Answer:
compare both to 1/2: 2/6 < 1/2 < 5/8
Explanation:
There are many strategies that could be used:
- use a common denominator (24)
- compare both numbers to some easy reference (1/2)
- subtract one from the other
- convert both to decimal (a variation of "common denominator")
- "cross multiply" (another variation of "common denominator")
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Common denominator
Recognize that denominators 6 and 8 have a least common multiple of 24. That means both fractions can be expressed using 24 as a denominator.
2/6 = 8/24
5/8 = 15/24
Then 8/24 < 15/24, so 2/6 < 5/8.
Some easy reference
We notice both fractions have even denominators, so they can be easily compared to 1/2
2/6 < 3/6
5/8 > 4/8
One is less than the reference, and the other is greater, so ...
That is, 2/6 < 1/2 < 5/8, so 2/6 < 5/8
Subtract one from the other
2/6 -5/8 = (16 -30)/48 = -14/48 . . . . a negative number
This means the second fraction is larger than the first:
2/6 < 5/8
Note that we have used the simple form a/b -c/d = (ad -bc)/(bd) so we don't have to mess with least common denominator.
Convert both to decimal
Often, it is sufficient to use 2 or 3 decimal places for comparison purposes. Here, we can do the comparison with one decimal place.
2/6 ≈ 0.3
5/8 ≈ 0.6
We know that 0.3 < 0.6, so 2/6 < 5/8.
Cross multiply
If you take a look at the subtraction formula we used above, you can see that the sign of the difference is equal to the sign of the difference of the cross products. That is, we can determine the relation from ...
a/b ?? c/d ⇒ ad ?? bc
Here, that is ...
2/6 ?? 5/8 ⇒ (2)(8) ?? (6)(5) ⇒ 16 < 30
That means 2/6 < 5/8.