Pablo counts on in quarters. What are the two missing numbers?

[tex]\frac{1}{4} \quad \frac{1}{2} \quad \frac{3}{4} \quad 1 \quad \square \quad 1 \frac{1}{2} \quad \square \quad 2[/tex]



Answer :

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]