Integer multiplication and division rules

Learning Objectives Identify the sign of the product when multiplying two integers. Identify the sign of the quotient when dividing two integers. Apply the rules for multiplying integers with the same sign. Apply the rules for multiplying integers with different signs. Apply the rules for dividing integers with the same sign. Apply the rules for dividing integers with different signs. Solve real-world problems involving integer multiplication and division. Have you ever wondered how to calculate temperature changes when it drops several degrees each hour? 🌡️ Or how to keep track of money when you owe someone? In this lesson, you'll learn the simple yet powerful rules for multiplying and dividing positive and negative numbers, called integers. Understanding these rule...

TermDefinitionExample IntegerWhole numbers (0, 1, 2, 3, ...) and their opposites (-1, -2, -3, ...). Integers include positive numbers, negative numbers, and zero.-5, 0, 12, -100 Positive IntegerAny integer greater than zero. They are usually written without a sign or with a '+' sign.7, 25, 100 Negative IntegerAny integer less than zero. They are always written with a '-' sign.-3, -15, -50 ProductThe result obtained when two or more numbers are multiplied together.In 4 x 5 = 20, the product is 20. QuotientThe result obtained when one number is divided by another number.In 10 / 2 = 5, the quotient is 5. Absolute ValueThe distance of a number from zero on the number line, always expressed as a positive value.The absolute value of -7 is 7, written as |-7| = 7. The absolute...

Rule 1: Multiplying or Dividing Integers with the Same Sign `(+a) \times (+b) = + (a \times b)` `(-a) \times (-b) = + (a \times b)` `(+a) \div (+b) = + (a \div b)` `(-a) \div (-b) = + (a \div b)` When you multiply or divide two integers that have the same sign (both positive or both negative), the result (product or quotient) will always be positive. First, multiply or divide their absolute values, then make the answer positive. Rule 2: Multiplying or Dividing Integers with Different Signs `(+a) \times (-b) = - (a \times b)` `(-a) \times (+b) = - (a \times b)` `(+a) \div (-b) = - (a \div b)` `(-a) \div (+b) = - (a \div b)` When you multiply or divide two integers that have different signs (one positive and one negative), the result (product or quotient) will always be negati...