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Two fractions can be compared by translating them to have a common denominator and comparing them.
The lowest common denominator of 2/3 and 3/4 is 12.
Multiplying the top and bottom (also called the numerator and denominator) of 2/3 by 4/4 gives you 8/12. Multiplying the top and bottom of 3/4 by 3/3 gives you 9/12.
Since 8/12 is less the 9/12, we see that 2/3 is less than 3/4.
We can do this multiplication because both 3/3 and 4/4 are the value 1 and you can multiply any number by 1 without changing its value.
We can also convert the fractions to decimal form and compare them as decimal values.
To convert fractions to decimals, we do the actual division of the top by the bottom. 2 divided by 3 is .666666... it goes on forever so we truncate it to something reasonable and usable like 0.667 or even 0.67. 3 divided by 4 is .75. Since .67 is less than .75, we again see that 2/3 is less than 3/4.
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