Introduction to integers
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Integers are defined as whole numbers that can be positive, negative, or zero, and are used to represent real-world situations involving amounts above and below zero like elevation, temperature, financial gains and losses, and distances. Integers are located on a number line and adding integers involves moving right on the number line while subtracting involves moving left, with examples provided of calculating distances between elevations represented as integers.
Introduction to integers
- 1. Introduction to Integers
- 2. Integers Defined… • An integer (pronounced IN-tuh-jer) o is a whole number o Is not a fraction. o Is a number that can be positive, negative, or zero. opposite integers -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 negative integers positive integers
- 3. Four real life situations in which integers can be used. • Spending and earning money • Rising and falling temperatures • Stock market gains and losses • Gaining or losing metres in an NRL game. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 Note: A positive integer does not have to have a + sign. For example, +3 and 3 are the same.
- 6. Adding and Subtracting with Integers Using a number line you add by moving to the right. e.g. -2+3 = 1 (As shown on the diagram below).
- 7. Subtracting Integers Similarly, when you are subtracting integers, you are Moving the arrow to the left. No matter where you start on the number line, you always move to the left. E.g. (-5) – 2 = -7
- 8. Adding and Subtracting Integers Some different, slightly more difficult examples •3+(-7) becomes 3 – 7 = -4 •-5 + (-2) becomes -5 – 2 = -7 •5-(-3) becomes 5 + 3 = 8 •-6-(-3) becomes -6 + 3 = -3
- 9. • The Problem: The highest elevation in Northern Lookout is Snow Peak, which is 15 237 metres above sea level. The lowest elevation is Tree Valley, which is 368 metres below sea level. What is the distance from the top of Snow Peak to the bottom of Tree Valley?
- 10. Solution We can represent each elevation as an integer: Elevation Integer 15 237 metres above +15 237 sea level Sea level 0 368 metres below -368 sea level The distance from the top of Snow Peak to the bottom of Tree Valley is the same as the distance from +15 237 to -368 on the number line. We add the distance from +15 237 to 0, and the distance from 0 to -368, for a total of 15 605 metres.
- 11. • Integers are the set of whole numbers and their opposites • Whole numbers larger than zero are called positive integers; whole numbers less than zero are called negative integers • The integer zero is neither positive nor negative. • Two integers are opposites if they are the same distance away from zero, but on opposite sides of the number line. • Positive integers may be written with or without a sign.