Narration: Here are some examples of adding and multiplying integers. Negative 4 plus 8 equals 4.
Negative 6 times zero equals zero. Negative 8 times negative 4 equals 32. Negative 6 plus negative 1 equals negative 7.
Image description: Each equation appears onscreen as it is spoken.
Narration: Look closely at the solutions. What set of numbers (natural, whole or integer) do the solutions fall into?
Image description: The solutions of the equations, 4, 0, 32 and negative 7 are highlighted in a box, and then shown in a row across the top of the screen.
Narration: All of the solutions are integers. The sum or product of two integers is always an integer. To disprove this, see if you can find a counterexample. Remember, the set of integers is the set of whole numbers and their opposites.
Image description: A graphic organizer displaying the Real Number system using two circles is shown. The circle on the left is the circle graphic organizer containing the Rational Numbers circle with the nested Integers circle, Whole Numbers circle and the Natural Numbers circle. Examples in the Rational Numbers circle include negative eight halves, two thirds, and the repeating decimal 111 thousandths. Examples in the integers circle include negative 4, negative 3, negative 2, negative 1, etcetera. The example given in the whole numbers circle is zero, and the examples given in the Natural numbers circle includes 1, 2, 3, 4, and so on. The circle on the right is a graphic organizer labeled Irrational Numbers, with examples including the square root of 2, pi, and the square root of 3.
Narration: Addition and multiplication of whole numbers and their opposites will never result in a action or a decimal. That is why the sum or product of two integers is always an integer.
Image description: The four equations from the beginning of the video reappear. Shown are the following equations. Negative 4 plus 8 equals 4. Negative 6 times zero equals zero. Negative 8 times negative 4 equals 32. Negative 6 plus negative 1 equals negative 7.