Fractions, Number Lines, And Order Worksheet With Answers Page 3
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1
2
3
4
51
1
1
5
Further note that we could have compared all four of the fractions
,
,
, and
by changing
4
3
2
6
3
4
6
10
1
1
1
5
them all to the common denominator of twelfths. Since
, we have
.
12 12 12 12
4
3
2
6
By converting the fractional values to fractions with common denominators, we are able to easily
compare their relative sizes.
Notice that the least common denominator is the least common multiple (LCM) of 2, 3, 4, and 6. The
value of the LCM(2, 3, 4, 6) is 12 as illustrated below with the set intersection method for finding
the least common multiple.
Multiples of 2: {2, 4, 6, 8, 10, 12, 14 . . . }
Multiples of 3: {3, 6, 9, 12, 15, . . . }
Multiples of 4: {4, 8, 12, 16, . . . }
Multiples of 6: {6, 12, 18, 24, . . . }
Reminder: we can also find the least common multiple (LCM) by prime factorization into the
exponential form.
2 = 2
Taking the largest exponent of each prime factor we get
3 = 3
2
∙ 3 = 4 ∙ 3 = 12. So, LCM(2, 3, 4, 6) = 12.
2
4 = 2
2
6 = 2 ∙ 3
Finding the Median of a Set of Fractions
Five students brought identical sized pans of bars to sell in a bake sale. The bars were all cut to
be the same size. By the end of the sale, three-fourths of Cary’s bars, two-thirds of Dana’s bars, half
of Jamie’s bars, five-eighths of Lynn’s bars, and seven-eighths of Terry’s bars were sold. Whose pan
of bars was the median amount sold?
The median of a set of fractions can be found by using the same method that we used for a set
of whole numbers. Remember that the median is found by first ordering the set of values, and that a
good method for ordering fractional values is to rewrite them with a common denominator.
Solution: For the above problem, we first find the least common denominator by finding the
least common multiple for 4, 3, 2, 6, and 8. We find the LCM by the prime
factorization method.
2
4 = 2
Now we change each fraction to the
3 = 3
common denominator of 24.
2 = 2
3
2
1
5
7
6 = 2 ∙ 3
4
3
2
6
8
3
8 = 2
3
∙ 3 = 24.
LCM(4, 3, 2, 6, 8) = 2
18
16
12
20
21
24
24
24
24
24
MDEV 102
p. 86
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