Math Makes Sense 8 Homework and Practise Book - Answers
Unit 1 – Square Roots and the Pythagorean Theorem
Pg.1
What Do You Notice The final result is 6174
The final result is 6174, no matter what the original number.
Letter Symmetry HIOX
Pg.3
Check 1.a) 6cm x 3 cm = 18 cm² b) 8.5 Square units c) 25 cm² d) ½ (5cm x 6cm) = 15 cm²
e) 17.5 cm² f) 22.95 m²
Pg.5~6
Practice 1.a) – iii)16 b) – i) 36 c) – ii) 8 2. a) 64 = 8 x 8 = 8² b) 49 = 7 x 7 = 7²
3.a) 4² 4x4 16 b) 3² 3x3 9 c) 7² 7x7 49 d) 11² 11x11 121
4. a) 25cm² ---- iii) 5cm b) 64cm² ---- iv) 8cm c) 4 cm² ---- i) 2cm d) 100cm²---- ii) 10cm
5. Diagrams may vary. No, 32 is not a square number. 6. Diagrams may vary.
Yes, 64 is a square number.
7.a) 81 , 81 is a perfect square because 81 = 9 x 9 = 9²
b) 18 , 18 is not a perfect square because I cannot draw a square with area 18 square units on a grid paper. c) 20 ,20 is not a perfect square because I cannot draw a square with area 20 square units on grid paper. d) 25 ,25 is a perfect square because 25 = 5 x 5 = 5²
8. a) 49 cm² , 7 x 7 = 49, so the length of the side is 7 cm. b) 900 mm² ,30 mm c) 121 cm² ,11 cm
d) 169 m² ,13 m
9. a) side length 6 cm Perimeter = 6cm + 6cm + 6cm + 6cm = 24cm
b) area 25 m² Side length is 5 m, because 5 x 5 = 25 so, perimeter = 5 m+ 5m + 5m + 5m = 20m
c) area 144 m² 48 m
10. Sample Answer : Yes. 5² x 2² = 25 x 4 = 100 = 10²
Pg. 8
1. a) 196: 1, 2, 4, 7, 14, 28, 49, 98, 196 Square number with square root 14
b) 200: 1, 2, 4, 5, 10, 20, 40, 50, 100, 200 not a square number
c) 441: 1, 3, 7, 9, 21, 49, 63, 147, 441 Square number with square root 21
2. a) square number: 16 square root: 4 b) square number: 49 square root: 7
3. a) because b) because c) because
d) because
4. a) because b) because c) because
d) because 5. a) – iv) 3 b)– ii) 9² c) 3² – i) 9 d) 9 – iii)
6. a) 8 b) 20 c) 15 d) 18 7. a) 5 b) 8 c) 16 d) 54 8. a) b) 484 c) 900
Pg.10
- a) b) c) 2a) A = 81 cm², l = 9cm; whole number b) A = 30 cm², l = cm c) A = 144mm², l = 12mm; whole number d) A = 58m², l = m
3a) l = 7cm, A = 49cm² b) l = 15m, A = 255m² c) l = cm, A = 36cm²
d) l = mm, A = 50mm² e) l = cm, A = 24cm² f) l = mm, A = 121mm²
4. a)16, 2, Area of shaded square = area of large square –4 x area of each triangle
= 16 square units – 4x2 square units
= 8 square units
side length = units
b) 17 square units; units c) 20 square units; units 5.a) 26 square units, units
b) 8 square units; units c) 25 square units; 5 units
Pg 11
1. a) between 2 and 3 b) between 4 and 5 c) between 7 and 8 d) between 1 and 2
pg. 12 2. a) between 11 and 12 b) between 14 and 15 c) between 10 and 11 d) between 12 and 13
e) between 13 and 14 3. a) False b) True c) True d) True 4. a) Not a good estimate b) Good estimate 5. a) 4.5 b) 7.5 c) 10.7 d) 13.2 6.a) A = 50cm²; s = 7.1cm b) A = 125cm²; s = 11.2cm c) A = 18cm²; s = 4.2cm 7. 9.95 ; methods may vary
8 = 15.81m, 15.81m + 15.81m + 15.81m + 15.81m = 63.24m, 63.24m of fencing is required.
Pg. 14
1. a) j and p are legs; g is hypotenuse b) n and r are legs; d is hypotenuse 2. a) b) 5 c) 17
3a) b) c) d)
4a) b) c)
p. 16
1a) is, b) is not, 2a) right triangle because b) not a right triangle because c) not a right triangle because
p. 17
3a) b) c) d)
not a right triangle a right triangle a right triangle not a right triangle
4. 5a) is not a Pythagorean Triple b) is
6a) 25, square root, squares, b) 34 c) 24
7. Right. . The triangle formed by the width, length, and diagonal is a right triangle, so the lawn is a rectangle.
p.19
1. 4, 6, 8, 64, 52 2. a) 11.7mm b) 10.3 cm c) 20.2 mm d) 5.7 cm
3.
