<h3><u>Label Them to Least to greatest</u></h3>
-2.25, -1.25, 0.75, 1.25, 1.75, 2.25
<em><u>Solution:</u></em>
We have to order from least to greatest
Given are:
![-2\frac{1}{4}\\\\\frac{3}{4}\\\\|-2\frac{1}{4}|\\\\|1\frac{1}{4}|\\\\|-1\frac{3}{4}|\\\\-1\frac{1}{4}](https://tex.z-dn.net/?f=-2%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5Cfrac%7B3%7D%7B4%7D%5C%5C%5C%5C%7C-2%5Cfrac%7B1%7D%7B4%7D%7C%5C%5C%5C%5C%7C1%5Cfrac%7B1%7D%7B4%7D%7C%5C%5C%5C%5C%7C-1%5Cfrac%7B3%7D%7B4%7D%7C%5C%5C%5C%5C-1%5Cfrac%7B1%7D%7B4%7D)
Absolute value means magnitude of a quantity without regard to sign
Therefore, convert them into decimal for easier comparisons
![\rightarrow -2\frac{1}{4} = -\frac{4 \times 2+1}{4} = -\frac{9}{4} = -2.25](https://tex.z-dn.net/?f=%5Crightarrow%20-2%5Cfrac%7B1%7D%7B4%7D%20%3D%20-%5Cfrac%7B4%20%5Ctimes%202%2B1%7D%7B4%7D%20%3D%20-%5Cfrac%7B9%7D%7B4%7D%20%3D%20-2.25)
![\rightarrow \frac{3}{4} = 0.75](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cfrac%7B3%7D%7B4%7D%20%3D%200.75)
![\rightarrow |-2\frac{1}{4}| = 2\frac{1}{4} = \frac{9}{4} = 2.25](https://tex.z-dn.net/?f=%5Crightarrow%20%7C-2%5Cfrac%7B1%7D%7B4%7D%7C%20%3D%202%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B9%7D%7B4%7D%20%3D%202.25)
![\rightarrow |1\frac{1}{4}| = 1\frac{1}{4} = \frac{5}{4} = 1.25](https://tex.z-dn.net/?f=%5Crightarrow%20%7C1%5Cfrac%7B1%7D%7B4%7D%7C%20%3D%201%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%3D%201.25)
![\rightarrow |-1\frac{3}{4}| = 1\frac{3}{4} = \frac{7}{4} = 1.75](https://tex.z-dn.net/?f=%5Crightarrow%20%7C-1%5Cfrac%7B3%7D%7B4%7D%7C%20%3D%201%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B7%7D%7B4%7D%20%3D%201.75)
![\rightarrow -1 \frac{1}{4} = -\frac{5}{4} = -1.25](https://tex.z-dn.net/?f=%5Crightarrow%20-1%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20-%5Cfrac%7B5%7D%7B4%7D%20%3D%20-1.25)
Arrange them from least to greatest
-2.25 is the most negative and so it is the smallest
-2.25, -1.25, 0.75, 1.25, 1.75, 2.25
Thus the ascending order is found