Certainly! Let's solve the problem step-by-step:
1. Understanding the Problem:
We need to find the sum of three fractions: [tex]\( \frac{1}{4} + \frac{1}{4} + \frac{1}{4} \)[/tex].
2. Sum of the Fractions:
When we add these fractions together, they all have the same denominator (4), so we can simply add the numerators:
[tex]\[
\frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{1+1+1}{4} = \frac{3}{4}
\][/tex]
3. Shading the Model:
We will use the given grid to visually represent the fractions and their sum. The grid provided seems to be a 3x3 grid, which is not perfectly conducive to representing quarters accurately, but we will interpret it appropriately for the purpose of visualization.
Since we are dealing with quarters, it’s beneficial to use a shape or grouping to divide the region into four equal parts.
4. First Fraction ([tex]\(\frac{1}{4}\)[/tex]):
Let's shade one section out of the four:
[tex]\[
\begin{tabular}{|c|c|c|c|} \hline
\shade & & & \\ \hline
& & & \\ \hline
& & & \\ \hline
& & & \\ \hline
\end{tabular}
\][/tex]
5. Second Fraction ([tex]\(\frac{1}{4}\)[/tex]):
Shade another section out of the four:
[tex]\[
\begin{tabular}{|c|c|c|c|} \hline
\shade & \shade & & \\ \hline
& & & \\ \hline
& & & \\ \hline
& & & \\ \hline
\end{tabular}
\][/tex]
6. Third Fraction ([tex]\(\frac{1}{4}\)[/tex]):
Shade yet another section out of the four:
[tex]\[
\begin{tabular}{|c|c|c|c|} \hline
\shade & \shade & \shade & \\ \hline
& & & \\ \hline
& & & \\ \hline
& & & \\ \hline
\end{tabular}
\][/tex]
7. Result ([tex]\(\frac{3}{4}\)[/tex]):
The above steps show that when three quarters are shaded in the model, it represents the fraction [tex]\(\frac{3}{4}\)[/tex].
Therefore, the sum [tex]\(\frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4}\)[/tex] is visually represented by shading three parts out of four in the model, totaling up to 0.75. This aligns with your provided models and numerical results.
