Answer:
[tex]-2 \frac{1}{4}<-1 \frac{1}{4} < \frac{3}{4}< |1 \frac{1}{4}|< |-1 \frac{3}{4}| < |-2 \frac{1}{4}|[/tex]
Step-by-step explanation:
Given the numbers:
[tex]-1 \frac{1}{4} , |-1 \frac{3}{4}| , \frac{3}{4} , -2 \frac{1}{4} , |1 \frac{1}{4}| , and |-2 \frac{1}{4}|[/tex]
To find:
The ascending order of the given numbers.
Solution:
First of all, let us have a look at the definition of absolute value function i.e. Modulus function.
[tex]|y|=\left \{ {-{y}\ if\ y<0 \atop {y}\ if\ y>0} \right.[/tex]
i.e. if the numbers is negative, then a negative sign is added to make the number positive.
Now, let us have a look at the given numbers with modulus one by one.
[tex]|-1 \frac{3}{4}| = -(-1 \frac{3}{4})=1 \frac{3}{4}\\ |1 \frac{1}{4}| = 1 \frac{1}{4}\\|-2 \frac{1}{4}| = -(-2 \frac{1}{4})=2 \frac{1}{4}[/tex]
Smallest numbers are with negative signs.
And negative numbers with larger magnitude are smaller.
Therefore, the ascending order will be:
[tex]-2 \frac{1}{4}<-1 \frac{1}{4} < \frac{3}{4}< |1 \frac{1}{4}|< |-1 \frac{3}{4}| < |-2 \frac{1}{4}|[/tex]
