Answer :

To arrange the given numbers in increasing order, we need to compare each value and sort them from the smallest to the largest. The given numbers are:

[tex]\[ -1.4, 2, -3 \frac{1}{2}, -1, -\frac{1}{2}, 0.25, -10, 5.2 \][/tex]

Let us first list these numbers clearly for comparison:

1. [tex]\(-10\)[/tex]
2. [tex]\(-3 \frac{1}{2}\)[/tex] or [tex]\(-3.5\)[/tex]
3. [tex]\(-1.4\)[/tex]
4. [tex]\(-1\)[/tex]
5. [tex]\(-\frac{1}{2}\)[/tex] or [tex]\(-0.5\)[/tex]
6. [tex]\(0.25\)[/tex]
7. [tex]\(2\)[/tex]
8. [tex]\(5.2\)[/tex]

Now, we will begin comparing these numbers to arrange them in increasing order:

- The smallest number is [tex]\(-10\)[/tex].
- Next in order is [tex]\(-3.5\)[/tex], which is greater than [tex]\(-10\)[/tex].
- Following that, [tex]\(-1.4\)[/tex] comes next because it is greater than [tex]\(-3.5\)[/tex].
- After [tex]\(-1.4\)[/tex], [tex]\(-1\)[/tex] is the next larger value.
- Then comes [tex]\(-0.5\)[/tex], which is greater than [tex]\(-1\)[/tex].
- The next number is [tex]\(0.25\)[/tex], which is positive and therefore greater than any negative number.
- After [tex]\(0.25\)[/tex], [tex]\(2\)[/tex] is the next number.
- Finally, the largest number in this list is [tex]\(5.2\)[/tex].

Putting it all together, the numbers arranged in increasing order are:

[tex]\[ -10, -3.5, -1.4, -1, -0.5, 0.25, 2, 5.2 \][/tex]

Answer:

-10, -3 1/2, -1.4, -1, -1/2, 0.25, 2, 5.2

Step-by-step explanation:

1/2 is also 0.5

you can convert all of these numbers into a decimal to compare them easily.

-3 1/2 is also -3.5

-1/2 is -0.5

now you can place these in order:

-10, -3.5, -1.4, -1, -0.5, 0.25, 2, 5.2

convert

-3.5 and -0.5 back:

-10, -3 1/2, -1.4, -1, -1/2, 0.25, 2, 5.2

hope this helps :)