Extra Practice Chapter 4 Topics Include: Solving Simple Equations Solving Multi-Step Equations Equations with Fractions Rearranging Formulas
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Date: _______________________________ …BLM 4.GR.1...
Practice: Get Ready 6. Find the measure of each unknown angle. a)
Collect Like Terms 1. Simplify. a) 6m + 7m + m c) 7y – y – 3y
b) 5x – 3x + 9x d) 4p + 2p – p
2. Simplify. a) 4x + 7 –3x + 1 b) 5b + 2 + 4b + 6 c) 3 + 3w –2 – w d) 9 – 7a + 4 + 9a
b)
Distributive Property 3. Simplify. a) 2(4x – 3) c) –7(2y – 5) e) 3(2m + 1) g) –(n + 2)
b) d) f) h)
6(a + 3) –3(8 + 2b) –6(1 – v) 3(5 + g)
4. Simplify. a) 3(5x + 4) + 2(4x + 1) b) 2(3a – 6) + (a – 4) c) 5(2y – 1) + (8y + 2) d) 6(b – 5) – 2(b + 3) e) 2(4z + 1) – 3(z + 2) f) 5(2k – 3) – (k + 8) Geometric Relationships 5. Find the measure of each angle x. a)
Lowest Common Denominator 7. Find the LCD for each pair of fractions. a) c)
1 1 , 3 4 1 1 , 5 2
b) d)
1 1 , 4 10 1 1 , 4 6
8. Find the LCD for each set of fractions. a) c)
1 1 1 , , 3 6 2 1 1 1 , , 5 4 2
b) d)
1 1 1 , , 8 4 12 1 1 1 , , 3 5 10
9. Evaluate. a)
b)
c)
2 3 5
+ −
8
1 6 1 4
b) d)
1 2 5
+ −
6
1 8 2 3
10. Find each sum or difference. a) c)
Principles of Mathematics 9: Teacher’s Resource
BLM 4.GR.1 Practice: Get Ready
3 10 8 9
+ −
1 3 5 6
b) d)
4 5 7 8
− −
1 2 1 6
Copyright © 2006 McGraw-Hill Ryerson Limited.
Name: ___________________________________
Date: _______________________________ …BLM 4.1.1...
Practice: Solve Simple Equations 1. Solve by inspection. a) x + 3 = 12 b) a + 4 = 7 c) y + 9 = 11 d) b + 5 = 14 e) m + 6 = 7 f) p – 4 = 2 2. Use the balance method to solve. a) h + 1 = 7 b) x + 8 = 12 c) m + 7 = 10 d) p + 5 = 6 e) r – 9 = 2 f) t – 3 = 5 3. Solve. Use opposite operations. a) d – 8 = 9 b) k + 2 = 5 c) c + 7 = 12 d) s – 4 = 6 e) g – 5 = 10 f) b – 1 = 2 4. Find each root. a) 4w = 32 b) 5y = 35 c) –2x = 18 d) –3z = –36
6. Solve. a) q – 1 = 8 b) c) d) e) f) g) h)
m
= 11
−3
n + 9 = 15 v–2=4 j + 7 = 18 y–6=8 – 4x = 36 d–5=4
7. Solve and check. a) 3x + 4 = 10 b) 5k – 3 = 17 c) –b + 8 = 3 d) 2g – 1 = 11 e) –3s + 2 = –13 f) 4r + 5 = 9 8. Solve. a) –3k = 18 b) b – 3 = 12 c) –c = 3 d) 6w – 4 = –22 e) –2g + 3 = –4 f) 5s + 3 = 2 g) −
x 4
=6
h) 3d – 5 = –1
5. Find each root. a) b) c) d)
k 4 u 2 r
=3 =8
−5 w −8
= −2 =2
Principles of Mathematics 9: Teacher’s Resource
BLM 4.1.1. Practice: Solve Simple Equations
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Name: ___________________________________
Date: _______________________________ …BLM 4.2.3...
