Extra Practice Chapter 4. Topics Include: Solving Simple Equations Solving Multi-Step Equations Equations with Fractions Rearranging Formulas

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1 Extra Practice Chapter Topics Include: Solving Simple Equations Solving Multi-Step Equations Equations with Fractions Rearranging Formulas

2 Practice: Get Ready BLM.GR... Collect Like Terms. Simplify. 6m + 7m + m 5x x + 9x 7y y y p + p p. Simplify. x + 7 x + 5b + + b w w 9 7a + + 9a Distributive Property. Simplify. (x ) 6(a + ) 7(y 5) (8 + e) (m + ) f) 6( v) g) (n + ) h) (5 + g). Simplify. (5x + ) + (x + ) (a 6) + (a ) 5(y ) + (8y + ) 6(b 5) (b + ) e) (z + ) (z + ) f) 5(k ) (k + 8) Geometric Relationships 5. Find the measure of each angle x. 6. Find the measure of each unknown angle. Lowest Common Denominator 7. Find the LCD for each pair of fractions.,, 5, 0, 6 8. Find the LCD for each set of fractions.,, 6,, 5 9. Evaluate ,, 8,, Find each sum or difference BLM.GR. Practice: Get Ready Copyright 006 McGraw-Hill Ryerson Limited.

3 Practice: Solve Simple Equations BLM.... Solve by inspection. x + = a + = 7 y + 9 = b + 5 = e) m + 6 = 7 f) p =. Use the balance method to solve. h + = 7 x + 8 = m + 7 = 0 p + 5 = 6 e) r 9 = f) t = 5. Solve. Use opposite operations. d 8 = 9 k + = 5 c + 7 = s = 6 e) g 5 = 0 f) b =. Find each root. w = 5y = 5 x = 8 z = 6 5. Find each root. k = u = 8 r = 5 w = 8 6. Solve. q = 8 m = n + 9 = 5 v = e) j + 7 = 8 f) y 6 = 8 g) x = 6 h) d 5 = 7. Solve and check. x + = 0 5k = 7 b + 8 = g = e) s + = f) r + 5 = 9 8. Solve. k = 8 b = c = 6w = e) g + = f) 5s + = x g) = 6 h) d 5 = BLM... Practice: Solve Simple Equations Copyright 006 McGraw-Hill Ryerson Limited.

4 Practice: Solve Multi-Step Equations BLM.... Solve. 6x + + x = 9 0m m + 8 = a + a + 9 = 5 b + b = e) y + + y = 9 f) 7f + f = 0 g) 9q + 8q = 0 h) 8 k + 5k = 0. Find each root. b + = b + 6 7p 8 = p x + = 5x 5 8g + = g + 0 e) 6h 5 = h + f) m 9 = m + 7 g) 5r 6 = r + h) y + 5 = y. Solve. (x ) = x 7 (a 8) + (a + 6) = 7 (p + ) = 5(p + ) 5d = (d + ) e) (t + 5) (t ) = 6 f) 5(k + ) = (k + 7) 5. Solve, then check. m + m = q + + q 9 = 0 g + g = g 6 (b + 7) = (b + ) + 5. A square and a rectangle have the same perimeter. Find the side lengths of each figure. 6. In a triangle, the measure of the middle angle is triple the measure of the smallest angle, and the measure of the largest angle is 55 greater than the measure of the smallest angle. Find the measures of the angles. BLM.. Practice: Solve Multi-Step Equations Copyright 006 McGraw-Hill Ryerson Limited.

5 Practice: Solve Equations Involving Fractions BLM.... Solve. e) f) c = 7 n = w = 5 h = 6. Find each root. = (s + 7) 8 v+ 8 = 5 (r ) = 6 u 8 = ( z 5) = ( e+ ) 5 =. Find each root. b+ b = e) f) d d = 6 ( z ) = ( z ) 6 x+ x+ 6 = 5 n+ n = 8 (y ) = ( y+ ) 9. Solve and check. k+ k = 5 z = 5 (9 + g) = g + h+ h = 5 5. The perimeter of the small square is one-third the perimeter of the large square. What are the side lengths of the squares? 6. The height of a triangle is cm less than its width. The area of the triangle is cm. What are the measures of the base and height? BLM.. Practice: Solve Equations Involving Fractions Copyright 006 McGraw-Hill Ryerson Limited.

6 Practice: Modelling With Formulas BLM.... The formula for area of a circle is A = π r where r is the radius of the circle. Which is the formula rearranged to isolate r? A A r= π B r = πa C r = π A D r= A π. The formula for the area of a trapezoid is A= ( a+ h.. Rearrange each formula to isolate the variable indicated. P = s for s I = Prt for P bh A= for b P = (l + w) for l e) d = st for t f ) V = π r h for h. The approximate number of pounds, P, in a kilogram, K, is given by the formula P =.K. Christine s mass is kg. Convert kilograms to pounds. Rearrange the formula to express K in terms of P. Katherine weighs 78 pounds. Convert 78 pounds to kilograms. Which is the formula rearranged to isolate h? A h= A a+ b B h = A (a + C h= D h= ( + A a A a+ b BLM.. Practice: Modelling With Formulas Copyright 006 McGraw-Hill Ryerson Limited.

