Mathematics
Grade 5
15 min
Properties of multiplication
Properties of multiplication
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1
Introduction & Learning Objectives
Learning Objectives
Identify and define the Commutative Property of Multiplication.
Identify and define the Associative Property of Multiplication.
Identify and define the Distributive Property of Multiplication.
Explain the Identity Property of Multiplication.
Explain the Zero Property of Multiplication.
Apply multiplication properties to simplify calculations and solve problems.
Use properties to check the accuracy of multiplication problems.
Have you ever wondered if changing the order of numbers in a multiplication problem changes the answer? 🤔 Let's find out how multiplication 'behaves'!
In this lesson, we'll discover special rules, called properties, that make multiplication easier and more predictable. Understanding these properties will help y...
2
Key Concepts & Vocabulary
TermDefinitionExample
Commutative Property of MultiplicationThis property states that you can multiply numbers in any order, and the product (answer) will always be the same.If you have 3 groups of 5 apples, it's the same as having 5 groups of 3 apples. Both give you 15 apples. So, $3 imes 5 = 5 imes 3$.
Associative Property of MultiplicationThis property states that when you multiply three or more numbers, you can group them in different ways, and the product will still be the same. The parentheses tell you which operation to do first.To multiply $2 imes 3 imes 4$, you can do $(2 imes 3) imes 4 = 6 imes 4 = 24$, or you can do $2 imes (3 imes 4) = 2 imes 12 = 24$.
Distributive Property of MultiplicationThis property lets you multiply a sum by multiplying each addend separat...
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Core Formulas
Commutative Property
$a imes b = b imes a$
You can swap the order of the numbers being multiplied without changing the product. This helps in mental math by rearranging numbers to make them easier to multiply.
Associative Property
$(a imes b) imes c = a imes (b imes c)$
When multiplying three or more numbers, you can change the grouping of the numbers using parentheses. This is useful for finding easier pairs to multiply first, especially with larger numbers.
Distributive Property
$a imes (b + c) = (a imes b) + (a imes c)$
To multiply a number by a sum, you can multiply the number by each part of the sum separately and then add the results. This is great for breaking down larger multiplication problems into smaller, easier ones.
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Challenging
Which equation is ALWAYS true for any numbers chosen for a, b, and c because of the Associative Property?
A.a x b x c = c x b x a
B.a x (b x c) = (a x b) x c
C.a x (b + c) = (a x b) + c
D.a x 1 + b x 0 = a
Challenging
The Distributive Property is usually shown with addition, like a x (b + c). It can also be used with subtraction. Which expression shows the best way to use this idea to solve 8 x 98 mentally?
A.8 x (100 - 2)
B.(8 x 100) - 2
C.8 x (90 + 8)
D.(8 x 90) - (8 x 8)
Challenging
Leo tried to solve 4 x (5 + 2). His work was: (4 x 5) + 2 = 20 + 2 = 22. The correct answer is 28. Which property did Leo apply incorrectly?
A.Distributive Property
B.Associative Property
C.Commutative Property
D.Identity Property
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