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Understanding Key Mathematical Properties and Expressions for Your Upcoming Test

Prepare for your vocabulary test on mathematical terms by familiarizing yourself with essential concepts. Explore the Associative, Distributive, and Commutative properties, which explain how grouping and order affect sums and products. Learn about numerical and algebraic expressions, equations, terms, variables, coefficients, and inequalities. Understanding these foundational elements will not only help you perform well on your test next week but also enhance your overall mathematical comprehension.

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Understanding Key Mathematical Properties and Expressions for Your Upcoming Test

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  1. Unit 6 vocabulary Test over words next week, it will benefit you to study and understand what there words mean.

  2. Associative Property (Grouping)- Changing the grouping of the numbers does not change the sum or product Examples: • (2 x 3) x 4 = 24 which is equivalent to 2 x (3 x 4) =24 • 10 x ( 3 x 4) which is equivalent to (10 x 3) x 4

  3. Distributive property • Distributive Property Example: • Example: • 5(6 + 8) = (5 × 6) + (5 × 8) • a × (b + c) = (a × b) + (a × c) and • a × (b – c) = (a × b) – (a × c), where a, b, and c stand for any real numbers. • The product of a number and the sum of two numbers is the same as the sum of the number multiplied by each of the other numbers.

  4. Commutative Property • (Order Property) Changing the order of the addends or factors does not change the sum or product. • Examples 7 + 3 = 10 which is equivalent to 3 + 7 = 10 25 x 4 = which is equivalent to 4 x 25

  5. Numerical Expression • The term “numerical” means “involving numbers” and the term “expression” means “phrase”.A numerical expression is a mathematical phrase involving only numbers and one or more operational symbols. • Examples • 4 + 20 – 7 • (2 + 3) – 7 • (6 × 2) ÷ 20 • 5 ÷ (20 × 3)

  6. Algebraic Expression • An algebraic expression is an expression that contains one or more numbers, one or more variables, and one or more arithmetic operations. • Examples • 2x + 9 • 3x -7 • 3

  7. Equation • Two things are the same using mathematical symbols. • Everything on one side of an equal sign (=) have to be equal to everything on the other side. • Examples • 8 + 4 = 12 • 4 x 5 = 20 • 7 +10 – 5 = 12

  8. Term • In Algebra a term is either:* a single number, or* a variable, or * numbers and variables multiplied together.

  9. Variable • is a symbol for a number we don't know yet. It is usually a letter like x or y, however it can be represented by any letter. • Examples • x + 3 • 3x – y

  10. Coefficient • A number used to multiply a variable • The numerical part of an algebraic term • Examples

  11. Inequality • Two values are not equal • Example • a ≠b says that a is NOT equal to b

  12. Solve • To work out a correct solution

  13. Solution • In an equation, it is an answer that can be substituted for a variable that makes the equation true. • Example • 5x + 3= 12 • - 3 = +3 • 5x = 15 • 5 = 5 • X = 3

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