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Big Ideas in Mathematics Chapter Three

Learn to identify and simplify algebraic terms, like terms, and expressions in mathematics. Includes examples and real-life applications.

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Big Ideas in Mathematics Chapter Three

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  1. Big Ideas in MathematicsChapter Three Expressions and Equations

  2. Lesson 3.1Algebraic Equations Parts of an algebraic expression are called terms. Liketerms are terms that have the same variables raised to the same exponents. Constant terms are also like terms. To identify terms and like terms in an expression, first write the expression as a sum of its terms.

  3. Lesson 3.1Algebraic Equations – Identifying Like Terms Example One: 9x − 2 + 7 − x Rewrite as a sum of terms: 9x +(−2) + 7 + (−x) Terms: 9x, −2, 7, −x Like terms: 9x and − x, − 2 and 7 Example Two: z² + 5z − 3z² + z Rewrite as a sum of terms: z² + 5z+(-3z²) + z Terms: z², 5z, -3z², z Like terms: z²,-3z² and 5z,z

  4. On Your Own Identify the terms and like terms in the expression. a) 7 + 4p – 5 + p + 2q b) 2r² + 7r - r² - 9

  5. Lesson 3.1Algebraic Equations – Simplifying Expressions Example Three: 3 (q + 1) – 4 3q + 3(1) – 4 Distributive Property 3q + 3 – 4 Multiplication 3q – 1 Commutative Property

  6. On Your Own Simplify the Expression: a) 14 – 3z - + 8 + z b) 2.5x + 4.3x - 5

  7. Lesson 3.1Algebraic Equations – Simplifying Expressions An algebraic expression is in simplest form when it has no like terms and no parentheses. To combine like terms that have variables, use the Distributive Property to add or subtract the coefficients.

  8. Lesson 3.1Algebraic Equations – Simplifying an Algebraic Expressions Example Four: 14 – 3z + 8+ z 14 + 8 – 3z + z Commutative Property of Addition 22 – (3 + 1)z Distributive Property 22 + (-2z) Simplify -2z + 22 Commutative Property of Addition

  9. On Your Own Simplify the expression: a) -2(g + 4) + 7g b) 7 – 4(.75x - .25)

  10. Lesson 3.1Algebraic Equations – Real Life Applications Example Five: Each person in a group buys a ticket, a medium drink, and a large popcorn. Write an expression in simplest form that represents the amount of money the group spends at the movies. Interpret the expression. Words: Eachticket is $7.50, each medium drink is $2.75, and each large Popcorn is $4. Variable: The same number of each item is purchased. So, x can represent the number of tickets, the number of medium drinks, and the number of large popcorns. Expression: 7.50x + 2.75 x+ 4 x (7.50 + 2.75 + 4)x Distributive Property 14.25x Add coefficients

  11. On Your Own You buy x packs of pencils, twice as many packs of erasers, and three times as many rolls of tape. Write an expression in simplest form for the total amount of money you spent.

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