Practice: Solve Multi-Step Equations 1. Solve. a) 6x + 3 + 2x = 19 b) 10m – 3m + 8 = 43 c) 4a + a + 9 = 44 d) 15 – 3b + b = 3 e) 2y + 4 + 3y = 9 f) 7f – 12 + f = 20 g) 9q + 2 – 8q – 13 = 0 h) 8 – 3k + 5k = 0 2. Find each root. a) 3b + 4 = 2b + 6 b) 7p – 18 = 3p – 2 c) 2x + 4 = 5x – 5 d) 8g + 3 = g + 10 e) 6h – 5 = 2h + 3 f) 4m – 9 = m + 7 g) 5r – 6 = 2r + 3 h) –3y + 15 = y – 13 3. Solve. a) 4(x – 3) = 3x – 7 b) 2(a – 8) + 3(a + 6) = 17 c) 3(2p + 1) = 5(p + 1) d) 5d = 4(d + 2) e) 2(3t + 5) – 4(2t – 1) = 6 f) 5(k + 3) = 2(4k + 7) – 5
Principles of Mathematics 9: Teacher’s Resource
BLM 4.2.3 Practice: Solve Multi-Step Equations
4. Solve, then check. a) 2m + 1 – m = 4 b) q + 4 + 2q – 19 = 0 c) g – 3 + 4g = 2g – 6 d) 2(2b + 7) = 3(b + 3) + 3 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.
Copyright © 2006 McGraw-Hill Ryerson Limited.
Name: ___________________________________
Date: _______________________________ …BLM 4.3.1...
Practice: Solve Equations Involving Fractions 1. Solve. a) b) c) d)
c 2 n
4. Solve and check.
−3 w −3 h 6
a) k − 3 =
=7 =4
b)
= −5
c)
= −3
d)
2. Find each root. 1
a) 2 = b) c) d)
(s + 7)
8 v+8
5 1
−5
=3
(9 + g) = g + 1
3 h+2 3
=
3h − 2 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?
=4
5 3
2z − 3
k +3
(r – 1) = 6
4 u −8 2 1
= −1
e) − ( z − 5) = −1 4
f)
2 ( e + 5)
= −2
3
3. Find each root. a) b) c) d) e) f)
b+3 4 d −1 6 1
= =
3 1
=
3 3n + 2 8 9
2 d −3
( z − 4) = ( z − 2)
6 x+4
1
b −1
6. The height of a triangle is 2 cm less than its width. The area of the triangle is 24 cm2. What are the measures of the base and height?
2 x+6
=
5 3n − 2 4 1
(2 y − 1) = ( y + 1) 3
Principles of Mathematics 9: Teacher’s Resource
BLM 4.3.1 Practice: Solve Equations Involving Fractions
Copyright © 2006 McGraw-Hill Ryerson Limited.
Name: ___________________________________
Date: _______________________________ …BLM 4.4.1...
Practice: Modelling With Formulas 1. The formula for area of a circle is A = π r 2 where r is the radius of the circle. Which is the formula rearranged to isolate r? A r=
A
π
B r = πA C r = πA A
D r=
c) A =
bh 2
for b
d) P = 2(l + w) for l e) d = st for t 2 f) V = πr h for h
π
2. The formula for the area of a trapezoid is A=
3. Rearrange each formula to isolate the variable indicated. a) P = 4s for s b) I = Prt for P
( a + b) h . 2
4. The approximate number of pounds, P, in a kilogram, K, is given by the formula P = 2.2K. a) Christine’s mass is 34 kg. Convert 34 kilograms to pounds. b) Rearrange the formula to express K in terms of P. c) Katherine weighs 78 pounds. Convert 78 pounds to kilograms.
Which is the formula rearranged to isolate h? A h=
2A a+b
B h = 2A – (a + b) C h= D h=
A ( a + b) 2 a+b 2A
Principles of Mathematics 9: Teacher’s Resource
BLM 4.4.1 Practice: Modelling With Formulas
Copyright © 2006 McGraw-Hill Ryerson Limited.
Name: ___________________________________
Date: _______________________________ …BLM 4.5.2...
Practice: Modelling With Algebra 1. Write an algebraic expression for each phrase. a) double a number b) triple a number c) quadruple a number d) one half of a number e) one third of a number f) one quarter of a number
6. The sum of three consecutive odd integers is 57. a) Let x represent the least integer. Write an algebraic expression to represent each of the other integers. b) Write an equation to represent the sum of the integers. c) Find the integers.
2. Write an algebraic expression for each phrase. a) 6 more than a number b) a number increased by 3 c) 2 increased by a number d) 5 decreased by a number e) 7 less than a number f) a number decreased by 6
7. Three consecutive even integers have a sum of 102. a) Write an algebraic expression to represent each integer. b) Write an equation to represent the sum of the integers. c) Find the integers.
