Order of Operations & Algebraic Properties

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What is the Order of Operations?

Back

The Order of Operations is a set of rules that determines the sequence in which calculations are performed in a mathematical expression. The acronym PEMDAS helps remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Front

Evaluate: 3 + 5 × 2

Back

13 (First, multiply 5 × 2 = 10, then add 3 + 10 = 13).

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What is the Identity Property of Addition?

Back

The Identity Property of Addition states that when you add zero to any number, the result is that number. For example, a + 0 = a.

Front

What is the Inverse Property of Addition?

Back

The Inverse Property of Addition states that for every number a, there exists a number -a such that a + (-a) = 0.

Front

Evaluate: (4 + 3) × 2

Back

14 (First, add 4 + 3 = 7, then multiply 7 × 2 = 14).

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a number by a sum by distributing the multiplication over each addend.

Front

Evaluate: 2 × (3 + 4)

Back

14 (First, add 3 + 4 = 7, then multiply 2 × 7 = 14).

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What is the Commutative Property of Addition?

Back

The Commutative Property of Addition states that changing the order of the addends does not change the sum. For example, a + b = b + a.

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What is the Commutative Property of Multiplication?

Back

The Commutative Property of Multiplication states that changing the order of the factors does not change the product. For example, a × b = b × a.

Front

What is the Associative Property of Addition?

Back

The Associative Property of Addition states that the way in which numbers are grouped does not change their sum. For example, (a + b) + c = a + (b + c).