Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3...
-
Upload
alison-elliott -
Category
Documents
-
view
214 -
download
1
Transcript of Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3...
![Page 1: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/1.jpg)
Warm UpAdd or subtract.
1 + – 1 5 11. 2
5
2. 7 123 – 2
3. 6.5 + –1.2
4. 3.4 – 0.9
5.3
2.5
3 5
11 12
1 3 1
![Page 2: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/2.jpg)
The Real Number System
![Page 3: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/3.jpg)
The Real Number System• A real number is basically a number
that is somewhere on a number line.• The Real Number System is divided into
two categories: Rational and Irrational.
![Page 4: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/4.jpg)
A rational number is any number that can be written as a fraction , where n
and d are integers and d 0.
nd
![Page 5: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/5.jpg)
• Fractions are rational numbers.• Decimals that terminate or repeat
are rational numbers.• Whole numbers are rational
numbers.• Integers are rational numbers.• 0 is a rational number.
![Page 6: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/6.jpg)
An Irrational Number is a number that cannot be written as a simple fraction - the decimal goes on forever without repeating.
It is called irrational because it cannot be written
as a ratio (or fraction),not because it’s crazy!
![Page 7: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/7.jpg)
• π (Pi) is an irrational number. The value of Pi is
3.141592653589793238462643383279 (and more...)
• There is no pattern to the decimals, and you cannot write down a simple fraction that equals Pi.
![Page 8: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/8.jpg)
• Square roots of non-perfect “squares” are irrational.
• For example,
is irrational.
![Page 9: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/9.jpg)
• Real numbers consist of all the rational and irrational numbers.
• The real number system has many subsets:– Natural Numbers – Whole Numbers – Integers
![Page 10: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/10.jpg)
• Natural numbers are the set of counting numbers.
{1, 2, 3,…}
![Page 11: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/11.jpg)
• Whole numbers are the set of numbers that include 0 plus the set of natural numbers.
{0, 1, 2, 3, 4, 5,…}
![Page 12: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/12.jpg)
• Integers are the set of whole numbers and their opposites.
{…,-3, -2, -1, 0, 1, 2, 3,…}
![Page 13: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/13.jpg)
Real Numbers
Rational Numbers Irrational Numbers
3
1/2-2
15%
2/3
1.456
-0.7
0
3 2
5 2
34
![Page 14: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/14.jpg)
Real Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456- 0.7
3 2
5 2
34
Integers
![Page 15: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/15.jpg)
Real Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456- 0.7
3 2
5 2
34
Integers
Whole
![Page 16: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/16.jpg)
Real Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456- 0.7
0
3 2
5 2
34
Integers
Whole
Natural
![Page 17: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/17.jpg)
System
![Page 18: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/18.jpg)
• Where do these numbers belong?0, ½, -3, , 117, 6.36, .3,
![Page 19: Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1.](https://reader036.fdocuments.net/reader036/viewer/2022071807/56649ed95503460f94be8856/html5/thumbnails/19.jpg)
0
117-3
1/2
6.36
.3
System