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Understanding Properties of Real Numbers in Algebraic Expressions

Learn about the properties of real numbers in algebraic expressions, such as Commutative Property, Multiplication Property of Zero, and Inverse Property of Addition. Practice simplifying expressions and solving equations step by step.

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Understanding Properties of Real Numbers in Algebraic Expressions

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  1. Properties of Real Numbers ALGEBRA 1 LESSON 1-8 (For help, go to Lessons 1-4 and 1-6.) Simplify each expression. 1. 8 + (9 + 2) 2. 3 • (–2 • 5) 3. 7 + 16 + 3 4. –4(7)(–5) 5. –6 + 9 + (–4) 6. 0.25 • 3 • 4 7. 3 + x – 2 8. 2t – 8 + 3t9. –5m + 2m – 4m 1-8

  2. Properties of Real Numbers ALGEBRA 1 LESSON 1-8 1. 8 + (9 + 2) = 8 + (2 + 9) = (8 + 2) + 9 = 10 + 9 = 19 2. 3 • (–2 • 5) = 3 • (–10) = –30 3. 7 + 16 + 3 = 7 + 3 + 16 = 10 + 16 = 26 4. –4(7)(–5) = –4(–5)(7) = 20(7) = 140 5. –6 + 9 + (–4) = –6 + (–4) + 9 = –10 + 9 = –1 6. 0.25 • 3 • 4 = 0.25 • 4 • 3 = 1 • 3 = 3 7. 3 + x – 2 = 3 + (–2) + x = 1 + x 8. 2t – 8 + 3t = 2t + 3t – 8 = (2 + 3)t – 8 = 5t – 8 9. –5m + 2m – 4m = (–5 + 2 – 4)m = –7m Solutions 1-8

  3. Properties of Real Numbers ALGEBRA 1 LESSON 1-8 Name the property each equation illustrates. a. 3 • a = a • 3 Commutative Property of Multiplication, because the order of the factors changes b.p • 0 = 0 Multiplication Property of Zero, because a factor multiplied by zero is zero c. 6 + (–6) = 0 Inverse Property of Addition, because the sum of a number and its inverse is zero 1-8

  4. Properties of Real Numbers ALGEBRA 1 LESSON 1-8 Suppose you buy a shirt for $14.85, a pair of pants for $21.95, and a pair of shoes for $25.15. Find the total amount you spent. 14.85 + 21.95 + 25.15 = 14.85 + 25.15 + 21.95Commutative Property of Addition = (14.85 + 25.15) + 21.95 Associative Property of Addition = 40.00 + 21.95 Add within parentheses first. “OoO” = 61.95 Simplify. The total amount spent was $61.95. 1-8

  5. Properties of Real Numbers ALGEBRA 1 LESSON 1-8 Name the property that each equation illustrates. 1. 1m = m2. (– 3 + 4) + 5 = – 3 + (4 + 5) 3. –14 • 0 = 0 4. Give a reason to justify each step. Iden. Prop. Of Mult. Assoc. Prop. Of Add. Mult. Prop. Of Zero Definition of Subtraction a. 3x – 2x – 10 = 3x + (– 2x) + (– 10) a. [3 + (– 2)]x + (– 10) b. 1x + (– 10) Addition c. 1x – 10 Definition of Subtraction Identity Property of Multiplication d. x – 10 1-8

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