64-9=9+-9
55=
b=7.4
7.4 m
p.20
4. Diagrams may vary. 15.6 km 5. 793 m 6. 50m, 50m, 30m + 40m = 70m, 70m – 50m = 20m
7. 100, 10, hypotenuse, 10cm, 10cm, 14.1cm
p.21
Square Root: a number that, when multiplied by itself, results in a given number. For example, 5 is the square root of 25
Legs Of A Right Triangle: the sides of a right triangle that form the right angle
Hypotenuse: the side of a right triangle that is opposite to the right angle; the longest side of a right triangle
Pythagorean Theorem: the rule that states that, for any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the legs
Pythagorean Triple: three whole-number side lengths of a right triangle. For example, 3-4-5 is a Pythagorean triple.
Square number, perfect square, irrational number
p.22
1. Diagrams may vary. 36, 121 2 a)64 b) 7 c) 144 d) 11 3 a) 1, 2, 5, 10, 25, 50
b) 1, 2, 4, 7, 14, 28, 49, 98, 196 c) 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 d) 1, 3, 5, 7, 15, 25, 45, 75, 225 4. a) cm b) 13cm (circle) c) cm 5. 10 square units. units
p.23
6. units 7. a) 8 b) 54 c) 153 8. a) 6 and 7 b) 4 and 5 c) 7 and 8 d) 11 and 12
9. a) 6.7 b) 4.2 c) 7.4 d) 11.6 10. a) 8.66 b) 9.49 11. a) 32 b) 100 12. a) 25 units
b) 8.9 units c) 10 units 13. a) not a right triangle because
b) right triangle because
p.24
14. a) 10, 24, 26 d) 11, 60, 61 15. 16.64 km 16. 10.82 m
p.27
1. a) +4 b) –5 c) –1 d) +2 2. a) 0 b) +6 c) +16 d) -11 e) -5 f) -8
p.28
3. a) +9 b) +1 c) 0 d) +14 e) -11 f) +2
4. From 8 degrees C to 3degrees C ---- (+3) – (+8) ---- -5
From 8 degrees C to -3 degrees C ---- (-3) – ( +8) ---- -11
From -8 degrees C to 3 degrees C ---- (+3) – (-8) ---- +11
From -8 degrees C to -3 degrees C ---- (-3) – (-8) ---- +5
p.29
1. a) (-2) b) 3 x (+11) c) 3 x (-5)
p.30
2. a) – 4 b) (+4) + (+4) + (+4) + (+4) + (+4), +20 c) (-3) + (-3), -6 3. a) -6 b) 5, +10
c) (-2), (-3), +6 d) (-9) x (-2) = +18 e) 4 x (-3) = -12 4. a) -14 b) +15 c) -6 d) -20
p.31
5. a) +12 b) -10 c) +14 d) -18 6. -2 represents a fall of 2 degrees C, 4 represents 4 hours,
4 x (-2) = -8 The temperature dropped 8 degrees C in 4h.
p.32
1. a) 0, (-1), -3, -6, -9 b) 0, (-3)(-1) = +3, (-3)(-2) = +6, (-3)(-3) = +9
p.33
2. positive, negative, negative, positive, positive, negative 3. a) -14 b) +12 c) -72 d) -50 e) -35
f) +36 i) +7 j) 0 k) -400 4. a) -5 b) -11 c) +32 d) -4 e) -7 f) -5 g) +12 h) -10 k) -8
5. -3, +9, -27, +81 ---- Start at -3. Multiply by -3 each time.
+2, -10, +50, -250 ---- Start at 2. Multiply by -5 each time.
+3, -3, +3, -3 ---- Start at 3. Multiply by -1 each time.
+1, -10, 100, -1000 ---- Start at 1. Multiply by -10 each time.
