Multiplying Integers

Below is a quick summary for the rules of multiplying integers.

rules for multiplying integers or integer multiplications the product of two integers with the same sign is always positive. on the other hand, the product of two integers with different signs is always negative

The rules that govern how to multiply and divide integers are very similar. In this lesson, we will focus on the multiplication of integers.

Rules on How to Multiply Integers

Step 1: Multiply their absolute values.

Step 2: Determine the sign of the final answer (in this case it is called the product because we are multiplying) using the following conditions.

  • Condition 1: If the signs of the two numbers are the same, the product is always a positive number.
This is an illustration showing that when you multiply two numbers with the same sign, the answer is always positive. That is, positive times positive is positive and negative times negative is negative. In math symbols, we have (+)*(+)=+ and (-)*(-)=+.
  • Condition 2: If the signs of the two numbers are different, the product is always a negative number.
This diagram shows that when you multiply two numbers with different signs, the answer is always negative. That is, positive times negative is negative and negative times positive is negative. In math symbols, we have (+)*(-)=- and (-)*(+)=-.

Examples of Integer Multiplications

Example 1: Multiply the integers below.

Positive 4 multiplied by negative 7

Solution: First, get the absolute value of each number.

The absolute value of positive 4 is equal to 4 while the absolute value of negative 7 is positive 7.

Next, multiply or find the product of the absolute values.

The product of positive 4 and positive 7 is positive 18 which can be written in a numerical equation as 4x7=28.

Finally, determine the sign of the final answer. The rule states that if the signs of the two integers are different then the final answer will be negative.

+4*(-7)=-28

Example 2: Multiply the integers below.

Negative 15 multiplied by negative 3.

Solution: Multiply the absolute values of the two numbers.

The product of the absolute value of -15 and the absolute value of -13 equals +45.

Since we are multiplying integers having the same sign, the final answer (product) should be positive.

Negative 15 times negative 3 is equal to positive 45. In numerical equation, we have -15*(-3)=+45.

Example 3: Find the product of the three integers below.

Here we have three integers to multiply which is positive 3 times negative 8 times negative 2. In math symbols, we can write this as +3x(-8)x(-2).

Solution: We can also multiply three or more integers. We just have to multiply two integers at a time. Let me put a parenthesis to show which two numbers we’re going to multiply first. The product of  +3  and 8 equals  − 24. It is negative because the signs are different. Then multiply – 24 by 2 to get  +48. Remember, the product of two integers with the same sign is always positive.

+3*(-8)*(-2)=[+3*(-8)]*-2=(-24)*(-2)=+48

You may also be interested in these related math lessons or tutorials:

Multiplying Integers Practice Problems with Answers

Adding Integers

Subtracting Integers

Dividing Integers