Download Adding and Subtracting Mixed Numbers

Page 1 of 5
Adding and Subtracting
Mixed Numbers
BEFORE
Now
WHY?
You added and subtracted
fractions.
You’ll add and subtract mixed
numbers.
So you can find the length of skis,
as in Ex. 36.
In the Real World
Word Watch
Review Words
simplest form, p. 229
mixed number, p. 244
Sports Korey is training to
compete in a race. What is
the total distance he will
run in the race?
Adding and subtracting
mixed numbers is similar
to adding and subtracting
fractions.
Adding and Subtracting Mixed Numbers
1. Rewrite the fractions using the LCD.
2. Add or subtract the fractions, then the whole numbers.
3. Simplify if possible.
EXAMPLE
1
Adding Mixed Numbers
1
1
To solve the real-world problem above, find the sum 2 4 .
3
3
1
3
1
4 3
2
6 3
2 Add the fractions. Then add the whole numbers.
2
3
ANSWER Korey will run 6 miles in the race.
Your turn now
Find the sum.
4
1
1. 1 3 9
9
284
Chapter 6
Addition and Subtraction of Fractions
3
5
2. 3 2 11
11
1
3
3. 2 2 5
5
1
3
4. 2 1 7
7
Page 2 of 5
EXAMPLE
2
Simplifying Mixed Number Sums
1
12
3
4
Find the sum 2 1 .
2 1
12
2 33
43
1 1 EXAMPLE
3
1
12
9
12
10
5
3 , or 3 12
6
3
4
Rewrite using the LCD, 12.
Add the fractions, then the
whole numbers. Simplify.
Solving Addition Problems
1
Sculpture The base of a sculpture is 1 2 feet tall. The sculpture is
2
3
2 feet tall. How tall is the sculpture with the base?
Solution
1
2
2
3
You need to find the sum 1 2 .
1 1 3
2 3
1 2 2
2 3 2
2 7
6
3
6
4
6
7
3 6
7
6
Rewrite both fractions using the LCD, 6.
Add the fractions, then the whole numbers.
1
6
1
6
Think of 3 as 3 , or 3 1 . To simplify, write the sum as 4 .
1
6
ANSWER The sculpture with the base is 4 feet tall.
Your turn now
4
1
5. 1 3 9
3
Find the sum. Simplify if possible.
3
1
6. 6 3 4
5
7
1
7. 4 5 8
4
9
3
8. 3 7 10
5
3
1
9. A clown is 5 feet tall while barefoot and 1 feet taller while
4
3
wearing stilts. How tall is the clown while wearing stilts?
1
10. You play two piano pieces at a recital. Each piece is 5 minutes long.
2
How long are the two piano pieces combined?
Lesson 6.4
Adding and Subtracting Mixed Numbers
285
Page 3 of 5
EXAMPLE
4
Subtracting Mixed Numbers
Volcanoes Before it erupted in 1980, the
height of the Mount St. Helens volcano
17
20
was about 1 miles. After the eruption,
3
5
the height was about 1 miles. What was
the decrease in the height?
Solution
17
20
3
5
You need to find the difference 1 1 .
17
20
12
1 20
5
1
, or 20
4
17
20
34
1 54
1 1
Mount St. Helens, after
the 1980 eruption
3
5
Rewrite using the LCD, 20.
Subtract the fractions, then the whole
numbers. Simplify.
1
4
ANSWER The decrease in the height was about mile.
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 713
Getting Ready to Practice
Vocabulary Write the mixed number in simplest form.
6
1. 2 8
4
2. 2 3
7
3. 3 4
15
4. 2 9
Find the sum or difference. Simplify if possible.
3
2
5. 2 1 7
7
3
1
9. 2 1 5
5
1
5
6. 6 3 10
6
7
1
10. 7 4 8
8
3
1
7. 2 3 4
2
1
5
11. 4 1 12
6
7
2
8. 5 1 9
9
3
1
12. 3 1 4
6
1
13. Frog Jumping In a jumping contest, your friend’s frog jumps 15 feet.
4
2
Your frog jumps 16 feet. How much farther does your frog jump?
