1. INTEGERS NUMBERS
1. INTEGERS
• Integers are like whole numbers, but they also include negative numbers ... but still no
fractions allowed! The number line goes on forever in both directions. This is indicated by the
arrows.
• Whole numbers greater than zero are called positive integers. These numbers are to the right
of zero on the number line.
• Whole numbers less than zero are called negative integers. These numbers are to the left of
zero on the number line.
• So, integers can be negative {-1, -2,-3, -4, -5, … }, positive {1, 2, 3, 4, 5, … }, or zero {0} The
integer zero is neutral. It is neither positive nor negative.
• Two integers are opposites if they are each the same distance away from zero, but on opposite
sides of the number line. One will have a positive sign, the other a negative sign. In the number
line above, +
3 and -
3 are labeled as opposites.
• We can put that all together like this:
Z = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
2. COMPARING INTEGERS
We can compare two different integers by looking at their positions on the number line. For any two
different places on the number line, the integer on the right is greater than the integer on the left. Note
that every positive integer is greater than any negative integer.
Examples: 9 > 4 6 > -9 -2 > -8 0 > -5
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2. 3. OPERATIONS WITH INTEGERS
1. Adding Integers
• When adding integers of the same sign, we add their absolute values, and give the result the
same sign.
Examples:
2 + 5 = 7(-7) + (-2) = -(7 + 2) = -9
• When adding integers of the opposite signs, we take their absolute values, subtract the smaller
from the larger, and give the result the sign of the integer with the larger absolute value.
Example:
8 + (-3) = + 5 8 + (-17) = -9
2. Subtracting Integers
• Subtracting an integer is the same as adding its opposite.
Examples:
7 - 4 = 7 + (-4) = 312 - (-5) = 12 + (5) = 17 -8 - 7 = -8 + (-7) = -15
3. Multiplying Integers
• Like signs yield a positive result.
• Unlike signs yield a negative result.
• If one or both of the integers is 0, the product is 0.
Examples:
4 × 3 = 12 (-4) × (-5) = 20 (-7) × 6 = - 42 12 × (-2) = -24.
4. Dividing Integers
The rules for division are exactly the same as those for multiplication. If we were to take the rules
for multiplication and change the multiplication signs to division signs, we would have an accurate
set of rules for division.
Examples:
4 ÷ 2 = 2 (-24) ÷ (-3) = 8 (-100) ÷ 25 = -4
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