Lesson
13 Adding Three Fractions
Problem Solving:
Choosing the Best Graph
Adding Three Fractions
How do we use good number sense
with fractions?
Let’s review least common multiples. Look at the following set of
numbers. What do you think the colors represent?
3
6
5
9
12
10
6
15
18
15
12
21
24
20
18
27
25
24
30
30
30
33
36
35
36
The colors surrounding each number show multiples of 3 (blue), 5 (red),
and 6 (yellow). The number surrounded by all three colors is the least
common multiple of 3, 5, and 6.
It is important to have good number sense when we do any kind of
calculation. Look at the problem below. It does not make sense to use
paper and a pencil to subtract. We just count backward in our heads
and get 998.
1,000 − 2
Good number sense is also important when we work with fractions. The
problem requires that we add three fractions. Look at the denominators
carefully.
Unit 1 • Lesson 13 61
Lesson 13
How do we find the least common multiple for
three fractions?
To solve this problem, we need to find the least common multiple of
all three denominators.
1
5
2
4
We might think it easiest
to multiply all three
denominators together
to get a common
denominator. If we
multiply 5 · 4 · 10, we
get 200. The number
200 is a multiple of 5,
4, and 10. However,
200 is so large that the
fractions would be hard
to understand.
3
+ 10
If we think about least common multiples, we can use one of two
strategies to find a smaller common denominator.
Use a Number Line
Multiples of 5:
0
5
10
15
20
25
30
35
40
45
50
Multiples of 4:
0
4
8
12
16
20
24
28
32
50
60
70
35
28
70
40
32
80
36
40
44
48
52
Multiples of 10:
0
10
20
30
40
80
90
100
110
Count by Multiples
5s
4s
10s
5
4
10
10
8
20
15
12
30
20
16
40
25
20
50
30
24
60
45
36
90
50 55
40 44
100 110
In all three numbers, 20 is the first, or least, common multiple.
62 Unit 1 • Lesson 13
60
48
52
56
60
Lesson 13
Now that we know that 20 is the least common multiple of 5, 4, and 10,
we can solve the problem in two steps.
Add: 1
5
2
4
3
+ 10
Step 1
Find the common denominator.
4
1 4
5 · 4 = 20
2 5 10
4 · 5 = 20
3 2
6
10 · 2 = 20
Step 2
Solve the problem.
4
20
10
20
6
+ 20
20
20
The answer is 20
20 , or 1.
In this problem, the numerator and the denominator are the same. So
we know that this fraction equals 1.
Let’s see how this works with three other fractions.
Unit 1 • Lesson 13 63
Lesson 13
Example 1
Find the least common multiple to make common denominators.
Count on a number line, or count by multiples.
2
3
1
6
+3
4
Multiples of 3:
0
3
6
9
12 15 18 21 24 27 30 33 36 39 42 45 48
Multiples of 6:
0
6
12
18
24
30
36
42
48
Multiples of 4:
0
3s
6s
4s
4
3
6
4
8
6
12
8
12
9
18
12
16
18
20
24
28
32
36
8
12
1 2
2
6 · 2 = 12
2
12
3 3
9
4 · 3 = 12
9
+ 12
19
12
The answer is 11 9
2.
Apply Skills
Reinforce Understanding
Turn to Interactive Text,
page 36.
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 13
44
48
12 15 18 21 24 27 30 33 36 39 42 45 48
24 30 36 42 48
16 20 24 28 32 36 40 44 48 52 56 60
2 4
8
Solve the problem. 3 · 4 = 12
64 40
Lesson 13
Problem Solving: Choosing the Best Graph
Which graph displays our data in the best way?
Each graph below shows data in a different way. Study each graph to
see why one type is better than another for showing different sets of data.
Vertical Bar Graph
Decline in Newspaper Subscribers
160,000
Number of Subscribers
155,000
150,000
145,000
140,000
135,000
130,000
125,000
120,000
1995
1996
1997
1998
Years
1999
2000
2001
2002
Horizontal Bar Graph
Speed of Race Cars for One Lap
Bar graphs are good for
showing relationships
between numbers
over time.
Olsen Racing
Team 7
Formula 1
Harmon Brothers
0
25
50
75 100 125 150 175 200
Seconds
Unit 1 • Lesson 13 65
Lesson 13
Pictograph
Flour Sold
Tons of Flour Sold (in millions)
4
Pictographs are
good when we want
to communicate a
general idea.
FLOUR
3
FLOUR
FLOUR
2
FLOUR
FLOUR
FLOUR
FLOUR
1998
1999
FLOUR
FLOUR
FLOUR
FLOUR
FLOUR
2000
2001
2002
1
0
Year
Line Graph
Sunsets in Seattle and San Diego
9:36 PM
8:24 PM
Seattle
7:12 PM
Time of Day
Line graphs are good
for showing trends.
San Diego
6:00 PM
4:48 PM
3:36 PM
2:24 PM
1:12 PM
Ja
n.
Fe
b.
M
ar
.
Ap
r.
M
ay
Ju
ne
Ju
ly
Au
g.
Se
pt
.
Oc
t.
No
v.
De
c.
0:00 PM
Month
66 Problem-Solving Activity
Reinforce Understanding
Turn to Interactive Text,
page 37.
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 13
Lesson 13
Homework
Activity 1
Tell which fraction goes in the blank on each number line.
1.
1
3
Is the missing fraction 14 , 34 , or 12 ? 2.
2
3
?
1
4
1
2
1
2
Is the missing fraction 34 , 24 , or 13 ? 3.
?
3
4
1
2
?
Is the missing fraction 34 , 23 , or 14 ? 1
1
4
Activity 2
Add the fractions. Find the least common multiple to help you find a common
denominator.
1.
1
2
1
+ 15 + 10
1
1
5
2. 3 + 2 + 6
3.
1
4
+ 28 + 46
4.
1
6
+ 19 + 23
1
2
1
3
1
4
1
6
5 1 2 1
10 5 10 10
2 1 3 5 5
6 2 6 6 6
6 2 6 4
24 8 24 6
3 1 2 2
18 9 18 3
1
10
2
6
16
24
12
18
5
2
1
10 10 10
3 5 10
6 6 6
6
6 16
24 24 24
3
2 12
18 18 18
8
10
28
24
17
18
Activity 3
Solve.
1.
1
2
− 15
3.
7
8
+ 14
1
4
5. 6 + 9
5
10
3
18
2
10
8
18
3
10
11
18
7
8
2
8
9
8
3
1
2
5
− 13
5
1
3
6
2. 6 + 2
4.
3
6
10
12
6. 6 − 4
6
6
3
12
7
12
6
15
5
15
1
15
Activity 4 • Distributed Practice
Solve.
1.
5,795
+ 5,045
10,840
2.
7,901
 1,097
6,804
3.
70
40
2,800
4.
700
8
5. 8q728
5,600
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Unit 1 • Lesson 13 67