-1, -2, -4, -8, -16 ---- Start at -1. Multiply by 2 each time.
p.35
1. a) (+6) x (+10) = +60, (+10) x (+6) = +60 b) (-4) x (-9) = +36, (-9) x (-4) = +36
c) (+5) x (-9) = -45, (-9) x (+50 = -45 d) (-8) x (+2) = -16, (+2) x (-8) = -16
2. , seven steps 3a) -3 b) +4 c) +5 d) +2
p.36
4a) -3 b) +2 c) -2 5) -4 represents the drop each hour, -28 represents the total drop,
It took 7 hours for the water level to drop 28cm. 6a) +5 b) +5 c) -5 d) -5 They are all either +5 or -5
7) -12 represents a drop of C, +4 represent 4 hours, , The temperature dropped C every hour.
p.37
+3, positive +2, positive -3, negative -2, negative -3, negative +2, positive +3, positive -2, negative
p.38
2) positive, negative 3a) b) positive, negative
4) a) -5 b) -8 c) -9 d) +6 e) -12 f) +8 g) +7 h) +12 i) -8 5) a)
b) c) d) 6) a) -19 b) +23 c) +11 d) -45
p.39
1) a) b) c) d) e) f)
g)
p.40
2) 3) a) b)
c) 4)
MEET ME AT THE CORNER
p.41
Quotient: the answer to a division question. For example, in the division equation , -4 is the quotient.
Zero pair: two opposite integers, such as +4 and-4, whose sum is 0.
Commutative property: order does not matter when multiplying integers. For example, .
Zero property: The answer when multiplying an integer by 0 is 0. For example, .
Order of operations: The order to perform operations in a mathematical expression. For example, in, perform the addition in brackets first, then do the multiplication, and finally do the addition outside the brackets.
Number line, opposite integers, multiplying by 1 property, distributive property, numerator, denominator
p.42
1) a) b) c)
d) 2) a) b) c)
d)
p.43
3) a) +2 represents a rise of 2°C, +6 represents 6h, , the temperature rose 12°C in 6 h b) , the temperature after 6 h was 8°C 4) Models may vary
5) a) Negative b) zero c) Positive 6) a) +6 b) -24 c)+220 d) -720 e)+180 f) +126 g)-162 h)0
7) a) b) c) d) e) f)
p.44
8) a) or b) or
c) or d) or
9) Models may vary 10) a) Positive, +5 b) negative, -4 c) negative, -6 d) zero, 0
11) a) -5 b) +3 c) -6 The quotients from least to greatest are: -6, -5, +3
12)
p.45
13) a) +256, -1023, +4096 Pattern rule: Start at +1. Multiply by -4 each time. b) -4, +1, Pattern rule: Start at -128. Divide by –4 each time. c) +25, -5, Pattern rule: Start at -3125. Divide by -5 each time. 14) a) multiply b) divide c) subtract d) multiply
15) a) b) c) d)
p.46
16) a) b) c) d) e) f)
p.47
Sample answer: cart, raft, craft, ratio, ration,…
p.48
1) a) ,, b) ,, c) ,, 2a) b) c) d) 3a) b)
c) d)
p.49
4) a) b) c) d) 5a) b) c) 6, 10, d)
p.50
1) a) 4, b) c) d)
p.51
2) a)or b) or c)or 3a) b) 15 c) 12 d)
e) f) 4a) iii b) v c) iv d) i e) ii 5)
p.52
1) a) b) c) d)
p.53
2) Models may vary. a) b) 3) Tom ate of the pie. 4). The numerator of the answer fraction is the product of the numerators of the fractions being multiplied. The denominator of the answer fraction is the product of the denominators of the fractions being multiplied.
5) a) b) c) d)
p.54
1) a) 3, 4, b) c) d) e)
p.55
2) a) b) c) d) 3a) b) c) d) 4a) b) c) d)
5) a) iii b) i c) iv d) ii 6) 7) 8),
p.56
1) a) b) c) d) 2a) b) c) d)
p.57
3) a) b) 3 4a) b) c) d) 6 e) f)
5) George practises for 3h on Saturdays.
p.58
1) a) 6 b) 6 c) 3 d) 2 2a) b) c) d)
p.59
3) a) 14 b) 9 c) 6 d) 10 4a) b) c) d) e) f) g) h)
6) a) b) 18 7a) Sample answers: or b) Sample answers: or
p.60
1) a) b) c) d) 2a) b) c)
p.61
3) a) 2, 2 b) c) d) 4a) 2, There are two-eights, b) 8 c) d)
5) a) b) c) d) 6a) 3 servings b) servings c) servings d) servings
7) a), 5, ,
p.62
1) a) b) c) d) 2a) 6, , , b) c) d)
p.63
3) a) 19, 19, 10, , , b) c) d) 4a) 7, 9, or b)
c) 3 d) 5a) b) c) d) 6) 4 7) 5 8) A:, B:, C:, A,
p.64
1) a) addition b) division c) multiplication
p.65
2 a) , , b) 8 c) 124 3) 4) , 5) 6) 10
p.66
7a) b) 8) 6 9a) b) 10a) b) c)
p.67
1) a) Add the functions in the brackets b) Multiply c) Subtract the fractions in the brackets
d) Divide the fractions in the brackets. 2) Her answer is not correct. She multiplied first instead of dividing first.
p.68
3) a) b) c) d) 4a) b) c) d) 5a)
b) c) d) 6a) b) c) d) 1 e) f)
p.69
Simplest form of a fraction: a fraction in which the numerator and the denominator have been divided by their greatest common factor.
