Math 6A ( Periods 2 & 5)

Integers and Absolute Value 11-1

The following numbers are integers:

… -3, -2, -1, 0, 1, 2, 3,…

The absolute value of an integer is the distance between the number and zero on a number line. The absolute value of a number a is written │a│

Find the absolute value of 2 and graph it on the number line

Find the absolute value of -3 and graph it on a number line

Remember plotting a point involves actually putting a “closed dot” on the number line at the point you are graphing! The numbers go BELOW the number line—not above it

Are absolute values always positive?  What about ZERO?

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

A number line can be used to compare and order integers.
Numbers to the left are LESS THAN numbers to the right.
Numbers to the right are MORE THAN numbers to the left.

Compare 1 and  │-4│     One way is to graph them on the number line.

The freezing point is the temperature at which a liquid becomes a solid.

Substance	Freezing Point ⁰C
Butter	35
Airplane Fuel	-53
Honey	-3
Mercury	-39
Candle Wax	55

Which substance has the lowest freezing point?

Is the freezing point of mercury or butter closer to the freezing point of water,  0⁰C?

The freezing point of water is  so you can use absolute values to compare
Mercury:  │-39│= 39                       Butter: │35│= 35

Because 35 is less than 39, the freezing point of butter is closer to the freezing point of water.

Good thinking: Determine whether the statement is true of false

A. If x < 0 then  │x│ = -x     ( THIS IS TRUE!... why?)

B. The absolute value of every integer is positive. (THIS IS FALSE… why?)