Question

How do you order the values \[4,|7|, - 1,| - 3|, - 4\] from least to greatest?

Answer 1

Hint: Here in this question, we have to arrange the given numbers from the least to the greatest. The numbers are integers and some numbers are in mod. By using the property of mod, we simplify the first mod terms and we arrange the numbers from the least to the greatest number.

Complete step-by-step answer:
 In the mathematics we have different kinds of numbers namely,
Natural number: The numbers are counting numbers and it starts from 1,2,3,…
Whole number: The set of natural numbers and also including zero.
Integers: It is a combination of whole numbers and all negative natural numbers.
Rational numbers: the number which are in the form of \[\dfrac{p}{q}\], where \[q \ne 0\], where p and q are any integers.
Irrational numbers: the numbers which are not rational.
Real numbers: the combinations of natural numbers, whole numbers, integers, rational numbers.
While arranging any kind of number we have two kind of arrangements namely,
Ascending order: The numbers are arranged from least to the greatest.
Descending order: The numbers are arranged from greatest to the least.
Now here in this the set of numbers are \[4,|7|, - 1,| - 3|, - 4\]. This is a combination of positive and negative numbers. So the numbers are integers. We have to arrange these from least to greatest then it is an ascending order. But some numbers are having mod. First we simplify them.
Now consider |7| and |-3|, the mod always takes positive number therefore |7| = 7 and |-3|= 3.
Therefore the numbers are written as
4, 7, -1, 3, -4.
The ascending order of these numbers is
-4, -1, 3, 4, 7.
\[ \Rightarrow - 4, - 1,| - 3|,4,|7|\]
So, the correct answer is “- 4, - 1,| - 3|,4,|7|”.

Note: The mod will always take positive values sometimes we will say it can be either positive value or negative value. But when the number is in the mod we consider it as a positive number. The number which contains the negative is the least value. Because the negative sign indicates the low or decreased value.