Reciprocal of a fraction: a fraction, either proper or improper that is inverted. For example, the reciprocal of is .
Mixed number: a number consisting of a whole number and a fraction. For example, is a mixed number.
Quotient: the result when one number is divided by another.
Order of operations: the rules that are followed when simplifying or evaluating an expression; brackets, multiplication and division, addition and subtraction.
Product, factor, equivalent fraction, divisor, dividend.
p.70
1) a) 6, or 3 b) 4, or 5 3a) b) c) 4) 5a) b) c)
p.71
6) a) b)16 c) 7) Models may vary. a) 6 b) c) 8a) b) c) 9a)
b) c) 10a) 6
p.72
11) 12) 9 13a) b) 14)
p.73
Handshakes: 6, 10, 15, 21. Starting from 1, as the number of people increases by 1, the number of handshakes increases in this pattern 1, 2, 3, 4, …
Word Search: 2) MATH IS GREAT
p.74
1) a) 42, 42 b) 9.52 2a) b = 6.4 cm, h = 3.5 cm, A = 11.2 b) b = 8.6 cm, h = 4.2 cm,
A = 18.06
p.75
3) a) 24, 12, 452.389, 452, centimetre b) 254.469, 254, metre c) 95, millimetre
d) 201, kilometre 4a) 12, 37.7 cm b) 8, 50.3 m c)17.6 mm d) 23.9 m
p.77
3) B 4a)A E, B F, C D b) A and E represent s regular pentagonal pyramid with one pentagonal base and five isosceles triangles. B and F represent a regular square pyramid with one square base and four isosceles triangles. C and D represent a hexagonal prism with two hexagonal bases and six squares.
5a) hexagonal pyramid b) triangular pyramid c) square prism d) right triangular prism
p.78
1) B
p.79
2) a) Is. It is the net of a hexagonal pyramid b) Is. It is the net of a triangular prism c) Is not. Move either square on the bottom edge to anywhere along the top edge to make the net of a cube. 3) triangular prism with two congruent right triangle faces and three rectangular faces.
p.80
4) a) right cylinder b) square prism c) pentagonal pyramid 5a) Add a 13cm by 5 cm rectangle to form the net of a right triangular prism b) Add a 12 cm by 5 cm rectangle to form the net of a triangular prism. c) Add a regular pentagon of edge length 5 m to form the net of a pentagonal prism.
p.81
1) 2) Rectangle A has area ; Rectangle B has area ; Rectangle C has area ; Surface Area = 3) Glenda’s package: SA=The surface area is 992cm²; Louis’s package: SA= The surface area is 888cm². Glenda’s package has the greater surface area. 4) a) Area of each face b) Edge length = 7cm 5) Total Area to be covered =
p.83
1) Rectangle A has area; Rectangle B has area; Rectangle C has area; Triangle D has area; Triangle E has area;
Area =. The area of the net is 36m².
p.84
2) a)200cm² b)360m² c)161cm² d)173.1m² 3) The surface area is 1104cm² 4) The area of the net is 210cm² 5) The surface area is 454mm²
p.85
1) a) The volume is 480cm³. b) The volume is 216 cm³. c) The volume is 108m³.
p.86
2) a) A V The volume is 357m³. b) The volume is 151.2cm³. c) The volume is 49mm³.
3) a) The volume is 960cm³. b) The new length is 8cm and the new height is 10cm. The new volume is 960cm³. 4) a) The volume is 97.2m³. b) The volume is 97.336m³; the volume of prism B is greater
5) a) The volume is 24 m. b) The height for this calculation is 1.5m. The length is 400cm, the width is 300cm, and the height is 150cm. The volume is 18000000cm³. This is the same as 18000L.
p.87
1) a) The volume is 60cm³. b) The volume is 280cm³.
p.88
2) a) The volume is 168cm³. b) The volume is 30m³. c) The volume is 5.7mm³.
3) The area of each triangular face is 5.56cm². 4) A = 1cm² l = 6cm; A = 2cm² l = 3cm; A = 3cm² l =2cm; A= 6cm² l =1cm
p.89
5) The volume is 270cm³. 6) a) The volume is 1500cm³. b) The depth of water is 16cm.
p.90
1) a) Area of net; 402cm².
p.91
1) b) 107cm² to the nearest square centimetre. c) The diameter = 2cm, so the radius = 1cm. The area is 1407cm². 2) a) Surface area of cylinder ; Surface area is 1005cm², to the nearest square centimetre. b) The diameter of each circle is 9m, so the radius of each circle is 4.5m. The surface area is 319m², to the nearest square metre. c) The surface area is 292cm², to the nearest square centimetre.
