06-NelsonMathGr6-Chap06 7/20/05 9:18 AM Page 170
CHAPTER 6
2
Goal
You will need
• centimetre
grid paper
• a calculator
Identifying Multiples
Solve problems by identifying multiples
of whole numbers.
Akeem and Isabella are studying comets. The comets
Kojima and Kowal-Mrkos were both visible in 2000.
Kojima appears about every 7 years. Kowal-Mrkos
appears about every 9 years.
is the next year that both comets
? When
will be visible?
multiple
A number that is the
product of two factors
8 is a multiple of 2
because 2 4 8
Isabella’s Method
I can solve the problem by identifying the
multiples of 7 and 9.
I’ll keep multiplying 7 and 9 by counting
numbers to create lists of multiples.
I’ll look for a multiple that is in both lists
and I’ll add that number to 2000.
Multiples of 7
1x7
7
2x7
14
3x7
21
Multiples of 9
1x9
9
2x9
18
3x9
27
Akeem’s Method
+7
If I keep adding 7, I’m adding multiples of 7 to 2000.
2000
The first multiples are 7, 14, and 21.
+9
I’ll keep adding 7s or 9s on number lines.
I’ll write the years on the number lines.
I’ll look for a year that is on both number lines.
2000
+7
2007
+7
2014
+9
2009
2021
+9
2018
2027
A. What will Isabella do to determine the next multiples of 7 and 9?
B. What will Akeem do to determine the next year that each
comet will appear?
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06-NelsonMathGr6-Chap06 7/20/05 9:18 AM Page 171
C. Identify the next 10 multiples of 7 and the next 10 multiples of 9.
D. Determine a year when both comets will be visible.
Reflecting
1. How do you know that 7 must be a factor of each
multiple of 7?
2. Is it possible to list all of the multiples of 9? Explain.
Checking
3. In 2001, the periodic comets Helin and Mueller 4 were both
visible. Helin appears about every 14 years. Mueller 4
appears about every 9 years.
a) List the first 10 multiples of 14.
b) List the first 15 multiples of 9.
c) What is the the next year the two comets will be visible?
Practising
4. List five multiples of each number.
a) 2
b) 3
c) 12
d) 15
e) 25
f) 100
5. In Abigail’s school, a room has 30 lockers numbered from
1 to 30. There are running shoes in each locker with a number
that is a multiple of 5. There are rubber boots
in each locker with a number that is a multiple of 3.
a) Which lockers have running shoes?
b) Which lockers have rubber boots?
c) Which lockers have both running shoes and rubber boots?
6. Show why the second number is a multiple of the first number.
a) 2 240
b) 3 39
c) 4 100
d) 7 714
7. The Winter Olympics are usually held every 4 years. In 2002,
they were held in Salt Lake City, Utah, U.S.A.
a) When will the 10th Winter Olympics after 2002 be held?
b) Will there be Winter Olympics in the year 2062? Explain.
8. During the month of April, Greg dried dishes every third day
and cleaned up his room every fifth day. On what days did
he do both chores?
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