Question

1. draw an area model for \\(\frac{3}{4}\\). write an equivalent fraction for \\(\frac{3}{4}\\). show the equivalent fraction on your model.

Explanation:

Step1: Recall Equivalent Fraction Rule

To find an equivalent fraction, we multiply numerator and denominator by the same non - zero number. For the fraction $\frac{3}{4}$, let's multiply numerator and denominator by 2.
The formula for equivalent fractions is $\frac{a}{b}=\frac{a\times n}{b\times n}$, where $n
eq0$.
So, $\frac{3\times2}{4\times2}=\frac{6}{8}$.

Step2: Draw Area Model for $\frac{3}{4}$

• Draw a rectangle. Divide it into 4 equal - sized parts (since the denominator is 4).
• Shade 3 of these parts (since the numerator is 3).

Step3: Draw Area Model for $\frac{6}{8}$

• Draw another rectangle (or the same rectangle, divided differently). Divide it into 8 equal - sized parts (since the denominator is 8).
• Shade 6 of these parts (since the numerator is 6). We can see that the shaded area of the $\frac{3}{4}$ model and the $\frac{6}{8}$ model are the same, which shows they are equivalent.

Answer:

An equivalent fraction of $\frac{3}{4}$ is $\frac{6}{8}$ (we can also have other equivalents like $\frac{9}{12}$, $\frac{12}{16}$, etc. by multiplying numerator and denominator by 3, 4, etc.). The area model for $\frac{3}{4}$ has a shape (e.g., rectangle) divided into 4 equal parts with 3 shaded, and the area model for $\frac{6}{8}$ has the same - sized shape divided into 8 equal parts with 6 shaded, showing the same area is shaded.