Prepare for a quiz on 9-14

Wednesday's quiz will be on multiple representations of data.  We have studied tables, graphs, and expressions as ways of representing information.  You will demonstrate your ability to create different representations from an initial set of numbers, and you will be able to convert from table, to graph, to an expression and vice versa.

You will be able to see the pattern in a table of numbers.

You will be able to write an expression for a pattern of numbers.

You will be able to draw a graph from a table.

You will be able to make a table from a graph.

You will be able to write the linear equation of a straight graph.

You will be able to draw a graph from a linear equation.

You will be able to discuss differences between shapes of graphs.

After the 9-8 quiz

Given the number 23, write an equation which relates it to its reciprocal and the identity element for multiplication.

The number is 23, the reciprocal is 1/23, the identity element for multiplication is 1, because 23 * 1 = 23, the identical number.
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23 times 1/23 is 1
23 * (1/23) = 1
1/23 is the reciprocal or multiplicative inverse of 23



Given the number 23, write an equation which relates it to its opposite and the identity element for addition.

The number is 23, the opposite is -23, the identity element for addition is 0, because 23 + 0 = 23, the identical number.

23 added to -23 is zero
23 + (-23) = 0
-23 is the opposite or additive inverse of 23

Algebra Properties 9-7-2011

Transitive - If a = b and b = c, then a = c
If two things are equal to a middle thing, they are equal to each other.
Substitute a for b into b = c.  This gives a = c.

Reflexive - A thing is equal to itself
a = a

Symmetric - You can write an equality in either order
if a = b then b = a




Identity elements -

0 is what you add to a number to get the identical number

1 is what you multiply by a number to get the identical number

To get from a number to the identity element for addition, add the opposite of the number
To get from a number to zero, add the negative of the number
To get from 7 to 0, add -7
7 + (-7) = 0

To get from a number to the identity element for multiplication, multiply by the reciprocal of the number
To get from a number to 1, multiply by the reciprocal of the number
To get from 7 to 1, multiply by 1/7
7 * (1/7) = 1

Study hints for Math 9 Quiz 9-8

Math 9 Quiz Thursday 9-8     - Study hints

Given some numbers, tell which numbers are in a category.

Which numbers are irrational?

2      pi      2.22     2/4     square root of 2    

Which numbers are rational?

2      pi      2.22     2/4     square root of 2

Which numbers are whole?

2      -2     2/4     -4/2      6/2

Be able to define real numbers with words or with a diagram

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Be able to place numbers correctly into an N-W-I-R / Irrational and Real diagram

Be able to give an example of an algebra property (Commutative, Associative, Distributive, Reflexive, Symmetric, Transitive)

Be able to place parentheses properly into an Associative equation.

From a list of examples, be able to identify an algebra property (Commutative, Associative, Distributive, Reflexive, Symmetric, Transitive)

Explain the difference between the identity element for addition and the identity element for multiplication.

Given a number, write its opposite and its reciprocal.

Identify or give an example of the Reflexive, Symmetric, and Transitive Properties of Equality

Use Substitution to explain the Transitive Property.

Inversesand identity elements

Identity means "that which stays the same".  If you move, or grow, many things about you stay the same even though you address or your height may change.  Those things stay identical.

If you get something that's identical, you get something that's the same.  An extra picture can be identical to a first picture.

In math an identity element is a number that, when used with a stated operation, gets you the same thing.

Zero is the identity element for addition because when you add 0 to any number, you get the same thing:
97 + 0 = 97     and      2z + 0 = 2z

One is the identity element for multiplication becasue when you multiply any number by 1, you get the same thing:     86 times 1 = 86     and     7b times 1 = 7b

An additive inverse, when added to a first number, gets you 0, the identity element for addition
4 plus -4 = 0, so -4 is the additive inverse of 4

A multiplicative inverse, when multiplied by a first number, gets you 1, the identity element for multiplication
4 times  1/4 = 1, so 1/4 is the multiplicative inverse of 4

An additive inverse is a also an opposite, since you change sign to get it
4 becomes its additive inverse, or opposite, by changing sign to -4

A multiplicative inverse is also a reciprocal,since you flip a numerator and a denominator to get it
4 becomes its multiplicative inverse, or reciprocal by flipping from 4/1 to 1/4

Commutative, Associative and Distributive Properties 9-1

Commutative, Associative and Distributive Properties for addition and multiplication.
(not for subtraction and division)

a + b   =   b + a
a times b   =   b times a

When you add or multiply two things, you can do them in either order.


(a + b) + c   =   a + (b + c)
(a x b) x c   =   a x (b x c)

When you add or multiply three things, you can start with the first two or the last two.


a times ( b + c )   =   a times b   +   a times c
a x ( b + c )   =   a x b   +   a x c

When you multiply a sum, the multiplication takes place with each of the things in the sum.


Homework for 9-6:  page 20-21;  items 7, 8, 9, 10

Three inequalities form a polygonal region 9-1