This document provides information about integers and operations involving integers. It defines integers as whole numbers that include negative numbers, and describes how they are represented on a number line with positive integers to the right of zero and negative integers to the left. It then explains how to compare integers based on their position on the number line. Finally, it outlines the rules for performing addition, subtraction, multiplication and division with integers, including keeping the same sign when adding/multiplying integers with the same sign and changing to the opposite sign when combining integers with different signs.

1. I.E.S. MARÍA BELLIDO - BAILÉN
1º E.S.O. BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA
UNIT 1. INTEGERS
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. 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
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) = 3 12 - (-5) = 12 + (5) = 17 -8 - 7 = -8 + (-7) = -15

3. 3. Multiplying Integers
Rules for Multiplication
Positive x Positive Positive
Positive x Negative Negative
Negative x Positive Negative
Negative x Negative Positive
• 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