3. Write an algebraic expression for each phrase. a) 4 more than triple a number b) half a number, less 5 c) quadruple a number decreased by 1 d) 2 less than double a number 4. Write an equation for each phrase. a) triple a number is 18 b) 7 more than a number is 11 c) half a number is 10 d) double a number, less 3 is 7 e) 5 less than one third a number is 1 f) 2 more than triple a number is 14
8. Katherine is 2 years older than Christine. The sum of their ages is 16. a) Write an algebraic expression for each girl’s age. b) Write an equation to represent the sum of their ages. c) How old is each girl? 9. The length of a rectangle is triple its width. The perimeter of the rectangle is 40 cm. What are the length and width?
5. The sum of two consecutive integers is 47. a) Let x represent the lesser integer. Write an algebraic expression to represent the greater integer. b) Write an equation to represent the sum of the integers. c) Find the integers.
Principles of Mathematics 9: Teacher’s Resource
BLM 4.5.2 Practice: Modelling With Algebra
Copyright © 2006 McGraw-Hill Ryerson Limited.
Name: ___________________________________
Date: _______________________________ …BLM 4.CR.1... (page 1)
Chapter 4 Review 4.1 Solve Simple Equations, pages 186–195 1. Solve. a) 5y = 35 x c) =7 4
b) b – 8 = –12 d) h + 5 = 13
2. Find each root. a) 8m + 9 = –15 b) 2p + 7 = 3 c) 5 – 4k = –7 d) 4 + 3c = –12
8. The perimeter of an isosceles triangle is 21 cm. The length of each equal side is triple the length of the base. Find the side lengths of the triangle. 4.3 Solve Equations Involving Fractions, pages 204–210 9. Solve. a) b)
3. Solve, then check. a) –2a = –22 b) 3 – q = –5 c)
1 g = –9 2
c) d)
t −6 2
=4
1 (c + 2) 3 4a + 1
= −5
3 2 3
=1
(s – 4) = 4
d) 7 – 6s = 19 4. Greg is 42. He is 3 years older than Sue. a) Write an equation relating Sue and Greg’s ages. b) How old is Sue? 4.2 Solve Multi-Step Equations, pages 196–203 5. Solve. a) 2m + 5m – 3 = 4 b) 4b – 6 + b – 9 = 0 c) 3x – x + 4 = 0 d) 2k + 3 = 4k – 5 6. Find the root of each equation. a) 2 + (4h – 1) = 11 + 2h b) 8 – (2g + 3) = 3g – 5 c) 2(d + 6) = 9(d – 1) d) 5(3r – 7) + r = 3(r – 3) 7. Find each root, then check. a) 4s + 3 – s = –6 b) p – 3 + 2p – 9 = 0 c) 5 – (c + 3) = 4 + c d) 3(4d – 7) – 6 = 2(d + 2) – 1 Principles of Mathematics 9: Teacher’s Resource
BLM 4.CR.1 Chapter 4 Review
10. Solve. a) b) c) d)
d +4 2 k −1
3d
= =
4 k +3
2 2
4
(q – 3) =
3 3c − 1 5
=
1
4 4c + 1
(q + 7)
9
4.4 Modelling With Formulas, pages 211–219 11. Rearrange each formula to isolate the variable indicated. a) A = lw for l b) P = 2a + 2b for b c) y = mx for x d) l = w + 4 for w e) P = 2a + b for b f) S = 2πr(r + h) for h
Copyright © 2006 McGraw-Hill Ryerson Limited.
Name: ___________________________________
Date: _______________________________ …BLM 4.CR.1... (page 2)
4.5 Modelling With Algebra, pages 220–229 12. Write an equation for each phrase. a) 4 less than triple a number is 23 b) the sum of double a number and 6 is 16 c) half a number, less 3, is 8 d) the area decreased by 7 is 14 e) the sum of two consecutive integers is 49 f) the distance increased by 8 is 25
Principles of Mathematics 9: Teacher’s Resource
BLM 4.CR.1 Chapter 4 Review
13. Together, Blackie and Jessie have a mass of 72 kg. Blackie’s mass is 4 kg less than Jessie’s mass. What is each dog’s mass? 14. 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 $42?
Copyright © 2006 McGraw-Hill Ryerson Limited.
