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Mastering Algebraic Expressions: Basics & Applications

Learn to identify parts of expressions, simplify algebraic expressions, apply properties of real numbers, and solve linear equations. Practice examples included.

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Mastering Algebraic Expressions: Basics & Applications

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  1. Lesson Menu Main Idea and New Vocabulary NGSSS Example 1: Identify Parts of an Expression Example 2: Simplify Algebraic Expressions Example 3: Simplify Algebraic Expressions Example 4: Real-World Example Five-Minute Check

  2. Simplify algebraic expressions. • term • coefficient • like terms • constant Main Idea/Vocabulary

  3. MA.912.A.3.1 Solve linear equations in one variable that includesimplifying algebraic expressions. MA.912.A.3.2Identify andapply the distributive, associative, and commutative properties of real numbers and the properties of equality. NGSSS

  4. Identify Parts of an Expression Identify the terms, like terms, coefficients, and constants in the expression 3x – 5 + 2x – x. 3x – 5 + 2x – x = 3x + (–5) + 2x + (–1x) Rewrite the expression. Answer: • terms: 3x, –5, 2x, and –x • like terms: 3x, 2x, and –x • coefficients: 3, 2, and –1 • constant: –5 Example 1

  5. Identify the terms, like terms, coefficients, and constants in the expression n – 4 + 7n – 6n. A.terms: n, –4, 7n, –6n; terms: like terms: n and 7n; coefficients: 1, 7, and –6; constant: –4 B.terms: n, –4, 7n, –6n; like terms: n, 7n, and –6n; coefficients: 1, 7, and –6; constant: –4 C.terms: n, 4, 7n, 6n; like terms: n, 7n, and –6n; coefficients: 1, –4, 7, and –6; constant: –4 D.terms: n, 4, 7n, 6n; like terms: n, 7n, and –6n; coefficients: 1, –4, 7, and –6; constant: none Example 1 CYP

  6. Simplify Algebraic Expressions Write the expression 6n – n in simplest form. 6n and n are like terms. 6n – n = 6n – 1n Identity Property; n = 1n = (6 – 1)n Distributive Property = 5n Simplify. Answer: 5n Example 2

  7. Write the expression 10w + w in simplest form. A. 10w B. 11w C. 10w + 1 D. 10 + w Example 2 CYP

  8. Simplify Algebraic Expressions Write the expression 8z + z – 5 – 9z + 2 in simplest form. 8z, z, and –9z are like terms. –5 and 2 are also like terms. 8z + z – 5 – 9z + 2 = 8z + z + (–5) + (–9z) + 2 Definition of subtraction = 8z + z + (–9z) + (–5) + 2 Commutative Property = [8 + 1 + (–9)]z + (–5) + 2 Distributive Property Example 3

  9. Simplify Algebraic Expressions = 0z + (–3) Simplify. = 0 + (–3) or –3 0z = 0 • z or 0 Answer: –3 Example 3

  10. Write the expression 4t + 3 – t + 7 in simplest form. A. 5t + 10 B. 4t – 4 C. 3t + 10 D. 3t – 4 Example 3 CYP

  11. GROCERIES Manfred buys some boxes of cereal for $4.85 each and the same number of bags of pretzels for $2.90 each. Write an expression in simplest form that represents the total amount spent. Example 4

  12. 4.85x + 2.90x = (4.85 + 2.90)x Distributive Property = 7.75x Simplify. Answer: The expression $7.75x represents the total amount spent. Example 4

  13. MOVIES Each person in a group buys a movie ticket for $7.50 and a tub of popcorn for $3.80. Write an expression in simplest form that represents the total amount spent. A. $11.30 B. $11.30x C. $7.50x + $3.80 D. $7.50 + $3.80 + x Example 4 CYP

  14. Identify the terms, like terms, coefficients, and constants in the expression 8y – 3 + y. A. terms: 8y, –3, y; like terms: 8y, y; coefficients: 8, 1; constant: –3 B.terms: 8y, –3, y; like terms: 8y, y; coefficients: 8, –3, 1; constant: none C.terms: 8y; –3; like terms: 8, –3; coefficients: 8, 1; constant: –3 D.terms: 8, –3, 1; like terms: 8y, y; coefficients: 8, 1; constant: none Five Minute Check 1

  15. Identify the terms, like terms, coefficients, and constants in the expression –22m – 2n + 1. A.terms: –22, n, 1; no like terms; coefficients: –22, –2; constant: 1 B.terms: –22m, –2n, 1; no like terms; coefficients: –22, –2, 1; constant: none C.terms: –22m, –2n, 1; no like terms; coefficients: –22, –2; constant: 1 D.terms: –22m, –2n, 1; like terms: –22m, –2n; coefficients: –22, –2; constant: 1 Five Minute Check 2

  16. Write the expression 7k + 9k in simplest form. A. 2k B. 16k C. 16 + 2k D. 7k + 9k Five Minute Check 3

  17. Write the expression 14h – 3 – 11h in simplest form. A. 0 B. –3h – 3 C. 3h – 3 D. 25h – 3 Five Minute Check 4

  18. Sara has x number of apples, 3 times as many oranges as apples, and 2 peaches. Write an expression in simplest form that represents the total number of fruits. A. 3x + 2 B. 4x + 2 C. 5x D. 7x + 2 Five Minute Check 5

  19. Which expression represents the perimeter of the triangle? A. 5x + 1 B. 3x C. 2x – 1 D. 6x Five Minute Check 6

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