Learn about multiplying and dividing integers through these examples with detailed step-by-step explanations.
Example 1: Rules for Multiplication of Integers
Explain the rules for multiplying two integers.
Rule 1: When multiplying two integers with the **same sign** (both positive or both negative), the product is always **positive**.
Example: 3 x 4 = 12 ; (-3) x (-4) = 12
Rule 2: When multiplying two integers with **different signs** (one positive and one negative), the product is always **negative**.
Example: 3 x (-4) = -12 ; (-3) x 4 = -12
Rule 3: The product of any integer and zero is always zero.
Example: 5 x 0 = 0 ; (-5) x 0 = 0
Example 2: Multiplying Integers
Calculate: (-6) x 5
Step 1: Identify the integers being multiplied: -6 and 5.
Step 2: Determine the signs of the integers. -6 is negative, and 5 is positive. The signs are different.
Step 3: Recall the rule for multiplying integers with different signs: The product is negative.
Step 4: Multiply the absolute values of the integers: 6 x 5 = 30.
Step 5: Apply the determined sign to the product. Since the signs were different, the product is negative.
Step 6: Therefore, (-6) x 5 = -30.
Example 3: Rules for Division of Integers
Explain the rules for dividing two integers.
Rule 1: When dividing two integers with the **same sign** (both positive or both negative), the quotient is always **positive**.
Example: 12 ÷ 4 = 3 ; (-12) ÷ (-4) = 3
Rule 2: When dividing two integers with **different signs** (one positive and one negative), the quotient is always **negative**.
Example: 12 ÷ (-4) = -3 ; (-12) ÷ 4 = -3
Rule 3: Dividing any non-zero integer by zero is undefined. Dividing zero by any non-zero integer is zero (0 ÷ 5 = 0, 0 ÷ -5 = 0).
Example 4: Dividing Integers
Calculate: (-20) ÷ 4
Step 1: Identify the integers being divided: -20 (dividend) and 4 (divisor).
Step 2: Determine the signs of the integers. -20 is negative, and 4 is positive. The signs are different.
Step 3: Recall the rule for dividing integers with different signs: The quotient is negative.
Step 4: Divide the absolute values of the integers: 20 ÷ 4 = 5.
Step 5: Apply the determined sign to the quotient. Since the signs were different, the quotient is negative.
Step 6: Therefore, (-20) ÷ 4 = -5.
Practice Mode
Enter a simple integer multiplication or division problem.
Note: This basic solver can calculate the product or quotient of two integers (e.g., "5 x -3", "-12 / -4", "calculate 8 * 2", "divide -25 by 5"). Use x, *, or 'times' for multiplication, and / or 'divided by' for division.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of integer operations.
Integers
The set of positive and negative whole numbers, including zero.
Positive Numbers
Numbers greater than zero.
Negative Numbers
Numbers less than zero.
Product
The result of multiplication.
Quotient
The result of division.
Rules of Signs
The rules for determining the sign of the result when multiplying or dividing positive and negative numbers.
