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Integers An integer is any whole number. A whole number is a number like 1,2,3,4,5 etc. It is not a fraction, like ˝ , or a decimal, like 3.5 Integers include the number 0 Positive integers are numbers that are greater than 0, like 1, 14, 29, …. Negative integers are numbers that are less than 0, like -1, -5, -28, -108, …. As you can see, there are an infinite number of integers. For positive integers, whatever number you come up with, you can always add 1 to it, and you have another integer. For negative integers, whatever negative integer you come up with, you can always subtract 1 and come up with another negative integer. Here is a graph of a few integers on a ‘Number Line’. ___.____.____.____.____.____.____.____.____. -4 -3 -2 -1 0 1 2 3 4
Zero is neither positive nor negative. Integers greater than 0 are ‘positive’ integers. Integers less than 0 are negative integers. Opposites are integers that are the same distance from zero in opposite directions on the number line. So -3 is the opposite of +3. Notice that integers to the right of 0 do not have a + sign. The + sign is implied. Note: the difference between a +3 and a -4 on the number line is 7, not -1. Start at -3 and count to the right. The absolute value of an integer on the number line is equal to its distance from 0. The absolute value of -4 is 4. The absolute value of +4 is also 4.
When you add integers, if they have the same sign, you add the two integers. The answer has the same sign. 5 + 6 = 11 - 5 - 4 = - 9 If the integers have different signs, you subtract the smaller integer from the larger integer. The answer has the sign of the larger integer. +5 – 6 = - 1 - 2 + 8 = 6
When subtracting integer b from integer a, change the sign of integer b, and then add. Example 1: + 5 – ( + 3) = Change the sign of ( + 3) to ( - 3) , and then add: + 5 + ( - 3 ) = + 5 – 3 = 2 Example 2: (- 4 ) – ( - 7 ) Change the sign of ( - 7 ) to ( + 7 ), and then add: ( - 4 ) + ( + 7 ) = - 4 + 7 = 3
When multiplying integers, multiply the two numbers as though they were both positive. (We could also say multiply the absolute value of the two numbers.) The sign of the answer is: Positive if the signs of the two numbers are the same. Negative if the signs of the two numbers are different. Example 1: - 7 X - 8 = 56 Example 2: 5 X - 9 = - 45
When dividing integers, divide the two numbers as though they were both positive. (We could also say divide the absolute value of the two numbers.) The sign of the answer is: Positive if the signs of the two numbers are the same. Negative if the signs of the two numbers are different.
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