2 1/4 2 3/20 2 29/60 put the lengths of fractions in order from lest to greatest.
use a common denominator.
Then just sort the numerators.
so then whats the answer ;-;
To compare the lengths of fractions, we need to convert them to a common denominator. First, let's convert the mixed numbers to improper fractions:
2 1/4 = (2 * 4 + 1)/4 = 9/4
2 3/20 = (2 * 20 + 3)/20 = 43/20
2 29/60 = (2 * 60 + 29)/60 = 149/60
Now we can compare the fractions. To do this, we will find a common denominator by taking the least common multiple (LCM) of the three denominators, which is 4, 20, and 60. The LCM of these numbers is 60.
Now, we'll convert each fraction to have a denominator of 60:
9/4 = (9 * 15)/60 = 135/60
43/20 = (43 * 3)/60 = 129/60
149/60 = 149/60
Now, we can compare the fractions:
135/60 > 129/60 = 149/60
So, the fractions in order from least to greatest are:
129/60, 135/60, 149/60
In mixed number form, they would be:
2 43/20 < 2 1/4 = 2 29/60
To compare and order fractions, it is helpful to have them in the same form. In this case, you have mixed numbers and improper fractions. Let's first convert the mixed numbers into improper fractions:
2 1/4 = (2 * 4 + 1) / 4 = 9/4
2 3/20 = (2 * 20 + 3) / 20 = 43/20
2 29/60 = (2 * 60 + 29) / 60 = 149/60
Now that we have all the fractions in the same form, we can compare them in order from least to greatest:
9/4, 43/20, 149/60
To compare fractions, we can use the cross-multiplication method. Multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the numerator of the second fraction by the denominator of the first fraction. If the products are equal, the fractions are equivalent. If one product is greater than the other, then the corresponding fraction is larger.
Comparing 9/4 and 43/20:
(9/4) * (20/43) = 180/172 = 15/14
Comparing 15/14 and 149/60:
(15/14) * (60/149) = 900/2086 ≈ 0.4314
Since 0.4314 is less than 1, we can conclude that:
9/4 > 43/20 > 149/60
Therefore, the fractions in order from least to greatest are: 149/60, 43/20, and 9/4.