Solve: Finding the Missing Divisor in 3/4 ÷ ? = 3/2

Fill in the missing part:

$\frac{3}{4}:_{\text{ —}}=\frac{3}{2}$

What is the missing number?

To solve this problem, we'll follow these steps:

• Express the division as a multiplication problem.
• Rearrange the equation to isolate the missing fraction.
• Perform the necessary algebraic manipulations to solve for the missing fraction.

Now, let's work through each step:

Step 1: Express the division as multiplication. The equation $\frac{3}{4} : \frac{a}{b} = \frac{3}{2}$ converts to $\frac{3}{4} = \frac{3}{2} \times \frac{a}{b}$.

Step 2: Rearrange the equation to isolate the missing fraction. Divide both sides by $\frac{3}{2}$ to find $\frac{a}{b}$.

To divide by a fraction, multiply by its reciprocal:

$\frac{3}{4} \div \frac{3}{2} = \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2}$.

Therefore, the missing fraction is $\frac{1}{2}$.