properties of real numbers. properties of addition & multiplication: for all real #’s, a, b,...
TRANSCRIPT
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Properties of Real Numbers
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Properties of Addition & Multiplication:For all real #’s, a, b, c…
Closure: then a+b is a real number ab is a real number
Commutative: a + b = b + aab = ba
Associative: (a+b)+c = a+(b+c) (ab)c = a(bc)
Identity: a + 0 = 0 + a = aa*1 = 1*a = a
Inverse: a + (-a) = 0 11a
a
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Distributive Property
For all real numbers a, b, and c:
a(b + c) = ab + ac and (b + c)a = ba + bc)
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State a property to justify the following statements…
6 +(-3) = (-3) + 6
3(4a+5) = 12a + 15
(x+3) + 6 = 6 + (x+ 3)
-5 + 5 = 0
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State a property to justify the following statements…
2(4 – 5) = (4- 5)2
-5 + (x + 2) = (-5 + x) + 2
4 ( 1) = 4
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Using Properties for Mental Math
A movie ticket costs $7.75. A drink costs $2.40 and popcorn is $1.25. What is the total cost?
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Using Properties for Mental Math
You buy a sandwich for $2.95, an apple for $.45, and a bottle of juice for $1.05. What is the total cost?
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Simplify – using properties
![Page 9: Properties of Real Numbers. Properties of Addition & Multiplication: For all real #’s, a, b, c… Closure: then a+b is a real number ab is a real number](https://reader036.vdocuments.site/reader036/viewer/2022073121/5697bfa61a28abf838c98263/html5/thumbnails/9.jpg)
Simplify – using properties
![Page 10: Properties of Real Numbers. Properties of Addition & Multiplication: For all real #’s, a, b, c… Closure: then a+b is a real number ab is a real number](https://reader036.vdocuments.site/reader036/viewer/2022073121/5697bfa61a28abf838c98263/html5/thumbnails/10.jpg)
Simplify – using properties
![Page 11: Properties of Real Numbers. Properties of Addition & Multiplication: For all real #’s, a, b, c… Closure: then a+b is a real number ab is a real number](https://reader036.vdocuments.site/reader036/viewer/2022073121/5697bfa61a28abf838c98263/html5/thumbnails/11.jpg)
Simplify – using properties
![Page 12: Properties of Real Numbers. Properties of Addition & Multiplication: For all real #’s, a, b, c… Closure: then a+b is a real number ab is a real number](https://reader036.vdocuments.site/reader036/viewer/2022073121/5697bfa61a28abf838c98263/html5/thumbnails/12.jpg)
Simplify – using properties
![Page 13: Properties of Real Numbers. Properties of Addition & Multiplication: For all real #’s, a, b, c… Closure: then a+b is a real number ab is a real number](https://reader036.vdocuments.site/reader036/viewer/2022073121/5697bfa61a28abf838c98263/html5/thumbnails/13.jpg)
Simplify – using properties
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Homework
Worksheet