Generating Equivalent Numerical Expressions

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1 ? UNIT Study Guide Review MODULE 10 Generating Equivalent Numerical Expressions How can you generate equivalent numerical expressions and use them to solve real-world problems? base (base (en numeración)) exponent (exponente) order of operations (orden de las operaciones) power (potencia) Find the value of each power. A = = 0.81 B Any number raised to the power of 0 is = 1 C. ( 1_ ) ( 1_ ) = ( 1_ ) ( 1_ ) ( 1_ ) ( 1_ ) = 1 6 EXAMPLE Find the prime factorization of = 3 60 = 3 The prime factorization of 60 is 3. EXAMPLE 3 Simplify each expression. A. ( 3 + ) = (8 + ) 3 = 8 = 13 Add. = B = = 3 6 = 18 3 = 9 Divide. Use exponents to write each expression. (Lesson 10.1) _ _ _ 07

2 Find the value of each power. (Lesson 10.1) ( _ 7) 3 Write the prime factorization of each number. (Lesson 10.) ? 10. Eduardo is building a sandbox that has an area of 8 square feet. What are the possible whole number measurements for the length and width of the sandbox? (Lesson 10.) 11. ( + 1) 1. - (3 + ) 1 MODULE 11 Generating Equivalent Algebraic Expressions How can you generate equivalent algebraic expressions and use them to solve real-world problems? Evaluate each expression for the given value of the variable. algebraic expression (expresión algebraica) coefficients (coeficiente) constant (constante) equivalent expressions (expresiónes equivalente) evaluating (evaluar) term (término (en una expresión)) A. (x - 9); x = ( - 9) = = (16) Subtract. = 3 When x =, (x 9) = 3. B. w - y + 3w; w =, y = () 6 = 36 = Add and subtract = -8 from left to right. When w = and y = 6, w - y + 3w = -8. EXAMPLE Determine whether the algebraic expressions are equivalent: (x + ) and 10 + x. (x + ) = x + 10 = 10 + x Distributive Property Commutative Property (x + ) is equal to 10 + x. They are equivalent expressions. 08 Write each phrase as an algebraic expression. (Lesson 11.1) 1. x subtracted from 1. 1 divided by t

3 Write a phrase for each algebraic expression. (Lesson 11.1) 3. 8p. s + 7 Evaluate each expression for the given value of the variable. (Lesson 11.). 8z + 3; z = (7 + x ); x = 7. s - t + s ; s =, t = x - y 3 ; x = -7, y = 3 9. The expression 1_ (h)(b 1 + b ) gives the area of a trapezoid, with b 1 and b representing the two base lengths of a trapezoid and h representing the height. Find the area of a trapezoid with base lengths in. and 6 in. and a height of 8 in. (Lesson 11.) Determine if the expressions are equivalent. (Lesson 11.3) x; 7 (x + 1_ 7) 11..(3 + x);.x + 7. Combine like terms. (Lesson 11.3) 1. 3m m - m + 1? 13. 7x + (x - 6) MODULE 1 Equations and Relationships How can you use equations and relationships to solve real-world problems? Determine if the given value is a solution of the equation. A. r - = 17; r = =? 17 Substitute B. x_ = -7; x = - 6 -? = = -7 equation (ecuación) solution (solución) Substitute. 1 is not a solution of r - = is a solution of x_ 6 =

4 EXAMPLE Solve each equation. Check your answer. A. y - 1 = = +1 y = Check: - 1? = 10 B. p = -30 p = -30 Add 1 to both sides. p = -6 Divide both sides by. Substitute. Check: (-6)? = -30 Substitute. 10 = = -30 Determine whether the given value is a solution of the equation. (Lesson 1.1) 1. 7x = 1; x = 3. y + 13 = -; y = -17 Write an equation to represent the situation. (Lesson 1.1) 3. Don has three times as much money as his brother, who has $.. There are s students enrolled in Mr. Rodriguez s class. There are 6 students absent and 18 students present today. Solve each equation. Check your answer. (Lessons 1., 1.3). p - = t_ = q = x = = x _ 7 = x 11. Sonia used $1.0 to buy a new journal. She has $3. left in her savings account. How much money did Sonia have before she bought the journal? Write and solve an equation to solve the problem. (Lesson 1.) 1. Tom read 13 pages in days. He read the same number of pages each day. How many pages did he read each day? Write and solve an equation to solve the problem. (Lesson 1.3) 10

5 ? MODULE 13 Inequalities and Relationships How can you use inequalities and relationships to solve real-world problems? solution of an inequality (solución de una desigualdad) Write and graph an inequality to represent each situation. A. There are at least gallons of water in an aquarium. g B. The temperature today will be less than 3 F. t < EXAMPLE Solve each inequality. Graph and check your solutions. A. x - 7 B. -y < -1 x 9 Add 7 to both sides. y > 3 Divide by -. Reverse the symbol Write and graph an inequality to represent each situation. (Lesson 13.1) 1. Orange Tech s stock is worth less than $.0 per share.. Tina got a haircut, and her hair is still at least 1 inches long. Solve each inequality. Graph and check your solutions. (Lessons 13., 13.3, 13.) q - 1 > 3. t_ -1. 9q > x 7. - _ x < x 11

6 9. Write a real-world comparison that can be described by x (Lesson 13.) 10. Omar wants a rectangular vegetable garden. He only has enough space to make the garden feet wide, and he wants the area of the garden to be more than 80 square feet. Write and solve an inequality to find the possible lengths of the garden. (Lesson 13.3)? MODULE 1 Quadrant II 3 Quadrant I 1 x 3 O (, ) 3 Quadrant III Quadrant IV y Relationships in Two Variables How can you use relationships in two variables to solve real-world problems? Graph the point (, -) and identify the quadrant where it is located. EXAMPLE (, -) is located units to the right of the origin and units down from the origin. (, -) is in quadrant IV. Tim is paid $8 more than the number of bags of peanuts he sells at the baseball stadium. The table shows the relationship between the money Tim earns and the number of bags of peanuts Tim sells. Identify the independent and dependent variables, and write an equation that represents the relationship. axes (ejes) coordinate plane (plano cartesiano) coordinates (coordenada) ordered pair (par ordenado) origin (origen) quadrants (cuadrante) x-axis (eje x) # of bags of peanuts, x Money earned, y The number of bags is the independent variable, and the money Tim earns is the dependent variable. 1 The equation y = x + 8 expresses the relationship between the number of bags Tim sells and the amount he earns.

7 Graph and label each point on the coordinate plane. (Lesson 1.1) y 1. (, ). (-3, -1) 3. (-1, ) x O Use the graph to answer the questions. (Lesson 1.) 10 Distance (km) 8 6 O Time (h). What is the independent variable?. What is the dependent variable? 6. Describe the relationship between the independent variable and the dependent variable. 7. Use the data on the table to write an equation to express y in terms of x. Then graph the equation. (Lessons 1.3, 1.) x y y O x 13