Download Adding and Subtracting Mixed Numbers

Page 1 of 4
Adding and Subtracting
Mixed Numbers
BEFORE
Now
WHY?
You added and subtracted
fractions.
You’ll add and subtract mixed
numbers.
So you can find how much a baby
has grown, as in Ex. 24.
In the Real World
Word Watch
Review Words
least common denominator
(LCD), p. 181
mixed number, p. 185
improper fraction, p. 185
World Series In the playoffs leading up
to the 2001 World Series, Curt Schilling
1
3
pitched 48 innings and his teammate
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3
Randy Johnson pitched 41 innings.
What is the total number of innings
they pitched?
To find the total number of innings,
you will need to add two mixed
numbers, using the rules below.
Adding and Subtracting Mixed Numbers
1. Find the LCD of the fractions, if necessary.
2. Rename the fractions, if necessary. Then add or
subtract the fractions.
3. Add or subtract the whole numbers.
4. Simplify if possible.
EXAMPLE
1
Adding with a Common Denominator
1
3
1
3
To solve the problem above, you need to find the sum of 48 and 41 .
Add the whole
numbers.
1
3
1
41 3
2
89 3
48 Add the
fractions.
2
3
ANSWER Schilling and Johnson pitched a total of 89 innings.
Lesson 5.2
Adding and Subtracting Mixed Numbers
211
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EXAMPLE
7
9
2
1
9
Subtracting with a Common Denominator
6
9
Subtract fractions and whole numbers.
2
3
Simplify.
6 4 2 2 Your turn now
Add or subtract. Simplify if possible.
1
5
1. 3 2 8
8
EXAMPLE
with
Solving
In Example 3, you can
estimate the answer by
rounding each mixed
number to the nearest
whole number. By doing
so, you have 5 4 9,
so the answer is
reasonable.
5
6
1
2
2. 7 1 5
5
3
3
4
5
1
3. 8 4 7
7
5
5
4. 12 9 6
6
Adding with Different Denominators
9
12
10
12
4 3 4 3 19
12
7 5
6
3
4
Rewrite fractions using LCD of and .
Add fractions and whole numbers.
7
12
7 1 7
12
8 Write improper fraction as a mixed number.
Add whole numbers.
Renaming When subtracting mixed numbers, you may have to rename the
first mixed number so that you can subtract the fractional parts.
EXAMPLE
1
6
4
2
3
Renaming to Subtract Mixed Numbers
1
6
4
6
Rewrite fractions using LCD of and .
7
6
4
6
Rename 6 as 5 .
6 3 6 3 5 3 212
Chapter 5
Fraction Operations
7
6
Subtract fractions and whole numbers.
1
2
Simplify.
2 1
1
5. 7 3 4
2
1
6
2
3
3
6
2 Your turn now
1
6
Add or subtract. Simplify if possible.
3
3
6. 1 4 4
8
1
7. 8 5 8
1
3
8. 8 6 6
4
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 709
Getting Ready to Practice
1. Vocabulary When is it necessary to rename a mixed number when
subtracting?
Find the sum or difference. Then estimate to check the answer.
4
2
2. 8 5 9
9
3
1
3. 7 3 5
5
2
4
4. 22 17 7
7
7
5
5. 8 4 12
12
1
4
6. 8 5 3
9
3
2
7. 4 6 4
3
1
5
8. 5 2 4
6
3
1
9. 7 3 10
5
1
10. Running At track practice, you run 5 miles and cool down by walking
2
1
1 miles. What is your total distance?
3
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
12–23
12–23
12–23
12–24
Online Resources
3
1
11. Writing Describe what steps you would take to find 2 1 .
4
4
Find the sum or difference. Then estimate to check the answer.
2
1
12. 3 2 3
3
3
1
13. 12 5 5
5
4
5
14. 6 5 7
7
3
5
15. 2 5 8
8
6
4
16. 8 2 7
7
5
1
17. 13 9 6
6
1
3
18. 4 3 4
8
5
1
19. 7 3 6
9
3
1
20. 12 9 4
6
2
1
21. 6 11 5
6
1
3
22. 5 3 4
4
1
4
23. 9 7 3
9
CLASSZONE.COM
• More Examples
• eTutorial Plus
1
24. Child Development Anastasia was 19 inches long at birth. At her
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1
3 month checkup, she measures 23 inches. How much has she grown?
2
1
4
25. Mental Math Explain how you can use mental math to find 4 7 .
5
5
2
5
1
3
3
7
Algebra Evaluate the expression when x 7 , y 5 , and z 3 .
26. y x
27. y z
28. x y z
29. z y x
30. Critical Thinking Can you subtract two fractions with common
denominators and get an answer with a different denominator?
Explain your reasoning and provide an example.
Lesson 5.2
Adding and Subtracting Mixed Numbers
213
Page 4 of 4
4
5
31. Cars Can two cars that measure 14 feet and 15 feet fit in a parking
5
6
1
space that is 31 feet long? Use estimation to answer the question.
2
Coins In Exercises 32 and 33, use the table below.
Coin
Mass (grams)
Dime
1
2
2 Penny
1
8
3 Nickel
Quarter
5
6 Half-dollar
1
4
1
2
12 32. What is the difference in mass between a half-dollar and two dimes?
33. What is the sum of the masses of a penny, a dime, and a quarter?
34. Challenge Find the missing side length if the
1
7
1 3 in.
perimeter of the figure is 9 inches.
15
?
1 5 in.
3
3 5 in.
1
Mixed Review
35. Find the area of a rectangle that has a length of 6.2 feet and a width
of 5.3 feet. (Lesson 2.3)
Find the sum or difference. (Lesson 5.1)
7
3
36. 8
8
4
9
37. 11
11
3
1
38. 8
2
11
3
39. 12
8
Basic Skills Find the product or quotient.
40. 326 p 12
41. 53 p 487
42. 225 5
43. 392 28
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
1
5
44. Multiple Choice Find the difference 8 3 .
4
6
1
5
1
B. 4 C. 4 A. 4 12
12
4
7
12
D. 5 45. Multiple Choice At the beginning of a trip, a boat’s gasoline tank
1
contained 14 gallons of gasoline. At the end of the trip, it contained
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2
8 gallons. How many gallons of gasoline did the boat use?
3
8
7
1
13
F. 5 G. 6 H. 6 I. 22 15
15
4
15
214
Chapter 5
Fraction Operations