Number Sense – Workbook 7, Part 1 Worksheet NS7-9 page 51 1. a) 3: 0, 3, 6, 9, 12, 15, 18. b) 4: 0, 4, 8, 12, 16, 20, 24. c) 5: 0, 5, 10, 15, 20, 25, 30. 2. a) Yes. b) No. c) Yes; Yes; Yes. 3. a) 0 b) All whole numbers, since any whole number times zero is zero. 4. a) 5 is a factor of 20. b) 1 is a factor of 9. c) 8 is a factor of 0. d) 4 is not a factor of 11. Investigation 1 A. a) 9, 10, 11, 12 b) 6, 8, 10, 12 c) 9, 12 d) 8, 12 e) 10, 15 f) 12 g) 14 h) 16. i) 18 j) 20 k) 22 l) -- m) 13 B. The largest factor of any number, n is n. C. a) 1, 2, 3, 4, 6, 12. b) Yes. 5. a) 0, 0, 0. b) No. c) No. d) 0 e) 0 6. a) 0, 13 b) If n is a whole number then we can always write n 1 = n. 7. a) 0, 1, 2, 3, 4, 5, 6, 7, 8. b) If n is a whole number then we can always write n 1 = n. 8. a) 0 0 0 0 b) Any number n. No. c) All numbers since any number times zero is zero. 9. a) 1 is a factor of 5 b) 1 is a factor of every number c) 8 is a factor of 8 d) Every number has itself as a factor e) 7 is a factor of 0 f) Every number is a factor of 0 10. a) 15 is a multiple of 5 b) 0 is a multiple of 3 c) Any non-zero multiple of 12 is at least 12 d) Any non-zero multiple of a number is at least the number e) 6 is a multiple of 6 f) Any number is a multiple of itself Worksheet NS7-10 page 53 1. a) 10 is the largest factor of 10 b) 0 is not a factor of 10 2. a) 1 st 2 nd 1 6 2 3 3 2 4 5 6 1 b) 1 st 2 nd 1 8 2 4 3 4 2 5 6 7 8 1 c) 1 st 2 nd 1 9 2 3 3 4 5 6 7 8 9 1 3. All except (3,3) 4. a) Connor thinks that if the blank is smaller than 4 then the rest of the pairs of factors will be repeats of the ones he already has. b) His list contains all unordered pairs of factors 5. The rest of the pairs of factors are the ones that he has but in reversed order. 6. a) 1 st 2 nd 1 20 2 10 3 4 5 5 4 b) 1 st 2 nd 1 12 2 6 3 4 4 3 c) 1 st 2 nd 1 15 2 3 5 4 5 3 d) 1 st 2 nd 1 14 2 7 3 4 5 6 7 2 e) 1 st 2 nd 1 25 2 3 4 5 5 f) 1 st 2 nd 1 5 2 3 4 5 1 g) 1 st 2 nd 1 26 2 13 3 4 5 6 7 8 9 10 11 12 13 2 h) 1 st 2 nd 1 30 2 15 3 10 4 5 6 6 5 i) 1 st 2 nd 1 42 2 21 3 14 4 5 6 7 7 6 j) 1 st 2 nd 1 72 2 36 3 24 4 18 5 6 12 7 8 9 9 8 k) 1 st 2 nd 1 63 2 3 21
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Number Sense – Workbook 7, Part 1
Worksheet NS7-9 page 51
1. a) 3: 0, 3, 6, 9, 12, 15, 18.
b) 4: 0, 4, 8, 12, 16, 20, 24.
c) 5: 0, 5, 10, 15, 20, 25, 30.
2. a) Yes.
b) No.
c) Yes; Yes; Yes.
3. a) 0
b) All whole numbers, since any whole number times zero is zero.
4. a) 5 is a factor of 20.
b) 1 is a factor of 9.
c) 8 is a factor of 0.
d) 4 is not a factor of 11.
Investigation 1 A. a) 9, 10, 11, 12
b) 6, 8, 10, 12
c) 9, 12
d) 8, 12
e) 10, 15
f) 12
g) 14
h) 16.
i) 18
j) 20
k) 22
l) --
m) 13
B. The largest factor of any number, n is n.
C. a) 1, 2, 3, 4, 6, 12.
b) Yes.
5. a) 0, 0, 0.
b) No.
c) No.
d) 0
e) 0
6. a) 0, 13
b) If n is a whole number then we can always write n 1 = n.
7. a) 0, 1, 2, 3, 4, 5, 6, 7, 8.
b) If n is a whole
number then we can always write n 1 = n.