3) a) The diameter is 15m, so the radius is 7.5m. Surface Area of cylinder; the surface area of the cylinder is 506.6m², to one decimal place.
p.92
3) b) The diameter is 4.8cm, so the radius is 2.4cm. The surface area of the cylinder is 364.9cm², to one decimal place.
4) The diameter is 1.8m, so the radius is 0.9m. Curved surface area of roller. The area of the curved surface of the roller is 29.4m².
5) a); the circumference = 37.7cm. b); radius = 6cm.
p.93
1) a) volume of a cylinder ; The volume is 110cm³, to the nearest cubic centimetre.
b) The volume is 3807cm³, to the nearest cubic centimetre. c) The volume is 4775m³, to the nearest cubic metre.
p.94
2) a) Volume; the volume is 254cm³, to the nearest cubic centimetre. b) The diameter is 18mm, so the radius is 9mm. The volume is 8906mm³, to the nearest cubic millimetre. c) The diameter is 48m, so the radius is 24m. The volume is 16286m³, to the nearest cubic metre. 3) a) 5428.7cm³
b) Diameter = 16.8m, the radius = 8.4m; the volume is 1197.0m³. 4) Volume of cylinder A = 411.8cm³; volume of cylinder B = 418.2cm³ so cylinder B has the greater volume by 6.4cm³. 5) a) 785.4cm³
b) Double the radius is 10cm; the new volume is 3141.6cm³, which is 4 times the original volume.
c) Double the height is 20cm; the new volume is 15708cm³, which is 2 times the original volume.
p.95
Net: A pattern that can be folded to make a solid
Polyhedron: An object whose faces are polygons
Regular prism: An object with 2 congruent faces that are regular polygons, and with remaining faces that are rectangles
Regular pyramid: An object whose base is a regular polygon and whose other faces are triangles
Surface area: The total area of the surface of an object
Volume: The amount of space occupied by an object
Sample answers: regular dodecagon, capacity
p.96
1) A square with 6cmx6cmsides and 4 triangles with a base of 6cm and a height of 10cm
2) Figure B is not the net of a cube. 3) Net A = object 2; Net B = object 1; Net C = object 3
p.97
4) The area of the net is 208cm². 5) a) The area of one face of the cube is ; the length of one edge is 8cm. b) The volume of the cube is 512cm³
6) a) l = 8, w = 1 h = 1; l = 4, w = 2, h = 1; l = 2, w = 2, h = 2 b) 34cm², 28cm², 24cm²
p.98
7) The surface area is 200m². 8) The volume of the triangular prism is 1800m³; the volume of the rectangular prism is 5400m³. The total volume is 7200m³. 9) a) The diameter is 16m, so the radius is 8m. The volume of the tank is 603m³. b) The area to be painted is 352m².
p.99
One at a time – Sample answer: 1st step: you get RADIO or PATIO. Working backward from RATES, words, such as RATED, require more than 2 steps to get to RADIO or PATIO.
Decimal – Sample answers: 2 letter words: ad, am, id, me; 3-letter words: dim, led, lad, die, dam, mad, cad, lam, lid; 4-letter words: lame, lace, male, dame, dime, mice, mace, dale, dial, dice, made; 5-letter words: laced, lamed; 6-letter words: malice; 7-letter words: claimed, declaim, medical
p.100
1) a) b) c) 2) a)36% = 0.35 = b) 5% =0.05 = c) 44% = 0.44 = d) 86% = 0.86 = 3) a) 6: 6, 12, 18, 24, 30 b) 9: 9, 18, 27, 36, 45 c) 15: 15, 30, 45, 60,75
p.101
4) a) Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150,… Multiples of 25: 25, 50, 75, 100, 125, 150… Two common multiples of 15 and 25 are 75 and 150. b) 30, 60 c) 60, 120
5) a) 3650cm b) 5260mL c)17kg d) 75km
p.103
1) a) 30% b) 7% c) 86% 2)a) 6% = =0.06 b) 87% = = 0.87 c) 48% = =0.48
3) a) b)
4) a) b)
p.104
5) a)0.5% b) 0.95% 6) a) b)
7) a) b) c) 8) a) Explanations may vary
b) or c)0.06 or 6% 9) In the parking lot, or 47.5% of the cars are hybrids.
