In math, the absolute value is also known as the modulus |x| of a real number x is x's arithmetic value without consider to its sign. So, for example, 5 is the absolute value of both 5 and −5.
A simplification of the absolute value for real numbers occurs in an extensive selection of math settings.
Properties of the math game absolute value:
The absolute value has the following four fundamental properties:
`|x| = sqrt(x^2)` (1) Basic
`|x| \ge 0 ` (2) Non-negativity
`|x| = 0 \iff x = 0` (3) Positive-definiteness
`|xy| = |x||y|\,` (4) Multiplicativeness
`|x+y| \le |x| + |y|` (5) Subadditivity
Other important properties of the absolute value include:
` |-x| = |x|\, ` (6) Symmetry
`|x - y| = 0 \iff x = y ` (7) Identity of indiscernible (equivalent to positive-definiteness)
`|x - y| \le |x - z| +|z - y|` (8) Triangle inequality (equivalent to sub additivity)
`|x/y| = |x| / |y| \mbox{ (if } y \ne 0) \,` (9) Preservation of division (equivalent to multiplicativeness)
`|x-y| \ge ||x| - |y||` (10) (equivalent to sub additivity)
If y > 0, two other useful properties concerning inequalities are:
`|x| \le y \iff -y \le a \le y`
` |x| \ge y \iff x \le -y \mbox{ or } y \le x`
Math game absolute value – Games:
Math game absolute value – Game 1:
Arrange the order of ascending -|-15|, |12|,|7|,|-99|,|-5|,|-8|, |-65|, |6|
Solution:
First we remove the modulus symbol
-15, 12, 7, 99, 5, 8, 65, 6
Then to arrange the given order
-15, 5, 6, 7, 8, 12, 65, 99
Math game absolute value – Game 2:
Arrange the order of descending -|-16|, |13|,|8|,|-9|,|-6|,|-7|, |-66|, |63|, -|21|, |-68|
Solution:
First we remove the modulus symbol
-16, 13, 8, 9, 6, 7, 66, 63, -21, 68
Then to arrange the given order
68, 66, 63, 13, 9, 8, 7, 6, -16, -21
Math game absolute value – Game 3:
Absolute Value
Arrange the descending order
Solution:
First we remove the modulus symbol
-81, -28,67,-59,98,71,38
Then to arrange the given order
98, 71, 67, 38, -28, -59, -81
No comments:
Post a Comment