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

Question

Fill in the missing part:

34: —=32 \frac{3}{4}:_{\text{ —}}=\frac{3}{2}

What is the missing number?

Video Solution

Step-by-Step Solution

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 34:ab=32 \frac{3}{4} : \frac{a}{b} = \frac{3}{2} converts to 34=32×ab \frac{3}{4} = \frac{3}{2} \times \frac{a}{b} .

Step 2: Rearrange the equation to isolate the missing fraction. Divide both sides by 32 \frac{3}{2} to find ab \frac{a}{b} .

To divide by a fraction, multiply by its reciprocal:

34÷32=34×23=3×24×3=612=12 \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 12 \frac{1}{2} .

Answer

12 \frac{1}{2}