Section 1.3 Properties of Real Numbers and Simplifying Algebraic Expressions 37 3f. Because we are multiplying fractions, we first simplify by dividing out the common factors. Note that 12 divided by 6 is 2 and 12 divided by 4 is 3. 12a2b - 7 6 b - 12ab - 5 4 b = 2(2b - 7) - 3(b - 5) Simplify the products. = 4b - 14 - 3b + 15 Apply the distributive property. = 4b - 3b - 14 + 15 Apply the commutative property of addition. = (4 - 3)b + 1 Apply the distributive property and combine like terms. = 1b + 1 Simplify. = b + 1 Recall 1b = b. Student Check 3 Simplify each expression. a. 7h + 3 - 9h b. y2 - 6y - 6y + 36 c. b3 - 3b2 + 9b + 3b2 - 9b +27 d. 0.04n + 0.06(8000 - n) e. 8 - 2(x -6) f. 8a 5y - 1 4 b - 8a y + 3 2 b Translating into Algebraic Expressions Translating phrases into algebraic expressions is an important skill for solving problems. Here is a chart showing some of the common phrases and their translations. Addition Subtraction Multiplication Division a + b a - b ab a b sum of a and b difference of a and b product of a and b a divided by b a increased by b b subtracted from a a times b quotient of a and b b more than a b less than a twice b, (2b) ratio of a to b a added to b a minus b a of b b into a a plus b a decreased by b total of a and b from a, subtract b There are also key statements that translate into equations or inequalities. Recall that a statement in which two expressions are equal is an equation. A statement in which two expressions are not equal is an inequality. For instance, to compare the numbers -2 and 5 using an inequality, we could write any of the following. -2 < 5, -2 ≤ 5, 5>-2, or 5≥-2 Note that the inequality symbol always points to the smaller number. Equals Greater Than or Greater Than or Equal To Less Than or Less Than or Equal To a = b a > b or a ≥ b a < b or a ≤ b a is equal to b. a is greater than b. a is less than b. a is the same as b. a is greater than or equal to b. a is less than or equal to b. a results in b. a is at least b. a is at most b. a equals b. a is not less than b. a is not greater than b. a is b. a is more than b. a is not more than b. a yields b. Objective 4 ▶ Translate phrases or statements into algebraic expressions, equations, or inequalities.
hendricks_intermediate_algebra_1e_ch1_3
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