8. a) 0
0
0
0
b) Any number n.
No.
c) All numbers since any number times zero is zero.
9. a) 1 is a factor of 5
b) 1 is a factor of every number
c) 8 is a factor of 8
d) Every number has itself as a factor
e) 7 is a factor of 0
f) Every number is a factor of 0
10. a) 15 is a multiple of 5
b) 0 is a multiple of 3
c) Any non-zero multiple of 12 is at least 12
d) Any non-zero multiple of a number is at least the number
e) 6 is a multiple of 6
f) Any number is a multiple of itself
Worksheet NS7-10 page 53
1. a) 10 is the largest factor of 10
b) 0 is not a factor of 10
2. a) 1st 2nd
1 6 2 3 3 2 4 5 6 1
b) 1st 2nd
1 8 2 4 3 4 2 5 6 7 8 1
c) 1st 2nd
1 9 2 3 3 4 5 6 7 8 9 1
3. All except (3,3)
4. a) Connor thinks that if the blank is smaller than 4 then the rest of the pairs of factors will be repeats of the ones he already has.
b) His list contains all unordered pairs of factors
5. The rest of the pairs of factors are the ones that he has but in reversed order.
6. a) 1st 2nd
1 20 2 10 3 4 5 5 4
b) 1st 2nd
1 12 2 6 3 4 4 3
c) 1st 2nd
1 15 2 3 5 4 5 3
d) 1st 2nd
1 14 2 7 3 4 5 6 7 2
e) 1st 2nd
1 25 2
3 4 5 5
f) 1st 2nd
1 5 2 3 4 5 1
g) 1st 2nd
1 26 2 13 3 4 5 6 7 8 9
10 11 12 13 2
h) 1st 2nd
1 30 2 15 3 10 4 5 6 6 5
i) 1st 2nd
1 42 2 21 3 14 4 5 6 7 7 6
j) 1st 2nd
1 72 2 36 3 24 4 18 5 6 12 7 8 9 9 8
k) 1st 2nd
1 63 2 3 21
Number Sense – Workbook 7, Part 1 (Continued) 2
4 5 6 7 9 8 9 7
l) 1st 2nd
1 100 2 50 3 4 25 5 20 6 7 8 9
10 10
m) 1st 2nd
1 64 2 32 3 4 16 5 6 7 8 8
n) 1st 2nd
1 91 2 3 4 5 6 7 13 8 9
10 11 12 13 7
8. a) 1 2 4
b) 1 2 4 8
c) 1 2 3 4 6 12
d) 1 3 5 15
e) 1 7
f) 1 2 3 4 6 8 12 24
g) 1 2 3 6 7 14 21 42
9. a) Yes.
b) 144
72
48
36
24
12
c) 144 n becomes smaller.
d) 1, 2, 3, 4, 6, 12, 24, 36, 48, 72, 144 These are not all of the factors since 8 18 = 144 [Since products of factors are factors].
10. 2 is the second smallest factor. The largest factor is 3 256 2 = 1 628
b) No. All rearrangements have sum of digits equal to 19.
13. If the sum of the digits of a number divided by 3 has remainder 0, then the number is divisible by 3.
14. a) Answers will vary.
b) If the sum of the digits of a number divided by 9 has remainder 0, then the number is divisible by 9.
15. a) Number
Sum of Digits
28 10 37 10 42 6 61 7 63 9 87 15 93 12 123 6
b) 3 3 and
9 9
42 9 87 63 93 123
c) The column
“divisible by 9”. All numbers divisible by 9 are also divisible by 3. Numbers can only belong to one column.
16. a) 2 2 and 3
3
2 0 3
4 6 9 8 12 15 10 18 21 14 24 27 16 30 20 22 26 28
b) In the intersection.
c) Divisible by 6 If the number is even and its sum of digits is divisible by 3.
d) 3 174 7314
Worksheet NS7-16 page 69
1. a) ii) 7, 7, 175
iii) 30,30,750
b) Yes.
2. b) 82, no
c) 60, yes
d) 46, no
e) 67, no
f) 84, yes
g) 26, no
h) 22, no
3. If the last 2 digits of a number form a number which is divisible by 4, then we can write it as a sum of a term divisible by 100 and a term divisible by 4. Sums of numbers both divisible by 4 are divisible by 4.
4. a) Yes. Since any number that ends in 3 zeros is a multiple of 1000.
b) Yes. Similar to #3. If the last 2 digits of a number form a number which is divisible by 4, then we can write it as a sum of a term divisible by 1000 and a term divisible by 8. Sums of numbers both divisible by 8 are divisible by 8.