# Notes and discussion

August 25-26, 2011

1. always line up the decimals. (they should form a straight line)

example:  123.456 + 456.123=    123.456

+456.123

579.579 (decimals should form a straight line)

subtraction example:  45.75 - 23. 5 =  45.75

-23.5

22.25 (decimals should form a straight line).

Key Note: REMEMBER TO ALWAYS KEEP NUMBERS BALANCED. YOU MAY HAVE TO ADD ZEROS WHEN SUBTRACTING SO THAT NUMBERS ARE BALANCED.

August 29 - Sept. 2

Multiplying Decimals:      35.2

x 2.3

1. multiply as normal     80 96

2. count the TOTAL numbers to the right of the decimal.  (there are only two numbers the 2 and 3).

3. starting at the end of your answer (moving to the left) move the same amount of spaces as the numbers behind the decimal. ( two number, two spaces)

4. insert decimal  80.96 (there are two numbers to the right of the decimal, therefore, you must have two numbers to the right of the decimal in your product).

Dividing Decimals:

When dividing by  a whole number

1. divide as normal.

2.  carry the decimal straight up into the quotient.

When dividing by a decimal.

1. move the decimal in the divisor to the right until you have a whole number.(move the decimal until it is behind the last digit)

2. move the decimal in the dividend the same amount of spaces that you moved in the divisor.

3. divide as normal

4. carry the decimal straight up into the quotient.

September 4 - 9

Adding and Subtracting with like and unlike denominators.

steps:

1. find common denominators

2. make equivalent fractions using the new denominator.

3. add or subtract the numerators.

Adding and Subtracting with unlike denominators using the Butterfly method.

1. make your wings by cross multiplying.

3. multiply the denominators

4. simplfy if possible

***** TO USE THE BUTTERFLY METHOD WITH MIXED NUMBERS YOU MUST CHANGE THE MIXED NUMBERS TO IMPROPER FRACTIONS THEN FOLLOW STEPS 1-4.********

September 12- 16

Multiplying and Dividing fractions and mixed numbers.

1. multiply numerators

2. multiply denominators

3. simplify if necessary

*****YOU CANNOT MULTIPLY MIXED NUMBERS. THEREFORE YOU MUST CHANGE MIXED NUMBERS TO IMPORPER FRACTIONS. THEN FOLLOW STEPS 1-3.*******

DIVIDING FRACTIONS AND MIXED NUMBERS

1. KEEP THE FIRST FRACTION THE SAME

2. CHANGE THE DIVISON SYMBOL TO MULTIPLICATION

3. USE THE RECIPROCAL OF THE SECOND FRACTION (FLIP IT AROUND)

4. MULTIPLY NUMERATORS

5. MULTIPLY DENOMINATORS

6. SIMPLIFY

****CHANGE MIXED NUMBERS TO IMPROPER FRACTIONS THEN FOLLOW STEPS 1-5.

Sept. 26-30

Adding, Subtracting, Multiplying, and Dividing with integers.

1.  if the signs are the same add and keep the same sign. 4+5 = 9

-4 + -5 = -9

2. if the signs are different , subtract the numbers and use the sign of the largest number.  4 + -5 = -1

5 + -4 = 1

Rules for subtracting integers:

1. add the opposite to the first integer.  4 - 5

4 + -5 + -1

2. then use the addition rules.

Rules for multiplying and dividing integers:

1.  if the signs are the same the answer is POSTIVE.

2. if the signs are different the answer is NEGATIVE.

THESE RULES APPLY TO BOTH MULTIPLY AND DIVIDE.

REMEMBER: SAME SIGN = POSITIVE ANSWER