BLM Answers BLM 4.GR.1 Practice: Get Ready 14m 3y x+8 1 + 2w 8x − 6 −14y + 35 6m + 3 −n − 2 23x + 14 18y − 3 5z − 4 x = 85° x = 45° 12 b) 6 b) 9. a) 5 b) 6 10. a) 19 b) 30 1. a) c) 2. a) c) 3. a) c) e) g) 4. a) c) e) 5. a) 6. a) 7. a) 8. a)
b) d) b) d) b) d) f) h) b) d) f) b) b) 20 24 5 8 3 10
11x 5p 9b + 8 13 + 2a 6a + 18 −24 − 6b −6 + 6v 15 + 3g 7a − 16 4b − 36 9k − 23 x = 60° x = 25° c) 10 c) 20 c) 3 8 c) 1 18
BLM 4.3.1 Practice: Solve Equations Involving Fractions 1. a) 14 b) −12 c) 2. a) 9 b) 12 c) d) 6 e) 9 f) 3. a) 5 b) 5 c) d) −1 e) 2 f) 4. a) 2 b) 9 c) 5. 1; 3 6. base: 8 cm; height: 6 cm
BLM 4.4.1 Practice: Modelling With Formulas d) 12 d) 30 d) 1 6 d) 17 24
BLM 4.1.1 Practice: Solve Simple Equations 9 9 6 1 17 10 8 12 9 11 2 6 −6 e) 7 2
1. a) d) 2. a) d) 3. a) d) 4. a) 5. a) 6. a) e) 7. a) d) 8. a)
3 1 4 11 3 15 7 16 −33 14 4 5 15 f) − 1 5
b) e) b) e) b) e) b) b) b) f) b) e) b)
c) f) c) f) c) f) c) c) c) g) c) f) c)
2 6 3 8 5 3 −9 10 6 −9 5 1 −3
g) −24
d) d) d) h)
12 −16 6 9
d) −3 h) 4 3
BLM 4.2.3 Practice: Solve Multi-Step Equations 1. a) 2 e) 1 2. a) 2
3. 4. 5. 6.
b) 5 c) 7 f) 4 g) 11 b) 4 c) 3 e) 2 f ) 16 g) 3 3 a) 5 b) 3 c) 2 d) 8 e) 4 f) 2 a) 3 b) 5 c) −1 square: 7; rectangle: 5 by 9 25°, 75°, 80°
15 9 −8 1 −4 3
d) 6 h) − 4 d) 1 h) 7
d) −2
1. D 2. A 3. a) s = P 4 b) P = I rt 2 c) b = A h d) l = P − w 2 d e) t = s f) h = V 2 πr 4. a) 75 pounds b) K = P 2.2 c) 35 kg
BLM 4.5.2 Practice: Modelling With Algebra 1. a) 2x d) 1 x 2 2. a) x + 6 d) 5 − x 3. a) 3x + 4
b) 3x e) 1 x 3 b) x + 3 e) x − 7
c) 4x 1 f) x 4 c) 2 + x f) x − 6
1 x−5 2 d) 2x − 2 b) x + 7 = 11
b)
c) 4x − 1 4. a) 3x = 18 c) x = 10 d) 2x − 3 = 7 2 x e) − 5 =1 f ) 3x + 2 = 14 3 5. a) x + 1 b) x + x + 1 = 47 c) 23, 24
d) −18
d) 4
BLM Answers 6. a) x + 2, x + 4 b) x + x + 2 + x + 4 = 57 c) 17, 19, 21 7. a) x, x + 2, x + 4 b) x + x + 2 + x + 4 = 102 c) 32, 34, 36 8. a) C, C + 2 b) 16 = C + C + 2 c) Katherine: 9; Christine: 7 9. 5 cm, 15 cm
BLM 4.CR.1 Chapter 4 Review 1. a) 7
b) −4
c) 28
2. a) −3
b) −2
c) 3
a) 11 b) 8 a) s + 3 = 42 a) 1 b) 3 a) 5 b) 2 a) −3 b) 4 3 cm, 9 cm, 9 cm a) 14 b) 1 a) 8 b) 5 11. a) l = A w P − 2a b) b = 2 y c) x = m d) w = l − 4 e) b = P − 2a
3. 4. 5. 6. 7. 8. 9. 10.
c) b) c) c) c)
−18 39 −2 3 −1
c) −4 c) 9
d) 8 d) −16 3 d) −2 d) 4 d) 2 d) 3 d) 10 d) 2
f) h = S − r 2π r 12. a) 3x − 4 = 23 b) 2x + 6 = 16 x c) −3=8 d) A − 7 = 14 2 e) x + x + 1 = 49 f ) d + 8 = 25 13. Blackie: 34 kg; Jessie: 38 kg 14. 40
