What Are Some Similarities Between Adding, Subtracting, Multiplying & Dividing Integers?

Adding Integers

• When adding positive integers, such as in 3 + 4, begin at the positive 3 on the number line and move 4 spaces to the right to land on the 7. When adding negative integers, such as in -2 + -5, begin on the -2 on the number line and move 5 spaces to the left (because the 5 is negative) to land on -7. For the addition of a positive and negative integer, such as -8 + 1, find the -8 on the number line and move 1 space to the right (since the 1 is positive) to land on -7.

Subtracting Integers

• The addition of negative numbers can also be turned into a subtraction problem, and vice versa. For example, 5 + -3 can also be written as 5 - 3 to get the answer 2. The subtraction of a negative number cancels the subtraction and changes it to adding a positive. For example, 3 - (-1) = 3 + 1. Because of this relationship, movements on a number line work the same for subtraction as for addition. For example, 5 - 3 or 5 + -3 takes the 5 and moves it 3 spots to the left for 2.

Multiplying Integers

• Multiplication works differently from addition and subtraction in that it isn't a simple number line shift. In the example 4 * 3, the multiplication represents adding the first number the number of times of the second number: 4 * 3 = 12 and 4 + 4 + 4 = 12. Multiplying two positive integers always produces a positive integer answer.

  Multiplying a positive and negative integer produces a negative answer. For example, 2 * -3 = -6. This is the same as -3 + -3 = -6. Multiplying two negative integers produces a positive answer. For example, -5 * -4 = 20. This is equal to -(-5) - (-5) - (-5) - (-5) = 5 + 5 + 5 + 5 = 20.

Dividing Integers

• When multiplying 3 * 2 for an answer of 6, the equation can also be worked backward by dividing the 6 by 3 for an answer of 2 (or 2 for an answer of 3). As addition is the opposite operation of subtraction, division is the opposite of multiplication.

  When dividing two positive integers, the answer will be positive. For example, 4 / 2 = 2. Check the answer by multiplying the second, smaller number from the division by the answer: 2 * 2 = 4. When a positive integer is divided by a negative integer, the answer is negative: 12 / -4 = -3. Check: -3 * -4 = 12. Two negative numbers produces a positive answer: -15 / -5 = 3. Check: 3 * -5 = -15.