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

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

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

Example 1 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 CYP 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 Identify the terms, like terms, coefficients, and constants in the expression n – 4 + 7n – 6n.

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

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

Example 3 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) + 2Definition of subtraction = 8z + z + (–9z) + (–5) + 2Commutative Property = [ (–9)]z + (–5) + 2 Distributive Property

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

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

Example 4 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 x x= ( )xDistributive Property = 7.75x Simplify. Answer:The expression $7.75x represents the total amount spent.

Example 4 CYP A.$11.30 B.$11.30x C.$7.50x + $3.80 D.$ $ x 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.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 Identify the terms, like terms, coefficients, and constants in the expression 8y – 3 + y. Five Minute Check 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 Identify the terms, like terms, coefficients, and constants in the expression –22m – 2n + 1. Five Minute Check 2

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

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

A.3x + 2 B.4x + 2 C.5x D.7x + 2 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. Five Minute Check 5

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