University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

225

Pages:

1
Author:

Jameson Hunt

Mini-Lecture 1.8 Properties of Real Numbers Learning Objectives: 1. Use the commutative and associative properties. 2. Use the distributive property. 3. Use the identity and inverse properties. Examples: 1. Use the commutative property of addition or multiplication to complete each statement. a) 3 + y = _____ b) a + (-9) = _____ c) -10 · x = _____ d) s·t = ____ Use the associative property of addition or multiplication to complete each statement. e) (3 + x) + y = _______ f) -2 · (5x) = ________ Use the commutative and associative properties to simplify each expression. g) 12 + (4 + x) h) -7(5x) ⎛ 1 ⎞ 5 i) ⎜ − + x ⎟ + ⎝ 3 ⎠ 12 j) 0.13(-1.2y) 2. Use the distributive property to write each expression without parentheses. Then simplify the result, if possible. a) 8(x + y) b) -3(7x – 9) c) -2(-6y – 10) d) 6(4x – 3y –9) Use the distributive property to write each sum as a product. e) 6·x + 6·y f) 13· x + 13 · 4 g) (-2)x + (-2)y h) 1 1 a + i6 3 3 3. Name the property that is illustrated by each true statement. a) 0 + 11 = 11 1 b) 3i = 1 3 c) 5 + (-5) = 0 d) 12 · 1 = 12 Teaching Notes: • • • Many students use the Properties of Real Numbers without realizing that they are using these properties. Some students, when using the distributive property, forget to multiply the second term. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) y+3; 1b) -9+a; 1c) x·-10; 1d) t·s; 1e) 3 + (x + y); 1f) (-2 · 5) x; 1g) 16 + x; 1h) -35x; 1i) 1/12 + x; 1j) -0.156y; 2a) 8x + 8y; 2b) -21x + 27; 2c) 12y + 20; 2d) 24x – 18y – 54; 2e) 6(x + y); 2f) 13(x + 4); 2g) -2(x + y); 2h) 1/3 (a + 6); 3a) addition property of zero; 3b) inverse property of multiplication; 3c) inverse property of addition; 3d) multiplication property of one