Number Properties and Order of Operations

Learn order of operations, distributive property.

Lesson 1 of 32 parts Practice Flashcards

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Order of Operations

Objective: Explain order of operations, apply the stated method, and check its conditions.

Evaluate grouping symbols first, then exponents, multiplication and division from left to right, and addition and subtraction from left to right. Operations at the same priority have equal rank; multiplication does not automatically precede division. Multiplication and division share a priority, as do addition and subtraction.

Formulas

$Grouping → powers → × and ÷ → + and −$

Worked examples

Try itEvaluate 6+7·7.Show answer

Step 1: Multiplication comes before addition. Step 2: 7·7=49. Step 3: Add 6 to obtain 55.

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Order of Operations

Objective: Explain order of operations, apply the stated method, and check its conditions.

Formulas

$Grouping → powers → × and ÷ → + and −$

Worked examples

Try itEvaluate 6+7·7.Show answer

Step 1: Multiplication comes before addition. Step 2: 7·7=49. Step 3: Add 6 to obtain 55.

Distributive Property

Objective: Explain distributive property, apply the stated method, and check its conditions.

For real numbers a,b,c, a(b+c)=ab+ac. A factor outside parentheses multiplies every term inside. Distribution changes the expression’s form while preserving its value; an outside negative must be distributed to each term too. Distribute to every term, not only the first.

Formulas

$a(b+c)=ab+ac$

Worked examples

Try itFind the x coefficient after expanding 6(x+7).Show answer

Step 1: Multiply each term inside the parentheses. Step 2: The result is 6x+42. Step 3: The x coefficient is 6.

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