7 Practice: Modelling With Algebra BLM Write an algebraic expression for each phrase. double a number triple a number quadruple a number one half of a number e) one third of a number f) one quarter of a number. Write an algebraic expression for each phrase. 6 more than a number a number increased by increased by a number 5 decreased by a number e) 7 less than a number f) a number decreased by 6. Write an algebraic expression for each phrase. more than triple a number half a number, less 5 quadruple a number decreased by less than double a number. Write an equation for each phrase. triple a number is 8 7 more than a number is half a number is 0 double a number, less is 7 e) 5 less than one third a number is f) more than triple a number is 6. The sum of three consecutive odd integers is 57. Let x represent the least integer. Write an algebraic expression to represent each of the other integers. Write an equation to represent the sum of the integers. Find the integers. 7. Three consecutive even integers have a sum of 0. Write an algebraic expression to represent each integer. Write an equation to represent the sum of the integers. Find the integers. 8. Katherine is years older than Christine. The sum of their ages is 6. Write an algebraic expression for each girl s age. Write an equation to represent the sum of their ages. How old is each girl? 9. The length of a rectangle is triple its width. The perimeter of the rectangle is 0 cm. What are the length and width? 5. The sum of two consecutive integers is 7. Let x represent the lesser integer. Write an algebraic expression to represent the greater integer. Write an equation to represent the sum of the integers. Find the integers. BLM.5. Practice: Modelling With Algebra Copyright 006 McGraw-Hill Ryerson Limited.

8 Chapter Review BLM.CR... (page ). Solve Simple Equations, pages Solve. 5y = 5 b 8 = x = 7 h + 5 =. Find each root. 8m + 9 = 5 p + 7 = 5 k = 7 + c =. Solve, then check. a = q = 5 g = 9 7 6s = 9. Greg is. He is years older than Sue. Write an equation relating Sue and Greg s ages. How old is Sue?. Solve Multi-Step Equations, pages Solve. m + 5m = b 6 + b 9 = 0 x x + = 0 k + = k 5 6. Find the root of each equation. + (h ) = + h 8 (g + ) = g 5 (d + 6) = 9(d ) 5(r 7) + r = (r ) 7. Find each root, then check. s + s = 6 p + p 9 = 0 5 (c + ) = + c (d 7) 6 = (d + ) BLM.CR. Chapter Review 8. The perimeter of an isosceles triangle is cm. The length of each equal side is triple the length of the base. Find the side lengths of the triangle.. Solve Equations Involving Fractions, pages Solve. t 6 = (c + ) = a+ = 5 (s ) = 0. Solve. d + d = k k+ = (q ) = (q + 7) c c+ = 5 9. Modelling With Formulas, pages 9. Rearrange each formula to isolate the variable indicated. A = lw for l P = a + b for b y = mx for x l = w + for w e) P = a + b for b f) S = πr(r + h) for h Copyright 006 McGraw-Hill Ryerson Limited.

9 .5 Modelling With Algebra, pages 0 9. Write an equation for each phrase. less than triple a number is the sum of double a number and 6 is 6 half a number, less, is 8 the area decreased by 7 is e) the sum of two consecutive integers is 9 f) the distance increased by 8 is 5 BLM.CR... (page ). Together, Blackie and Jessie have a mass of 7 kg. Blackie s mass is kg less than Jessie s mass. What is each dog s mass?. Chantal works at a music store. She earns $8 per hour plus $0.05 for each CD she sells. Tonight she is working a 5-h shift. How many CDs must Chantal sell to earn $? BLM.CR. Chapter Review Copyright 006 McGraw-Hill Ryerson Limited.

10 BLM Answers BLM.GR. Practice: Get Ready. m x y 5p. x + 8 9b w + a. 8x 6 6a + 8 y + 5 6b e) 6m + f) 6 + 6v g) n h) 5 + g. x + 7a 6 8y b 6 e) 5z f) 9k 5. x = 85 x = x = 5 x = BLM.. Practice: Solve Simple Equations. 9 9 e) f) 6. 6 e) f) e) 5 f) e) f) g) 9 h) e) 5 f) e) 7 f) g) h) 5 BLM.. Practice: Solve Multi-Step Equations e) f) g) h). e) f) 6 g) h) e) f) square: 7; rectangle: 5 by , 75, 80 BLM.. Practice: Solve Equations Involving Fractions e) 9 f) e) f) ; 6. base: 8 cm; height: 6 cm BLM.. Practice: Modelling With Formulas. D. A. s= P P= I rt b= A h l = P w e) t = d s f) h= V π r. 75 pounds K = P. 5 kg BLM.5. Practice: Modelling With Algebra. x x x x e) x f) x. x + 6 x + + x 5 x e) x 7 f) x 6. x + 5 x x x. x = 8 x + 7 = x = 0 x = 7 x e) 5 = f) x + = 5. x + x + x + = 7,

11 BLM Answers 6. x +, x + x + x + + x + = 57 7, 9, 7. x, x +, x + x + x + + x + = 0,, 6 8. C, C + 6 = C + C + Katherine: 9; Christine: cm, 5 cm BLM.CR. Chapter Review s + = cm, 9 cm, 9 cm l = A w P a b= y x= m w = l e) b = P a f) h= S r π r. x = x + 6 = 6 x = 8 A 7 = e) x + x + = 9 f) d + 8 = 5. Blackie: kg; Jessie: 8 kg. 0