Exit Divide fractions using models vinea Pick the model that represents this division equation. \[ \frac{3}{8} \div \frac{3}{4}=? \] Hint: Use a related multiplication equation. \( \square \) \( \square \)

To divide fractions using models, we can use the concept of multiplying by the reciprocal. The division equation can be rewritten as a multiplication equation. Given the equation: \[ \frac{3}{8} \div \frac{3}{4} \] We can express this as: \[ \frac{3}{8} \times \frac{4}{3} \] Now, let's break this down step by step: 1. **Identify the reciprocal**: The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\). 2. **Rewrite the division as multiplication**: \[ \frac{3}{8} \div \frac{3}{4} = \frac{3}{8} \times \frac{4}{3} \] 3. **Multiply the fractions**: To multiply fractions, multiply the numerators together and the denominators together: \[ \frac{3 \times 4}{8 \times 3} = \frac{12}{24} \] 4. **Simplify the fraction**: \[ \frac{12}{24} = \frac{1}{2} \] Thus, the result of the division \(\frac{3}{8} \div \frac{3}{4}\) is: \[ \frac{1}{2} \] ### Model Representation To represent this division equation using models, you can visualize it as follows: - **Model 1**: A rectangle divided into 8 equal parts (representing the denominator of \(\frac{3}{8}\)), where 3 parts are shaded (representing the numerator). - **Model 2**: A rectangle divided into 4 equal parts (representing the denominator of \(\frac{3}{4}\)), where 3 parts are shaded. When you take \(\frac{3}{8}\) and multiply it by the reciprocal \(\frac{4}{3}\), you can visualize how the shaded parts relate to each other, ultimately showing that the result is \(\frac{1}{2}\) of the original rectangle. In summary, the division equation can be represented by the multiplication of the fraction \(\frac{3}{8}\) by the reciprocal \(\frac{4}{3}\), leading to the final answer of \(\frac{1}{2}\).