Numbers of Algebra 9
Examples
(2 · 7) is a real number.
1
35
8
⎛ ⋅
⎝
⎛⎛⎛⎛
⎝⎝
⎛⎛⎛⎛ ⎞
⎠
⎞⎞⎞
⎠⎠
⎞⎞⎞⎞ is a real number.[(2.5)(10.35)] is a real number.
1
2⎛ ⋅ 3
⎝
⎛⎛⎛⎛
⎝⎝
⎛⎛⎛⎛ ⎞
⎠
⎞⎞⎞⎞
⎠⎠
⎞⎞⎞⎞ is a real number.- Commutative Property of Addition.a + b = b + a. This property allows you to
reverse the order of the numbers when you add, without changing the sum.
Examples
455 = 545 = 9
1
2
3
4
3
4
1
2
5
4
+=+= =
05 .. 5464666. 1616 = ... 101101 54 = 66. 4
233 2323222 + = 42
- Commutative Property of Multiplication.a · b = b · a. This property allows
you to reverse the order of the numbers when you multiply, without
changing the product.
Examples
277 = 722 = 14
1
3
5
8
5
8
1
3
5
24
⋅=⋅=
(.. 5 )( 10 .)==(.( 3535 )()( 22 ..)) 25. 875
1
2
33
1
2
3
2
⋅ 3 ⋅=
- Associative Property of Addition. (a + b) + c = a + (b + c). This property
says that when you have three numbers to add together, the fi nal sum will
be the same regardless of the way you group the numbers (two at a time)
to perform the addition.
Example
Suppose you want to compute 6 + 3 + 7. In the order given, you
have two ways to group the numbers for addition:
(6 + 3) + 7 = 9 + 7 = 16 or 6 + (3 + 7) = 6 + 10 = 16
Either way, 16 is the fi nal sum.