Answer:
To compare 2 2/3 to another mixed number, you need to convert both mixed numbers to improper fractions.
To convert 2 2/3 to an improper fraction, you need to multiply the whole number (2) by the denominator of the fraction (3), and then add the numerator (2). This gives you:
2 2/3 = (2 x 3) + 2/3 = 6 + 2/3 = 20/3
Now that you have the improper fraction for 2 2/3, you can compare it to the improper fraction of another mixed number.
For example, if you want to compare 2 2/3 to 4 1/2, you would convert 4 1/2 to an improper fraction:
4 1/2 = (4 x 2) + 1/2 = 8 + 1/2 = 17/2
Now that you have both mixed numbers as improper fractions, you can compare them by finding a common denominator and then comparing the numerators. In this case, the common denominator is 6, so you need to multiply 17/2 by 3/3 to get:
17/2 = (17 x 3)/(2 x 3) = 51/6
Now you can compare 20/3 and 51/6 by looking at their numerators:
20/3 = 6.666...
51/6 = 8.5
So 2 2/3 is less than 4 1/2.