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Integers

This document defines integers and describes their properties. Integers include all whole numbers and their opposites on the negative number line, including zero. Positive integers are greater than zero, while negative integers are less than zero. A number line visually represents integers extending in both directions from zero. Negative numbers are used to represent temperatures below zero and depths below sea level. Integers can be added, subtracted, multiplied, and divided, with specific rules governing the sign of the resulting integer based on the signs of the integers in the operation.

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INTEGERS MADE BY – DEEPANSHA SINGH CLASS – VI A ROLL NO. - 13
What Are Integers? • Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero. i.e. 7 opposite -7
What Are Positive Integers? • Positive integers – a number greater than zero. 0 1 2 3 4 5 6
What Are Negative Integers? • Negative integers – a number less than zero. -6 -5 -4 -3 -2 -1 0
What Is A Number Line? Number line - • A line with arrows on both ends that show the integers with slash marks • Arrows show the line goes to infinity in both directions ( + and -) • Uses a negative sign (-) with negative numbers but no positive sign (+) with positive numbers • Zero is the origin and is neither negative nor positive
Negative Numbers Are Used to Measure Temperature
Negative Numbers Are Used to Measure Under Sea Level 30 20 10 0 -10 -20 -30 -40 -50
Negative Numbers Are Used to Show Debt Let’s say our parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in -$5.000 to show they still owe the bank.
Positive & Negative Numbers Working with positive and negative numbers is like driving in traffic. We have to watch the traffic signs and follow the driving rules.
Hint • If we don’t see a negative or positive sign in front of a number it is positive. i.e. 9 means + 9
What Can We Do to Integers? • Integers are numbers, so we can add, subtract, multiply, and divide them • Each operation has different rules to follow
Adding Rules – Same Signs • If the integers have the SAME signs: ADD the numbers & keep the same sign! • Positive + Positive = Positive Answer • Negative + Negative = Negative Answer Examples: -3 + (-10) = ? ? = -13 • 6 + (8) = ? ? = 14
Adding Rules – Different Signs • If the integers have the DIFFERENT signs: SUBTRACT the numbers & use sign of the BIGGER number! • Bigger # is Positive = Positive Answer • Bigger # is Negative = Negative Answer Examples: -13 + (7) = ? ? = -6 • 23 + (-8) = ? ? = 15
Subtracting Rules • Put ( ) around second number & its sign • Change SUBTRACTION sign to an ADDITION sign • Change sign of 2nd number to its opposite • Follow the rules for ADDITION: -SAME signs: Add & keep the same sign -DIFFERENT signs: Subtract & use sign of bigger Examples: -5 – -10 = ? ? = 5 9 - 23 = ? ? = -14
Multiplying Rules • Multiply the numbers like usual • If the integers have the SAME signs: ANSWER will be POSITIVE • If the integers have DIFFERENT signs: ANSWER will be NEGATIVE Examples: -3 · (-5) = ? ? = 15 • -9 · (-10) = ? ? = 90 -7 · 7 = ? ? = -49 • 6 · -6 = ? ? = -36
Dividing Rules • Divide the numbers like usual • If the integers have the SAME signs: ANSWER will be POSITIVE • If the integers have DIFFERENT signs: ANSWER will be NEGATIVE • Examples: -33 ÷ (-3) = ? ? = 11 • -90 ÷ (-10) = ? ? = 9 -20 ÷ 2 = ? ? = -10 • 6 ÷ (-6) = ? ? = -1
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