9. Find one rational number between 1/4 and 1/2 .
Answers
Answer:
Two rational numbers between 1/4 and 1/2 are 5/16 and 3/8.
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Step-by-step explanation:
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Well, there are more than just five. In fact, there are infinitely many rational numbers between any two points on the number line. Shall we pick five? Easily done. To find a rational number between two other rational numbers, simply calculate the average of those two numbers.
14+122=14+242=342=38
If you need two more rational numbers, just take the average of 1/4 and 3/8, and of 3/8 and 1/2.
14+382=28+382=582=516
38+122=38+482=782=716
We can finish up by finding two more averages, and we have our pick of endpoints. Let’s say we find the average between 1/4 and 5/16, and between 7/16 and 1/2
14+5162=416+5162=9162=932
716+122=716+8162=15162=1532
So there are five rational numbers that lie between 1/4 and 1/2. Not in numerical order:
3/8
5/16
7/16
9/32
15/32
Of course, there is another way to approach this problem. Suppose you wanted five rational numbers spaced at even intervals between 1/4 and 1/2. For the purpose of this exercise, we’ll assume that we don’t want to include 1/4 and 1/2. So that’s six intervals. The gap between 1/4 and 1/2 is 1/4, and one-sixth of the gap is
146=124
So starting at 1/4 (or 6/24) we can count up by 1/24 each time to find five evenly-spaced rational numbers between 1/4 and 1/2.
7/24
8/24 = 1/3
9/24 = 3/8
10/24 = 5/12
11/24