10) is the same as 8.25%. The interest rate is or 0.0825.
p.105
1) a) 125% b) 150% c) 200% 2) a) 175% = 1.75 b) 0.5% = 0.005 3) a) 2.3 b) 1.85 c) 3.24 d) 0.0074
e) 0.007 f) 0.0009
p.106
4) a) 50% b) 150% c) 250% d) 1% e) 0.5% f) 1.5% 5) a) 1cm x 1cm b)The new square has sides of length 2 cm. 6) a) i) 80 ii) 8 iii) 0.8 b) Each answer is one-tenth the size of the previous answer. c) i) 800 ii) 0.08 7) runners completed the run in under 40 min. runners completed in under 34min.
8) 120.3% of $1000 is the greater amount of money.
p.107
1) a) 40 b)120 c) 75 d) 200
p.108
2) a) b) c) 3) a) Increase = 4cm; Increase as a fraction =; Percent Increase = b) Percent increase = %. 4) a) Decrease = 8L; Decrease as fraction = ; Percent decrease = b) Percent decrease = 10%. 5) There were 600 eggs in the batch.
p.109
6) a) $12 b) $6 7) a) The population of Quebec is about 7500000. b) About 40% of the population of Yukon Territory lives in rural areas. 8) The new volume of water is 27L. 9) The result is 217.
10) a) The new production rate is 1008 items/week. b) The new unit cost is $63.
p.110
1) a) b) c) 2) a) b) c)
3) a) Discount: ; Sale Price: b) Discount: Sale Price:
p.111
4) Discount: $2.90; Sale Price: $26.05; 13% tax: $3.26; Total cost: $29.31 b) Discount: $59.75; Sale price: $179.25; 13% tax: $22.41; Total cost: $201.66 5) Increase in price: $9.00; Total cost: $45.00.
6) Assume $100 sales. Find the selling price: Store A: Store B: ; Store A offers greater discount. 7) The original price is $180. 8) a)
b) ; Discounts are the same for both. 9) 113% is $32.77.
1% is:; 100% is: ; The fishing pole cost $29.00 before sales tax.
p.112
1) a) 3:5 b) 7:6 c) 5:9
p.113
2) a) 5:12, , 41.67% b) 7:12, , 58.33% 3) a) 3 b) 8:3 c) 3:11 4) a) 13:6 b) 13:19 c) 6:19
p.114
5) a) 3:5 b) 5:3 c) 3:8 d) 5:8 e) 4:4 f) 2:1:2 6) a) Carrots b) carrots c) tomatoes to carrots to cauliflowers
d) cauliflowers to carrots e) tomatoes to total vegetables f) cauliflowers to total vegetables
7) a) red: green = 3: 5; yellow: red = 7:3; black: total pencil crayons = 1:16; yellow: total pencil crayons = 7:16; yellow: red: green = 7:3:5 b)10:16; 62.5% c) 5:4 d) red: green = 3:3; yellow: red = 5:3;
black: total pencil crayons = 1:12; yellow: total pencil crayons = 5:12; yellow: red: green = 5:3:3
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1) a) 8:10, 12:15, and 16:20 b) 16:12, 8:6, 4:3 c) Three ratios equivalent to 16:28 are 4:7, 8:14, and 32:56.
2) a) Sample answer – 16:10:4, 24:14:6 b) Sample answer – 12:8:6, 6:4:3
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3) a) 10:4 b) 6:15 c) 1:2 d) 5:2 4) a) i) 5:6 = 15:18; 18:3 = 6:1;
9:18 = 1:2; 4:20 = 8:40 ii) 1:8 = 2:16; 3:27 = 1:9; 12:36 = 1:3; 18:2 = 9:1 b) 12:36 and 1:3 are equivalent because and 5) sample answer – 12 cats and 15 dogs = 20 cats and 25 dogs; 8 cats and 10 dogs = 16 cats and 20 dogs = 32 cats and 40 dogs 6) the poster is 60 cm wide; 3:2 = 90:60
p.119
1) a) 2 mixture A and 1 scoop; 2 and a half of mixture B and 1 scoop b) Mixture A is stronger because it has less water for every scoop of powder.
p.120
2) a) 20 mice in each cage; 40 mice in total b) 8 white mice in A; 15 white mice in B; cage B contains more white mice. 3) Red paint to white paint – A 4:3 B 7:5; A 20:15 B 21:15;; Mixture B will give a darker shade of red.
p.121
4) Jan’s school; 9 computers to 15 students; Karl’s school 10 computers to 15 students; Karl’s school has more computers 5) Hamid 55 laps in 66 minutes; Amelia 48 laps in 66 minutes; Hamid jogs faster. 6);
The Rebels have won 60% of their games, and the Sabres have won about 58% of their games. The Rebels have the better record.
p.122
1) a) 6 b) 15 c) 3 2) a) b) c:12 = 5:6 c=10 c) 3:14 = t:70 t=15
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3) a) 8 b) 32 c) 2 d) 8 e) 6 f) 20 4) p:70 = 7:5; There are 98 purple cubes. 5) PQRS is 45cm.
