Intro To Integers

Integers Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative(-), positive(+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the valve of the integer.

Positive Integers Are to the right of zero Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3.

Negative Integers Are to the left of zero Are valued less than zero. Express ideas of down or a lose. The sign for a negative integer is (-). This sign is always needed.

Zero is neither positive or negative Positive integers are valued more than zero, and are always to the right of zero. Negative integers are valued less than zero, and are always to the left of zero.

End of Part One

The “net worth” of opposite integers is zero.

Opposite Integers Opposite integers always have a “net worth” of 0. This is called the ZERO PRINCIPAL. Opposite integer have the same “absolute value”, meaning the distance from the points on a number line to zero is the same. This can be referred to as the integers magnitude.

Movement on a Number Line Magnitude and Direction Every integer represents a magnitude and a direction. The integer +3 describes a movement of 3 units in a positive direction.(right) The sign (+) tells you the direction. The number (3) indicates how far to move or the MAGNIUDE( a move- ment of 3 units) + 3 Direction Magnitude

Which integer has a higher value? Comparing Integers Which integer has a higher value? -4 or -8

Comparing Integers Use your number line to help you compare each set of number. (i.e. for the numbers 3 ,and - 2 …. 3 > -2 -2 < 3) - 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15 e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14

Putting Things Together What is the greatest valued negative integer?

Comparing Integers Use your number line to help you compare each set of numbers. Copy the question and write two sentences for each pair of numbers. (i.e. for the numbers 3 ,and - 2 …. 3 > -2 -2 < 3) - 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15 e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14 i) 8, 7 j) - 8, - 7 k) 5, -1 l) 0, -2 m) 0, 3 n) - 5, 0 o) – 14, -10 p) - 9, 0 q) -7, -6 r) -1, 0 s) 4, -4 t) 0, -15

Comparing Integers Again For each of the previous questions (a) to (t), write a new mathematical sentence showing how much bigger or smaller the first number is than the second. (i.e. 3, - 2 ….. 3 is 5 more than –2)

Review What We Know

Direction + 3 Magnitude

Comparing Integers -5 ___ -8 0 ___ -3 3 ___ +2

Positive and Negative Integers For each of the following numbers, write down an example of where it could be used and what it means in that situation. -3 -100m +15 +3050m -$45.83