Question

How do the values compare? Order the values from least to greatest. -1 1/4 , |-1 3/4-| , 3/4 , -2 1/4 , |1 1/4-| , and |-2 1/4| ​

Answer 1

`-2 (1)/(4)<-1 (1)/(4) < (3)/(4)< |1 (1)/(4)|< |-1 (3)/(4)| < |-2 (1)/(4)|`

Explanation:

Given the numbers:

`-1 (1)/(4) , |-1 (3)/(4)| , (3)/(4) , -2 (1)/(4) , |1 (1)/(4)| , and |-2 (1)/(4)|`

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.

`|y|=\left \{ {-{y}\ if\ y<0 \atop {y}\ if\ y>0} \right.`

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.

`|-1 (3)/(4)| = -(-1 (3)/(4))=1 (3)/(4)\\ |1 (1)/(4)| = 1 (1)/(4)\\|-2 (1)/(4)| = -(-2 (1)/(4))=2 (1)/(4)`

Smallest numbers are with negative signs.

And negative numbers with larger magnitude are smaller.

Therefore, the ascending order will be:

`-2 (1)/(4)<-1 (1)/(4) < (3)/(4)< |1 (1)/(4)|< |-1 (3)/(4)| < |-2 (1)/(4)|`