6);The actual length is 1.6 cm. 7) There are 24 boys and 4 teachers
p.125
1) a) 4km/h b) 3 books/ week c) 25 drops/min 2) a) ; Average driving speed = 75km/h
b) ; The helicopter’s rate of travelling is 60km/h. c) Gerald’s rate of walking is 4km/h
3) a) rate: $10.89 per kg b) Ratio: 3:7 c) rate: 620km per 6 h d) ratio: 5:4:6 e) rate: 23 points per 7 games
4) a) Maria charges $5/h. b) Maria charges $25. c) 10 h
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5) a) 75km b) 75km/h 6) ; I can buy 15 bars. 7) a) $525.00 Can b) $168.30Can/day
c) $38.05 US
p.127
1) a) b) 70words / min c) $141/week d) $1.30/100mL
2) a) ; First one is the better buy.
b) ; First one is the better buy.
p.128
3) a) 60.5 km/h b) 62km/h c) 61.8km/h; Greatest average speed = 62km/h 4) Tasha 5) a) 14.5points/game b) 377points 6) Twenty-four 500-mL bottles for $9.18 is the better buy. 7) a) British Columbia
b) Saskatchewan c) Ontario d) British Columbia
p.129
Discount: The amount that a price is reduced due to a sale.
Sales tax: The tax based on a percent of the selling price that is set by the government. It is calculated at the place of sale, collected by the retailer, and passed onto the government.
Ratio: A comparison between two quantities measured in the same unit.
Equivalent ratios: Ratios that are equal. For example, 8:6 and 4:3 are equivalent ratios because you can multiply each term in the ratio 4:3 by 2 to get 8:6
Rate: A comparison of two quantities with different units. For example, 10km travelled in 2 h is a rate. You compare distance (10km) with time (2h).
Proportion:A statement that two ratios are equal. For example, . The value of an unknown x can be found by solving the proportion.
Other mathematical words: percent increase, percent decrease, two-term ratio, three-term ratio, part-to-whole ratio, part-to-part ratio, unit rate
p.130
1) a) b) c) d)
2), so Analise’s class has a greater ratio of girls to students.
3) a) b) c) d)
4) a) b) c) d)
5) a) ; the population was 2438 in 1905 b); the increase in population was 318.
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6) a) 700kg b) 68cm c) 17500L 7) Four students completed this distance. 8) a) percent increase = 4%
b) Percent decrease = 17.5% 9) The volume of the water in the tank after 1 h is 1419L.
10) a) Before: $112.50; After: $126.00 b) Before: $1365; After: $1528.80 c) Before: $5.78; After: $6.47
11) The regular price is $878 12) ; the selling price is $61.88.
p.132
13) a) 6:5 b) 12:6 c) 5:18 14) a); ; b); ;
p.133
15) a) b) c) 16) ; ; Class 8B has more globes. 17) s:45=3:5; 27 students sailed. 18) 75 cubes are red.
p.134
19) a) 1 cm on the map represents 6000000cm of actual distance; The actual distance is . b) ; The distance between the two towns on the map is 20.8cm. 20) a) The van travels at an average speed of 70km/h. b) Mikki jogs at an average speed of 6 km/h. 21) 3.8L of detergent for $5.78 is the better buy. 22) It will take 43.75h to travel 1050km. 23) The United Kingdom, with a population density of about 245 people/km
p.135
Date Palindrome: 20022002,
Sample Answers: 17022071 (Feb 17, 2071), 14022041 (Feb 14, 2041)
Sample Answer: 21022012 (Feb 21, 2012)
Word Scramble:
MULTIPLY, SUBTRACT, VARIABLE, PERCENT, FRACTION, SOLVE, INTEGER
Four Fours:
p.136
1) T(0,2), I (2,3), G(4,5), E(7,4), R(6,0) 2) A(0,5), B(2,4), E(4,3), R(5,0) 3) a) 6 bracelets b) 5h
p.137
4) a) Add 2 to both sides. Divide both sides by 3. b) Subtract 3 from both sides. Multiply both sides by 2.
