Terminology
• Positive integers are to the right of zero on a number line.
• Negative integers are to the left of zero on a number line.
• Zero is neither positive nor negative.
• > means greater than, < means less than
• An integer is larger than a given integer if it is to the right of that integer on a number line. -4 > -5 and 5 > 4. (-4 is greater than -5 and 5 is greater than 4)
• The absolute value of an integer is its distance from zero. Distance is always a positive number. The symbol for absolute value is |#| |-4| is 4 (-4 is 4 units away from zero)… |5| is 5 (5 is 5 units away from zero).
Addition on a number line
Start at the first number given and go in the direction and magnitude of the second number. (You would actually start at zero and go in the direction and magnitude of the first number and that is why the first number can be considered your starting point)
RULE FOR ADDING 2 NUMBERS WITH THE SAME SIGNS (both numbers are either positive numbers or they are both negative numbers) – ADD THE MAGNITUDE OF THE NUMBERS (absolute value of that number) AND KEEP THE SIGN OF BOTH NUMBERS
RULE FOR ADDING 2 NUMBERS WITH THE OPPOSITE SIGNS (adding a positive number to a negative number or adding a negative number to a positive number…addition is commutative which means the order in which the numbers are written does not matter in the valuation of their sum…3 + 4 = 4 + 3 , -2 + (-5) = -5+ (-2) , 5 + (- 3) = -3 + 5
* All integers or numbers are considered to be positive unless they are preceded by a negative sign. If the second number is negative it will usually have a parenthesis around it to avoid the confusion…….. -3 + -4 looks confusing so it is written instead as -3 + (-4)….some books put the negative sign near the top of the number to avoid this confusion…
Most books state the rule for adding 2 integers with opposite signs is to take the absolute value of the two numbers and subtract the smaller number from the larger number, giving the answer the sign of the larger number. This simply means that if you went 7 units in the positive direction and only 5 units in the negative direction (opposite direction of positive) you would end up 2 units on the positive side of the number line. If you go 5 units in the negative direction and then 9 units in the positive direction you would end up 4 units on the positive side of the number line.
