Integers and Negative Number Rules

Integers: Definition and Representation

Definition of Integers

  • Integers consist of all positive whole numbers, negative whole numbers, and zero.

  • Examples of integers: −3,−5,0,1,7,18-3, -5, 0, 1, 7, 18

  • Examples of non-integers: 1.6,12,5%,−2.431.6, \frac{1}{2}, 5\%, -2.43

Integers on a Number Line

  • Integers can be illustrated using a number line.

  • Numbers are arranged from left to right in increasing order.

  • Negative numbers are to the left of 0.

  • Positive numbers are to the right of 0.

  • Zero is neither positive nor negative.

Plotting Integers on a Number Line

  • To plot an integer, locate the corresponding point to the left or right of 0.

  • Example: Plotting 4

    • Since 4 is positive, move 4 units to the right of 0.

  • Example: Plotting -2

    • Since -2 is negative, move 2 units to the left of 0.

Real-World Examples of Integers

  • Temperature:

    • Below freezing: 10∘10^\circ below zero is −10∘-10^\circ

  • Elevation/Depth:

    • Below sea level: Death Valley is 282 feet below sea level, which is −282-282 feet.

    • Above sea level: Commercial airplanes fly at altitudes between 30,000 and 42,000 feet, represented as +30,000+30,000 to +42,000+42,000 feet.

  • Finances:

    • Overdraft/Negative balance: Spending more money than available results in a negative balance, like −-20.

  • Sports:

    • Yardage loss in football: A 5-yard loss is represented as −5-5 yards.

Scuba Diver Example

  • A scuba diver starts at the surface of the ocean (0 feet).

  • First dive: 35 feet down to a coral reef (−35-35 feet).

  • Second dive: Another 20 feet deeper to the sea floor.

  • The final depth is −55-55 feet.

Vocabulary for Solving Equations

  • Find the Sum = Add

  • Find the Difference = Subtract

  • Find the Product = Multiply

  • Evaluate this = Divide

  • Simplify this = Make a number or fraction smaller

Negative Number Rules

Sign Rules for Adding and Subtracting

  • Negative number: Move left on the number line.

  • Positive number: Move right on the number line.

  • Mixed Signs:

    • If the Positive number is larger, the answer is Positive.

    • If the Negative number is larger, the answer is Negative.

Sign Rules for Multiplying and Dividing

  • Mixed Signs (Positive and Negative):

    • The answer is always negative.

  • Both numbers are positive:

    • The answer stays positive.

  • Both numbers are negative:

    • The answer changes to positive.

  • One negative ruins the party, two negatives party to be positive.