{2\times6}{5\times3}=\frac{12}{15}$, then simplify by dividing numerator and denominator by 3: $\frac{12\div3}{15\div3}=\frac{4}{5}$? Wait, no, $\frac{3}{6}$ simplifies to $\frac{1}{2}$, so reciprocal is $2$. So $\frac{2}{5} \times 2=\frac{4}{5}$. Wait, maybe better to not simplify early. Let's redo:

Step1: Apply division rule

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. So for $\frac{2}{5} \div \frac{3}{6}$, $a = 2$, $b = 5$, $c = 3$, $d = 6$. So it becomes $\frac{2}{5} \times \frac{6}{3}$.

Step2: Multiply numerators and denominators

Numerator: $2\times6 = 12$. Denominator: $5\times3 = 15$. So we have $\frac{12}{15}$.

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 3. $\frac{12\div3}{15\div3}=\frac{4}{5}$. Wait, but $\frac{3}{6}$ is $\frac{1}{2}$, so reciprocal is 2. Then $\frac{2}{5} \times 2=\frac{4}{5}$. Correct.

Problem 2: $\boldsymbol{\frac{3}{8} \div \frac{2}{5}}$

Step1: Apply fraction division rule

$\frac{3}{8} \div \frac{2}{5} = \frac{3}{8} \times \frac{5}{2}$ (since reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$).

Step2: Multiply numerators and denominators

Numerator: $3\times5 = 15$. Denominator: $8\times2 = 16$. So the result is $\frac{15}{16}$.

Answer:

s:

1. $\frac{4}{5}$
2. $\frac{15}{16}$