Comparing and Ordering Fractions › 4... · Comparing Fractions Examples: Graph and compare each...
Transcript of Comparing and Ordering Fractions › 4... · Comparing Fractions Examples: Graph and compare each...
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Comparing and Ordering Fractions
Lesson 5-1
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Least Common Multiple
a multiple of a number is the product of that number and any nonzero whole number.
LCM is the smallest multiple that they share (or have in common).
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How to find the LCM
list the multiples of both numbers in ascending order until one multiple appears in both lists.
for larger numbers it’s faster to find the prime factors of each number. The LCM consists of all the factors that appear in either number raised to the greatest power that appears in any one of the numbers.
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Find the LCM by listing multiples
Examples:
Multiples of 2:
Multiples of 4:
The number 4 is the least common multiple (LCM).
Multiples of 5:
Multiples of 6:
The number 30 is the least common multiple (LCM).
2, 4, 6, 8, …
4, 8, …
2, 4, 6, 8, …
4, 8, …
5, 10, 15, 20, 25, 30, 35, …
6, 12, 18, 24, 30, …
5, 10, 15, 20, 25, 30, 35, …
6, 12, 18, 24, 30, …
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Try This
Find the LCM by listing multiples
3, 4 3: 3, 6, 9, 12, 15, …
4: 4, 8, 12, …
3: 3, 6, 9, 12, 15, …
4: 4, 8, 12, …
3, 4, 8 3: 3, 6, 9, 12, 15, 18, 21, 24, …
4: 4, 8, 12, 16, 20, 24, …
8: 8, 16, 24, …
3: 3, 6, 9, 12, 15, 18, 21, 24, …
4: 4, 8, 12, 16, 20, 24, …
8: 8, 16, 24, …
LCM is 12
LCM is 24
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Find the LCM by using Prime Factorization
Examples:
To find LCM use the greatest power of each factor and
multiply.
40
12
52
32
3
2
1205323
LCM is 120
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Find the LCM by using Prime Factorization
4216
326
6, 16
48324LCM
9, 15
5315
39 2
45532LCM
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Try More
Find the LCM by using Prime Factorization
2
2
3218
5315
3212
12, 15, 18 ,6 2a
180532 22LCM
318a
323
22
3218
326
aa
aa
332 1832 aaLCM
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Comparing Fractions
Examples: Graph and compare each pair of fractions.
is to the right of
0 1
,11
9
11
6
11
9
11
6
11
9,
11
6so >
11
9
11
6
is to the left of
-1 0
,2
1
10
1
10
1
2
1
2
1,
10
1so <
2
1
10
1
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Try This
Examples: Graph and compare each pair of fractions.
0 1
,9
4
9
2
9
4
9
2
9
4
9
2>
,9
4
9
4<
-1 09
4
9
29
2
9
2
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rewrite the fractions with a common denominator
then compare the numerators
the least common denominator (LCD) of two or more fractions is the LCM of the denominators.
Comparing Fractions with different denominators
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Comparing Fractions with different denominators
,8
5Example:
10
7
Step 1: Find the LCM of 8 and 10328 5210
LCM = 40523
Step 2: Write equivalent fractions with a
denominator of 40.
,40
25
5
5
8
5
40
28
4
4
10
7
Step 3: Compare the fractions
40
25< ,
40
28so
8
5<
10
7
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Try this
Compare each pair of fractions.
,7
6
5
4 717 515LCM = 3557
,35
30
5
5
7
6
35
28
7
7
5
4
LCM = 12322
,12
8
4
4
3
2
12
9
3
3
4
3
,3
2
4
3 313 224
7
6
5
4>
<
3
2
4
3