Question

a rectangle representing one whole has been divided into 3 equal parts. the shaded portion of the model represents a fraction. use the tiles to create true statements about how the fraction would changed if the equal parts were divided into smaller parts. if each equal part shown in the model was divided into 2 equal parts, the new fraction represented would be. if each equal part shown in the model was divided into equal parts, the new fraction represented by the model would be 6/9

Explanation:

Step1: Determine the original fraction

The rectangle is divided into 3 equal parts and 2 are shaded, so the original fraction is $\frac{2}{3}$.

Step2: Find the new - fraction when each part is divided into 2 equal parts

If each of the 3 parts is divided into 2 equal parts, then the total number of parts is $3\times2 = 6$, and the number of shaded parts is $2\times2=4$. So the new fraction is $\frac{4}{6}$.

Step3: Find the number of sub - divisions to get $\frac{6}{9}$

Let the number of sub - divisions of each of the 3 original parts be $x$. Then the total number of parts is $3x$ and the number of shaded parts is $2x$. We want $\frac{2x}{3x}=\frac{6}{9}$. Cross - multiply: $2x\times9 = 6\times3x$. Solving for $x$, we know that when each part is divided into 3 equal parts, the total number of parts is $3\times3 = 9$ and the number of shaded parts is $2\times3 = 6$.

Answer:

If each equal part shown in the model was divided into 2 equal parts, the new fraction represented would be $\frac{4}{6}$. If each equal part shown in the model was divided into 3 equal parts, the new fraction represented by the model would be $\frac{6}{9}$.