Transcript Solve a Simpler Problem and Look for a Pattern

COURSE 2 LESSON 3-7
Solve a Simpler Problem and Look for a Pattern
When you simplify 823, what is the ones digit?
You know that 823 is a large number to calculate. You need to find out what
number is in the ones place.
It is not easy to simplify 823 with paper and pencil. You could simplify easier
expressions, like 82, 83, and 84, to see what number is in the ones place.
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COURSE 2 LESSON 3-7
Solve a Simpler Problem and Look for a Pattern
(continued)
Step 1: Solve a Simpler Problem
Find the values of the first 10 powers of 8.
Refer to the table at the right. Notice that
the ones digits in the value column repeat
in the pattern 8, 4, 2, 6.
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Power
81
82
83
84
85
86
87
88
89
810
Value
8
64
512
4,096
32,768
262,144
2,097,152
16,777,216
134,217,728
1,073,741,824
COURSE 2 LESSON 3-7
Solve a Simpler Problem and Look for a Pattern
(continued)
Step 2: Look for a Pattern
Organize the information to see whether
there is a connection between the ones
digits and the exponents. Refer to
the table at the right.
Ones Place
8
4
2
6
Exponent of 8
1, 5, 9
2, 6, 10
3, 7
4, 8
If the exponent is divisible by 4, then the ones digit is 6. Since 20 is divisible
by 4, you can start there:
Exponent:
Ones digit:
20
6
21
8
22
4
The number in the ones place of 823 is 2.
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23
2
COURSE 2 LESSON 3-7
Solve a Simpler Problem and Look for a Pattern
(continued)
Look for a pattern in another row of the exponent table that might also work.
When the exponent of 8 is 2, 6, or 10, the ones digit is 4. The numbers 2, 6,
and 10 are divisible by 2, but not by 4. Since 22 is divisible by 2 but not by 4,
the ones digit of 822 is 4.
Exponent:
Ones digit:
22
4
23
2
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COURSE 2 LESSON 3-7
Solve a Simpler Problem and Look for a Pattern
1. What is the eighth number in the pattern:
5, 25, 125, 625, 3,125, 15,625, . . .?
390,625
2. A jump-rope manufacturer has invited 128 teams to participate in a
rope-jumping contest. Teams are paired, and any team that loses
one match is eliminated from the contest. How many matches are
needed
to determine the winner?
127
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