Question

explain fraction equivalence using visual models (mp) reason freida only has a \\(\frac{1}{4}\\)-cup measuring cup. she fills the measuring cup two times to get \\(\frac{1}{2}\\) cup. use visual models to explain why this works

Explanation:

Step1: Represent 1/2 cup visually

Imagine a rectangle representing 1 cup. Divide it into 2 equal parts (since we're dealing with 1/2). Each part is $\frac{1}{2}$ cup.

Step2: Represent 1/4 cup visually

Now, take the same rectangle (1 cup) and divide it into 4 equal parts (because the measuring cup is 1/4 cup). Each small part is $\frac{1}{4}$ cup.

Step3: Compare the two models

Notice that 2 of the $\frac{1}{4}$ - cup parts (from the 4 - part division) make up the same amount as 1 of the $\frac{1}{2}$ - cup parts (from the 2 - part division). Mathematically, $2\times\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$. Visually, if you shade 2 of the 1/4 - sized sections in the 4 - part rectangle, it will cover the same area as shading 1 of the 1/2 - sized sections in the 2 - part rectangle.

Answer:

Using visual models (like rectangles divided into equal parts), we see that 2 times $\frac{1}{4}$ cup (where a rectangle divided into 4 equal parts has each part as $\frac{1}{4}$ cup) equals $\frac{1}{2}$ cup (where a rectangle divided into 2 equal parts has each part as $\frac{1}{2}$ cup) because $2\times\frac{1}{4}=\frac{2}{4}=\frac{1}{2}$, and visually the shaded regions for 2 $\frac{1}{4}$ - cup amounts match the shaded region for 1 $\frac{1}{2}$ - cup amount.