Mathematics
Grade 6
15 min
Multiply and divide integers
Multiply and divide integers
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define integers, positive integers, and negative integers.
State the rules for multiplying integers with the same signs.
State the rules for multiplying integers with different signs.
State the rules for dividing integers with the same signs.
State the rules for dividing integers with different signs.
Accurately multiply any two integers.
Accurately divide any two integers (where the divisor is not zero).
Have you ever wondered how to calculate temperature changes when it gets really cold, or track money when you owe someone? 🥶💸 Integers help us understand numbers below zero!
In this lesson, you'll learn the essential rules for multiplying and dividing integers. Understanding these operations is crucial for solving more complex math problems and...
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Key Concepts & Vocabulary
TermDefinitionExample
IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero.... -3, -2, -1, 0, 1, 2, 3 ...
Positive IntegerAn integer greater than zero. These are often written without a sign, or with a '+' sign.5, 12, 100
Negative IntegerAn integer less than zero. These are always written with a '-' sign.-5, -12, -100
ProductThe result of multiplying two or more numbers.In $3 \times 4 = 12$, the product is 12.
QuotientThe result of dividing one number by another.In $12 \div 4 = 3$, the quotient is 3.
Absolute ValueThe distance of a number from zero on the number line, always a positive value. It tells us the 'size' of the number without its sign.The absolute value of -5 is 5, written as $|-5| = 5$. The absolute value of 5...
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Core Formulas
Multiplication/Division Rule: Same Signs
$$(+ \times +) = +$$ $$( - \times -) = +$$ $$(+ \div +) = +$$ $$( - \div -) = +$$
When you multiply or divide two integers with the same sign (both positive or both negative), the result is always positive.
Multiplication/Division Rule: Different Signs
$$(+ \times -) = -$$ $$( - \times +) = -$$ $$(+ \div -) = -$$ $$( - \div +) = -$$
When you multiply or divide two integers with different signs (one positive and one negative), the result is always negative.
Multiplication/Division Rule: Involving Zero
$$a \times 0 = 0$$ $$0 \div a = 0 \text{ (where } a \neq 0 \text{)}$$ $$a \div 0 = \text{undefined}$$
Any integer multiplied by zero is zero. Zero divided by any non-zero integer is zero. You cannot divide any number by zero; it i...
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Challenging
The product of seven integers is a negative number. Which of the following MUST be true?
A.All seven integers are negative.
B.There is an odd number of negative integers.
C.There is an even number of negative integers.
D.Exactly one of the integers is negative.
Challenging
If x and y are two different non-zero integers, and their product (x × y) is positive, what can you conclude about their quotient (x ÷ y)?
A.The quotient must be negative.
B.The quotient must be positive.
C.The quotient could be positive or negative.
D.The quotient must be an integer.
Challenging
An integer 'n' is multiplied by -1, and the result is then divided by -1. What is the final number?
A.1
B.-1
C.-n
D.n
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