3.4 Solutions pg. 77: 3,4,5
3.
a. Dividing stickers evenly among 5 students is the sharing division concept. You wish
to share the stickers. Base ten diagrams and division equations will vary.
b. Giving out stickers 5 at a time is the measurement division concept. You wish to
share the stickers. Base ten diagrams and division equations will vary.
4.
a
.
1: Set out
divisor
2: Fill in base ten pieces
3: Measure quotient (top)
96  4  24
b
.
1: Set out
divisor
2: Fill in base ten pieces
3: Measure quotient (top)
221  17  13
c.
1: Set out
divisor
2: Fill in base ten pieces
3: Measure quotient (top)
529  23  23
d
.
1: Set out
divisor
2: Fill in base ten pieces
3: Measure quotient (top)
397  34  11 R23
5.
a.
b.
c.
4.1
Solutions pg. 87: 5,8
5.
a. Numbers have an odd number of factors if they are square numbers. There are
ten square numbers less than or equal to 100: 1, 4, 9, 16, 25, 36, 49, 64, 81
and 100. In each case the square root factor forms a square array and adds
only 1 factor to the list of factors for the number.
b. Numbers have an even number of factors if they are not square numbers. Since
there are 10 square numbers less than or equal to 100, there are 90 numbers
less than or equal to 100 with an even number of factors. For these numbers, each
rectangular array is non-square and adds two factors.
8.
a. p  q
pq
Number of factors
Factors
4=22
1, p, q and p  q
b. p2  q
p2  q
Number of factors
Factors
6=32
1, p, p2, q, p  q and p2  q
c. p2  q2
p2  q 2
Number of factors
Factors
9=33
1, p, p2, q, q2, p  q, p2  q, p  q2 and p2  q2
d. p  q r
p  q r
Number of factors
Factors
8=222
1, p, q, r, p  q, p  r, q r and p  q r