Page 104 - Math Course 1 (Book 1)

Properties of Addition and Multiplication

Properties of Numbers

Property Words Symbols Examples

Additive When O is added to any For any number a,
Identity number, the sum is the a + 0 = 0 + a = a. 5 + 0 = 5
number.
Multiplicative When any number is For any number a,
Identity multiplied by 1, the a 1 = 1 a = a. 7 1 =7
product is the number 1 6 = 6

Multiplicative Property When any number is For any number a,
of Zero multiplied by 0, the a 0 = 0 a = 0. 4 0 = 0
product is 0 0 2 = 0

Find a Counterexample
Let’s Begin State whether the following conjecture is true

or false. If false, provide a counterexample.
Identify Properties Division of whole numbers is commutative.

Examples Write two division expressions using the
Commutative Property, and then check to see
whether they are equal.
Name the property shown by the statement
?
3 10 2 = 3 2 10 12 ÷ 6 = 6 ÷ 12 State the conjecture.

The order of the numbers We found a counterexample that is,
changed. This is the 12 ÷ 6 ≠ 6 ÷ 12.
Answer
Commutative Property of
Multiplication. So, division is not commutative.

Name the property shown by the statement.
Answer The conjecture is false.
(2 + 5) + m = 2 + (5 + m)

The grouping of the
numbers and variables Your Turn!
Answer changed. This is the
Associative Property of
Addition. Identify Properties
Name the property shown by the statement.
(4 6) 2 = 4 (6 2)
Mental Math

Find (18 20) 5 mentally. A. Commutative Property of Multiplication
Group 20 and 5 together because 20 5 = 100. B. Associative Property of Multiplication
It is easy to multiply by 100 mentally. C. Multiplicative Identity
D. Multiplicative Property of Zero
(18 20) 5 = 18 (20 5) Associative Property
of Multiplication Answer
= 18 100 Multiply 20 and 5
mentally.
= 1800 Multiply 18 and 100
mentally.
Answer 1800

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