Math 6A ( Periods 2 & 5)

Absolute Value 6.4

The absolute value of a number is the distance between the number and ZERO on a number line. The absolute value of a number a is written as │a│.

│-2│ = 2       │2│  = 2

  │a│ is read “ the absolute value of a.”

Distance is always positive OR zero!

When you write the notation for the absolute value, it means “take the absolute value of the number inside the symbols! “

When graphing  │-5│  first find the value of │-5│, which is 5, then graph it.  Make sure to identify the graph with the given number. In this case, │-5│

So we could conclude that  │-5│> 2.

Write these numbers in order from least to greatest.

│-12│, -8, -10, │6│, │-4│

We would get:

-10, -8, │-4│, │6│, │-12│

Which is greater  -50 or 25?   25

Now, which of those two has the greater absolute value?

 This time its -50 since

│25│= 25   and │-50│=50

The coldest possible temperature is called absolute zero. It is represented by 0 K on the Kelvin temperature scale.  See Page 273

Tell whether the statement is always, sometimes, or never true.

The absolute value of a number is greater than the number.  Sometimes- If the number is negative then its absolute value is greater, but if it is positive or zero then it is equal to its absolute value.

The absolute value of a negative number is positive. Always- The absolute value is the positive distance from zero on a number line.

The absolute value of a positive number is its opposite. Never- The absolute value of appositive number is the number itself

Math 6A ( Periods 2 & 5)

Fractions and Decimals on the Number line 6.3

How can we use a number line to compare positive and negative fractions and decimals?

Can you name a number between 1 3/6 and 1 4/6? Did you use equivalent fractions?

You can graph negative fractions and decimals in a similar manner to what we did with integers!  

Compare -1/2 and -3/4 
Notice -3/4 is farther to the left from 0. -1/2 is to the right of -3/4

So -1/2 > -3/4

Compare -4 5/6 and – 4 1/6

When you graph these two numbers, you notice that -4 5/6 is to the left of -4 1/6

So -4 5/6 < -4 1/6

Similarly with decimals

Comparing -3.08 and -3.8

-3.08 is to the right of -3.8 so

-3.08 > -3.8

Math 6A( Periods 2 & 5)

Comparing & Ordering Integers 6.2

On a  horizontal number line, numbers to the left are less than numbers to the right. Numbers to the right are greater than numbers to the left.

On a vertical number line, numbers below are less than numbers above. Numbers above are greater than numbers below.

When ordering numbers from least to greatest graph each number on a number line , then it is easy to list them! Write the integers as they appear on the number line from left to right!

Math 6A ( Periods 2 & 5)

Integers 6.1

Positive Numbers  are greater than 0. They can be written with or without a positive sign (+)

Negative Numbers are less than 0. They are written with a negative sign (-).

Two numbers that are the same distance from 0 on a number line, but on opposite sides of ZERO are called opposites. The opposite of 0 is 0.

Integers are the set of whole numbers and their opposites.

Note: ZERO (0) is neither positive NOR negative