Key Terms
What is a counting number, also called a natural number?
positive integer
Is zero is an integer?
Yes. Integers are the set of numbers that includes the counting numbers (also called “natural numbers”), 0, and the opposites of the counting numbers on the other side of 0 on the number line, that is, … –4, –3, –2, –1, 0, 1, 2, 3, 4 …
Positive numbers can be represented symbolically with or without a positive sign (+).
True. Positive numbers can be represented symbolically with or without a positive sign (+), but they can also be represented without a sign.
What is the opposite integer of 3?
-3
Is the temperature on a thermometer an example of integers in the real world?
Yes. The temperature on a thermometer can be a positive integer, 0, or a negative integer.
What is the set of numbers that includes the counting numbers(also called “natural numbers”), 0, and the opposites of the counting numbers on the other side of 0 on the number line, that is, … –4, –3, –2, –1, 0, 1, 2, 3, 4 …?
integers
Is zero a positive nor negative number?
No, zero is neither positive nor negative.
The only correct way to draw a number line is to extend to the left and right of zero, where the left is negative numbers and the right is positive numbers.
False. A horizontal number line extends to the left and right of zero, but a vertical number line extends above and below zero. Both are correct.
What is the opposite integer of 298?
-298
Is the number of days in a month an example of integers in the real world?
No. It is impossible to have a negative number of days in a month.
What is a number shown with a minus symbol that is to the left of 0 on a number line a countable number of spaces; for example, −1, −2, −3, and −4?
negative integer
What is the opposite integer of zero?
Zero.
Counting numbers are also known as negative integers.
False. Counting numbers are also known as positive integers.
What is the opposite integer of -4.5 Million?
4.5 Million
Is the distance below sea level an example of integers in the real world?
Yes. The distance below sea level (or distance above sea level) can be a positive integer, 0, or a negative integer.
What are the two numbers equally far from 0 on opposite sides of 0 on a number line; for example, the integers −2 and +2?
opposite integers (are also “additive inverses”)
What do we call the number of units counted or measured from zero (either in the positive or negative)?
Magnitude
Symmetry of the number line extends infinitely to the left and right of zero or above and below zero.
True
Does every positive number have an opposite negative number?
Yes. Every positive number has an opposite negative number with the same magnitude.
Is the money in your parents' bank account an example of integers in the real world?
Yes. The money in your parents' bank account can be a positive integer (like a payroll deposit), 0 (they are broke), or a negative integer (they are in debt or overdraft).
What is a number of units counted or measured from zero on the number line?
magnitude
On a number line visualized vertically, what numbers are negative?
The number below zero on the number line visualized vertically.
Negative numbers can be represented symbolically with a negative sign (−).
False! Negative numbers must be represented symbolically with a negative sign (−). If they did not have a sign, then they would be positive numbers.
What is another name for opposite integers?
additive inverses
Is π (pi or 3.14159...) an example of integers in the real world? (Hint: integers are defined as the set of numbers that includes the counting numbers (also called “natural numbers”), 0, and the opposites of the counting numbers on the other side of 0 on the number line, that is, … –4, –3, –2, –1, 0, 1, 2, 3, 4 …)
No. Pi is a positive integer (not a set of numbers), and is always a positive number.