ACE Project 2
p. 32 (21, 22, 25, 28, 31, 36)
21)Find all the common multiples of 4
and 11 that are less than 100.
Multiples of 4
Multiples of 11
4
56
11
8
60
22
12
64
33
16
68
44
20
72
55
24
76
66
28
80
77
32
84
88
36
88
99
40
92
44
96
48
100
52
22) The Olympic photograph below inspired a school pep club to
design card displays for football games. Each display uses 100 square
cards. At a game, groups of 100 volunteers will hold up the cards to
form complete pictures. They are most effective if the volunteers sit
in a rectangular arrangements. What rectangular seating
arrangements are possible?
•
•
•
•
•
100 fans in 1 row
50 fans in 2 rows
25 fans in 4 rows
20 fans in 5 rows
10 fans in 10 rows
▫ The dimensions of each rectangular arrangement
are factor pairs of 100.
 100 * 1 = 100, 50*2 = 100, 25 * 4 = 100,
20 * 5 = 100, 10 * 10 = 100
25) What is my number?
• Clue 1 – My number has two digits, and both digits are
even.
▫ Could be 28, 46, or 64 but not 72 so D is out
• Clue 2 – The sum of my number’s digits is 10.
▫ 2 + 8 = 10, 4 + 6 = 10, 6 + 4 = 10
• Clue 3 – My number has 4 as a factor.
▫ 4 * 7 = 28, 4 * 16 = 64, nothing times 4 equals 46 so B
is out
• Clue 4 – The difference between the two digits of my
number is 6.
▫ 8 – 2 = 6, 6 – 4 = 2 so C is out and the answer must be
A!
28) Allie’s eccentric aunt, May Belle, hides $10,000 in $20
bills under her mattress. If she spends one $20 bill every
day, how many days will it take her to run out of bills?
May Belle will run out
of $20 bills in 500
days.
31) Which number is a prime number?
• F – Factor Pairs of 91: 1, 91 and 7,13
▫ 91 is Composite
• G – Factor Pairs of 51: 1, 51 and 3, 17
▫ 51 is Composite
• H – Factor Pairs of 31: 1, 31
▫ 31 is Prime
• J – Factor Pairs of 21: 1, 21 and 3, 7
▫ 21 is Composite
36a) Find at least 5 numbers that belong in each region of
the Venn Diagram below.
Multiples of 12
12
24
36
48
72
Multiples of 20
60
120
180
240
300
1, 2, 3, 4, 5 and etc
20
40
80
100
140
36b) What do the numbers in the
intersection have in common?
• The numbers in the intersection are common
multiples of 12 and 20.
▫ In other words, they are both multiples of 12 and
20.