2.2 and 2.3

More on arithmetic

Properties for addition

Identity Property: There is a unique real number 0 such that for every real number a

a + 0 = a and 0 + a = a

Prop. Of Opposites: For every real number a, there is a unique real number –a such that

a + (-a) = 0 and (-a) + a = 0

Property of the Opposite of a Sum:

For all real numbers a and b

-(a + b) = (-a) + (-b)

Mishaps• -4 + -4

• 4 - (-4)

• -(-4) + 4

• -(-4) – 4

• -(4 + 4)

How would you rewrite using the communitive property?

4-3

200-(-300)

Subtraction is not communitive…you must convert to addition by using the property of opposites!!!

What would be a great way to use Associative and Communitive properties to do these mentally?

-16 + (-9) + 8 + 25

3.7 + 4.2 –x + y +6.3 + 12.8

-[24 + (-a)] + [-(-2 + a)]

Example• A submarine descended to a level 230 m

below the surface of the ocean. Later, it ascended 95 m and then dove 120 m. What was the new depth of the submarine?

SAT score break down for 1997 and 1998

Year Male Female Male Female

1997 507 503 530 494

1998 509 502 531 496

Verbal Math

Organize Data for the Verbal Portion

1997 1998

Male 507 509

Female 503 502

1997 1998

Male 530 531

Female 494 496

Notice that when we compare, they have the same format!!!

Organize Data for the Math Portion

Compare the overall SAT scores for the years 1997-1998 between girls and boys.

Organized Data for the Verbal Portion1997 1998

Male 507 509

Female 503 502

Organized Data for the Math Portion1997 1998

Male 530 531

Female 494 496

1997 1998

Male

Female

Totals

What are some things that need to be true in order to combine data?

Matrix:• Table of numbers without the headers.

• Usually represented with capital letters.

• Classified by its dimensions: rows x columns (m x n)

1997 1998

Male 507 509

Female 503 502

502503

509507

502503

509507A

Find two matrices comparing Matinee and Evening. Also determine the “total” matrix.

Theater Children Adult Children Adult

A 198 350 54 439

B 201 375 58 386

Matinee Evening