3
286
Chapter 6
Addition and Subtraction of Fractions
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
14–21, 28–35
14–21, 28–35
14–21, 26, 28–36
22–25, 27–35
Online Resources
Find the sum or difference.
2
5
14. 5 4 9
9
1
1
15. 2 8 6
6
1
3
16. 9 3 12
4
7
1
17. 4 3 10
5
3
1
18. 8 3 5
2
2
3
19. 3 6 3
4
7
1
20. 2 7 8
4
7
1
21. 9 6 9
3
7
1
22. 10 4 8
8
11
1
23. 7 4 12
3
6
1
24. 8 5 7
2
5
1
25. 5 3 6
4
CLASSZONE.COM
• More Examples
• eTutorial Plus
26. Find the Error Describe and correct
2
5
the error in the solution.
4
5
6
5
7 1 8 27. Top Hats You use two top hats for a
1
8 3
5
magic show. One hat is 8 inches tall,
4
1
and the other is 7 inches tall. How much taller is the first hat?
8
Choose a Method Find the sum or difference. Then tell whether
you used mental math or paper and pencil to find the answer.
5
28. 2 4
8
1
3
29. 8 3 3
5
2
1
30. 7 5 3
2
5
31. 12 3
6
3
3
32. 7 4
4
7
7
33. 8 10
10
5
2
34. 4 7
7
8
1
35. 3 9
9
1
36. Skis A 6 foot tall ski jumper buys skis that are 2 feet longer than
4
his height. How long are the skis?
1
3
1
2
Algebra Evaluate the expression when x 2 and y 1 .
37. x 5
38. x 1
39. y 1
40. 7 y
1
41. 1 x
6
4
42. 3 x
5
3
43. 2 y
4
2
44. y 2 3
1
1
45. Currency In 1838, bank notes worth 6 cents and 12 cents were
4
2
1
issued in Pennsylvania. What was the combined value of two 6 -cent
4
1
notes and two 12 -cent notes?
2
46. Writing Write and solve a real-world problem in which you would
1
2
subtract 1 from 3 .
2
3
Lesson 6.4
Adding and Subtracting Mixed Numbers
287
Page 5 of 5
1
5
47. Critical Thinking Find the sum 3 2 using the method in
4
6
Science
Example 3. Then find the sum by first rewriting both mixed numbers as
improper fractions. Compare the methods.
Ocean Tides In Exercises 48 and 49, use the information below.
A scientist measures the levels of ocean tides from a cliff overlooking the
1
2
ocean. The high tide is 9 feet below the edge of the cliff. The low tide is
20 feet below the edge of the cliff.
48. Challenge Choose the equation you can use to find how much higher
the high tide is than the low tide.
1
1
A. x 9 2 20
B. 9 2 x 20
49. Solve the equation you chose in Exercise 48 using mental math.
■
Ocean Tides
The tidal range is the
difference in water level
between a high tide and a
low tide. In the Hawaiian
Islands, tides have a tidal
range of about 2 feet. How
much less is this tidal range
than the one you found in
Exercise 49?
Mixed Review
Copy and complete the statement with <, >, or . (Lesson 5.5)
5
2
50. _?_ 9
3
1
2
51. _?_ 4
7
6
1
52. _?_ 12
2
4
3
53. _?_ 15
10
9
1
56. 12
4
7
5
57. 8
6
Find the difference. (Lesson 6.3)
2
1
54. 3
2
3
4
55. 10
5
Basic Skills Round the number to the place value of the red digit.
58. 52,834
59. 185,079
60. 329,761
61. 8,905,794
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
3
62. Multiple Choice You add 17 pounds of sand to one sandbox and
4
7
8 pounds to another. How many pounds of sand do you use?
8
7
8
A. 8 pounds
1
8
B. 9 pounds
5
8
C. 25 pounds
5
8
D. 26 pounds
3
63. Multiple Choice A shoemaker has 1 yards of leather. After some
4
5
leather is used, 1 yards are left over. How many yards are used?
8
1
8
F. yard
288
Chapter 6
Addition and Subtraction of Fractions
3
8
G. yard
1
8
H. 1 yards
3
8
I. 3 yards