To determine the two missing numbers in the sequence that Pablo counts in quarters, let's follow the pattern established by the given fractions:
The sequence starts as follows:
[tex]\[
\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1
\][/tex]
Let's convert these fractions to their decimal equivalents for clarity:
[tex]\[
0.25, 0.5, 0.75, 1
\][/tex]
Notice that the difference between each consecutive pair of numbers is \(\frac{1}{4}\) or 0.25. We continue this pattern to find the missing numbers.
1. Starting from the last number given (1), add \(\frac{1}{4}\) or 0.25 to find the next number:
[tex]\[
1 + \frac{1}{4} = 1 + 0.25 = 1.25
\][/tex]
This value, 1.25, is the first missing number.
2. Continuing from 1.25, add another \(\frac{1}{4}\) or 0.25 to find the next number:
[tex]\[
1.25 + \frac{1}{4} = 1.25 + 0.25 = 1.5
\][/tex]
This value, 1.5, corresponds to the already given number in the sequence.
Continuing from 1.5, add yet another \(\frac{1}{4}\) or 0.25 to find the next number:
[tex]\[
1.5 + \frac{1}{4} = 1.5 + 0.25 = 1.75
\][/tex]
This value, 1.75, is the second missing number.
Hence, the two missing numbers in the sequence are:
[tex]\[
1.25 \quad \text{and} \quad 1.75
\][/tex]
So, the final sequence correctly filled in would be:
[tex]\[
\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, 1.25, 1.5, 1.75, 2
\][/tex]
