Classification of Numbers Properties of Real Numbers Order of Operations R1 Real Numbers.
Other Properties of Real Numbers
-
Upload
india-keith -
Category
Documents
-
view
25 -
download
1
description
Transcript of Other Properties of Real Numbers
![Page 1: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/1.jpg)
Other Properties of Real Numbers
![Page 2: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/2.jpg)
Identity Properties
Identity properties tell us how we can
add or multiply and get an answer that
is identical to the number
we started with.
![Page 3: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/3.jpg)
Identity Property of Addition
The identity property of addition tells us that we can add zero to any number and get that identical
number as the answer.
a + 0 = a
That makes the identity element for addition:
![Page 4: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/4.jpg)
Identity Property of Multiplication
The identity property of multiplication tells us that we can multiply any number by 1 and get that
identical number as the answer.
That makes the identity element for multiplication:
1a a
![Page 5: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/5.jpg)
Inverse Properties
The inverse properties tell us how we can create the identity elements out of other numbers.
Sort of like building a sand castle!
![Page 6: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/6.jpg)
Additive Inverse Property
The identity element for addition is
How can we add and get an answer equal to zero?
Ah ha! - 5 + 5 = 0
In fact: - a + a = 0
![Page 7: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/7.jpg)
Additive Inverse Property
-a + a = 0
Numbers that have the same magnitude but different signs are called opposites.
Another term for opposite is additive inverse.
![Page 8: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/8.jpg)
Additive Inverse Property
The additive inverse property tells us that when we add any number and its opposite the answer
will be zero.
- a + a = 0
![Page 9: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/9.jpg)
Double Negative Property
Closely related to the concept of opposite is the double negative property.
- ( - a ) = a
We can think if that as two negative signs in a row convert to one positive sign.
(signs are the same, replace with +)
![Page 10: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/10.jpg)
Double Negative Property
Closely related to the concept of opposite is the double negative property.
- ( - a ) = a
Or we can think if it as ‘taking the opposite of an opposite gets you back where you started’!
![Page 11: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/11.jpg)
Multiplicative Inverse Property
The identity element for multiplication is
How can we multiply and get an answer equal to one?
Ah ha!
In fact:
12 1
21
1aa
![Page 12: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/12.jpg)
Reciprocals
Reciprocals are the gymnasts of
algebra.
They just love to do
headstands!
Watch them flip!
2 3 flip
3 21 5
flip or 55 1
16 flip
6
![Page 13: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/13.jpg)
Multiplicative Inverse Property
The multiplicative inverse property tells us that when we multiply any number by its reciprocal
the answer will be one.
Another term for reciprocal is multiplicative inverse.
![Page 14: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/14.jpg)
Multiplication Property of Zero
Zero has a unique property that we will use a lot later in the semester.
Any number multiplied by zero equals zero.
0 0a
![Page 15: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/15.jpg)
Reduction Property
When we reduce fractions, we are using the reduction property.
In other words, as long as b and c are not equal to zero, we can cancel and reduce.
ac ac a
bc bc b
![Page 16: Other Properties of Real Numbers](https://reader036.fdocuments.in/reader036/viewer/2022062720/568134ba550346895d9bdbaa/html5/thumbnails/16.jpg)
More Properties of Real Numbers
Identity properties
a + 0 = a and
Inverse properties – opposites and reciprocals
Double negative property
Multiplication property of zero
Reduction property
1a a