p.139
1) a) x+2=3; x=1 b) 5=2x+3; x=1 c)-3x+5= -4; x=3 2) Models may vary a) x+3=9; x=6 b) 3=2x-5; x=4
c) 4x+3 = 11; x=2 d) 14=5x+4; x=2
p.140
3) Models may vary a) a+4 =5; a = 1 b) 6 = c – 4; c=10 c) y – 2 = 4; y = 6 d) 5= x+3; x = 2
4) Models may vary a) 2v=6; v=3 b) 4n = - 8; n= - 2 c) 5=5y; y = 1 d) – 6=3r; r = -2
p.141
5) Models may vary a) 3x+2 = 11; x = 3 b) -5=5+2y; y = -5 6) a) 2n+5=7 b) Models may vary; n =1
c) Answers may vary. The number is 1. 7) Models may vary; 3n – 1 =11; n =4
p. 142
1) a) 3x+1 = -5; x = -2 b) 5 = -2x – 1; x= -3
p.143
2) Models may vary a) 2y – 1 = 7; y = 4 b) -4 = 2+3a; a = - 2 3) a) b)
c) 2+5y=2; y = 0 d) 4 – 3x = -5; x=3 4) a) y = 4 b) 5) a) 3n – 4 = 14; n = 6 b) 2n+12 =44; n= 16
p.145
1) a ) division b) multiplication c) addition d) multiplication 2) a) b) c)
d) 3) a) b) b = 21 c) Left side ; Right side = 7; There were 21 basketballs altogether.
p. 146
4) a) b) j = 88 c0 There were 88 jellybeans in the bag. 5) a) b)
c) d)
p.147
6) w = 12 7) a) Let j represent the number of cookies that were in the jar to start. b) j = 25
c) There were 25 cookies in the jar to start.
p.148
1) a) 4(c+5) = 4c+20 b) 4(a - 3) = 4a – 9
p.149
2) a) 2(y+5) = 2y +10 b) 3(w – 1) = 3w – 3 3) a) 3(u – 6) = 3u – 18 b) 2(5 – q) = 10+ 2q c) 5(r+1) =5r+5
d) 7(3 – p) = 21 – 7p 4) a) – 6(a – 7) = -6a+42 b) 4(-5 – w) = -20 – 4w c) – 2(x – 20) = -2x+40
d) – 1(b+8) = - b – 8 5) Yes, she made an error; 3(y – 2) = 3y – 6 6) a) 5(6+4); b) 50; 50
c)
p.150
1) a) b) 15= 3(p – 7) ; p = 12
p. 151
1) c) m= - 5 d) x = e) r = -12 f) h = 2 2) a) Sample Answer : C b) c – 4 c) 2(c – 4)
d) 2(c - 4)=12; c =10 e) Brittany had 10 cookies to start.
p. 153
1) a) y = -10, -9, -8, -7, -6, -5, -4 b) y = 17, 16, 15, 14, 13, 12, 11 c) y = 9, 6, 3, 0, -3, -6, -9
2) a) x = -3, -2, -1, 0, 1, 2, 3; y = 1, 2, 3, 4, 5, 6, 7 b) x = -3, -2, -1, 0, 1, 2, 3; y = 8, 6, 4, 2, 0, 2, 4
c) x = -3, -2, -1, 0, 1, 2, 3; y = 8, 7, 6, 5, 4, 3, 2
p. 154
3) a) 33 = 6r + 3 b) 4) a) (2, 15) b) (-4, -21) 5) a) (2,14) b) (3,18) c) (12, 54) d) (-4,-10)
6) a) n = 1, 2, 3, 4, 5; c = 4, 8, 12, 16, 20 b) 7 hamburgers would have to be sold
p. 155
1) x = 0, 1, 2, 3, 4; y = 2, 4, 6, 8, 10
p. 156
1) b) When x increases by 1, y increases by 2. The y values start at 2. 2) b) When x increases by 2, y decreases by 4. The y values start at 5. 3) a) x = -1, 0,1, 2, 3, 4; y = 5, 2, -1, -4, -7, -10
p. 157
4) a) x = 0, 1, 2, 3, 4, 5; y = -4, -1, 2, 5, 8, 11 6) a) n = 1, 2, 3, 4, 5, 6, 7; C= 90, 130, 170, 210, 250, 290, 330 b) Substitute 410 for c in the equation and solve ; 9 people could go on the trip with $410.
p.158
Distributive property: Multiplying a number by a sum of two numbers is the same as multiplying the first number by each number in the sum and then finding the sum of the products. For example, 5(a+b) = 5a+5b
Opposite operation: an oper4ation that “undoes” a given operation. For example, multiplication and division are opposite operations, and addition and subtraction are opposite operations.
Algebra tiles: tiles that can be used to represent numbers and variables. For example, a small white square tile represents +1, a small black square tile represents -1, and a white rectangular tile represents x.