1. No category

Page 1 of 7
Fractions with
Different Denominators
BEFORE
Now
WHY?
You added and subtracted with
common denominators.
You’ll add and subtract with
different denominators.
So you can find how much a plant
has grown, as in Ex. 23.
In the Real World
Word Watch
Review Words
least common denominator
(LCD), p. 239
Activities The circle graph
shows how Kate spent her
day. What fraction of her day
did she spend playing sports?
You add or subtract fractions
with different denominators
by finding the least common
denominator (LCD).
Adding and Subtracting Fractions
1. Find the LCD of the fractions.
2. Rewrite the fractions using the LCD.
3. Add or subtract the fractions. Simplify if possible.
EXAMPLE
with
Review
Need help with rewriting
fractions? See p. 239.
1
Adding Fractions
1
12
1
8
Kate spent of her day playing softball and of her day playing soccer.
1
8
1
12
To answer the real-world question above, find the sum .
13
83
12
12 2
3
24
2
24
5
24
Rewrite both fractions using the LCD, 24.
Add the fractions.
5
24
ANSWER Kate spent of her day playing sports.
Lesson 6.3
Fractions with Different Denominators
277
Page 2 of 7
EXAMPLE
with
Notetaking
In your summary of this
chapter, you may want to
include examples of adding
and subtracting fractions
with common and different
denominators.
2
Rewriting Sums of Fractions
5
8
3
4
Find the sum .
5
8
3 2
4 2
Your turn now
5
8
6
8
11
3
, or 1 8
8
Add the fractions.
Find the sum. Simplify if possible.
1
1
1. 3
9
EXAMPLE
3
4
Rewrite using the LCD, 8.
2
1
2. 3
2
3
7
5
4. 10
6
4
3
3. 5
4
Subtracting Fractions
2
4
Rainfall Last week, 3 inch of rain fell on Monday and 5 inch fell on
Tuesday. How much more rain fell on Tuesday than on Monday?
Solution
4
5
2
3
You need to find the difference .
4 3
5 3
25
35
12
15
10
15
2
15
Rewrite both fractions using the LCD, 15.
Subtract the fractions.
2
15
ANSWER On Tuesday, inch more rain fell than on Monday.
Your turn now
Find the difference. Simplify if possible.
5
3
5. 6
4
7
1
6. 8
4
1
4
7. 2
9
3
5
8. 10
6
2
3
9. One lap of Speedway A is mile. One lap of Speedway B is mile.
5
4
How much longer is one lap of Speedway B?
278
Chapter 6
Addition and Subtraction of Fractions
Page 3 of 7
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 713
Getting Ready to Practice
1. Vocabulary To add two fractions with different denominators, first find
the _?_ of the fractions.
Find the sum or difference. Simplify if possible.
3
1
2. 8
4
1
8
3. 6
9
9
1
5. 14
7
2
1
4. 3
2
1
6. Guided Problem Solving The monkey bars make up of an obstacle
4
5
1
course. The tires make up of the course. The tunnel makes up of
12
3
the course. How much shorter is the tunnel than the monkey bars and
tires combined?
1 How much of the course do the monkey bars and tires make up?
2 How much of the course does the tunnel make up?
3 How much shorter is the tunnel than the other two parts
combined?
Practice and Problem Solving
Find the sum or difference.
2
1
7. 9
3
with
Example
1
2
3
Homework
Exercises
7–22
7–22
7–24
Online Resources
9
1
8. 10
2
7
1
9. 10
3
5
2
10. 6
5
1
6
11. 2
7
7
2
12. 8
3
5
5
13. 12
6
13
1
14. 14
2
1
3
15. 6
4
3
5
16. 8
6
7
1
17. 10
8
3
1
18. 4
6
1
3
19. 15
5
1
11
20. 4
16
3
2
21. 4
7
6
1
22. 11
2
3
23. Plants Your peppermint plant is inch tall. After one week, it
10
1
is inch tall. How much did the plant grow in one week?
2
24. Find the Error Describe and
correct the error in the solution.
CLASSZONE.COM
• More Examples
• eTutorial Plus
Lesson 6.3
1
3
1
3
5
35
35
7
2
35
Fractions with Different Denominators
279
Page 4 of 7
1
3
3
4
Algebra Evaluate the expression when x and y .
1
25. x 2
5
26. y
6
11
27. y
12
3
28. x
8
2
29. x 9
1
30. y 18
31. x y
32. y x
Geometry Find the perimeter of the triangle.
33.
34.
43 in.
14 in.
35.
52 ft
87 in.
37 yd
25 ft
12 yd
72 yd
13 ft
Evaluate the expression.
1
1
1
36. 2
8
4
Geography
7
1
3
38. 10
6
5
1
1
1
37. 4
6
3
Extended Problem Solving In Exercises
39– 41, use the map.
The map shows the fraction of the
Appalachian Trail that is in each region.
Northeastern
Central
1
3
1
5
39. Calculate What fraction of the
trail is in the central and
northeastern regions combined?
40. Explain What fraction of the trail
is in the southern region? Explain
how you got your answer.
Southern
?
15
41. Compare Which two regions
N
together make up the longer
path, the northeastern and
central regions or the central
and southern regions?
■
Appalachian Trail
As of 2002, the length of
the Appalachian Trail was
set at 2168.8 miles. The
Appalachian Trail is about
how many times as long as
the distance across your
town?
42. Writing Write and solve a real-world
2
1
problem in which you would add and .
3
2
3
1
43. Critical Thinking Your friend finds the sum using the common
4
2
denominator 8. Will your friend get the correct answer? Explain.
Mental Math Evaluate the expression using mental math.
2
1
3
44. 3
3
7
280
Chapter 6
Addition and Subtraction of Fractions
5
5
4
45. 12
9
9
2
3
46. 1
5
5
Page 5 of 7
Challenge Use the information about
musical notes given at the right.
Eighth Note
47. What is the combined value of one
eighth note, one quarter note, and
one half note?
Quarter Note
48. What note do you need to add to
Half Note
the notes in Exercise 47 to equal
one whole note?
49. What note do you need to add to
Whole Note
three eighth notes and two quarter
notes to equal one whole note?
Mixed Review
Find the sum. (Lesson 6.2)
1
3
50. 8
8
3
3
51. 5
5
6
1
52. 7
7
Choose a Strategy Use a strategy from
the list to solve the following problem.
Explain your choice of strategy.
7
11
53. 12
12
Problem Solving Strategies
Guess, Check, and Revise
Make a List
■ Work Backward
■ Look for a Pattern
■
■
54. Of all the pairs of whole numbers
whose sum is 15, find the pair that
has the greatest product.
Basic Skills Order the numbers from least to greatest.
55. 540, 455, 504, 450, 545
56. 1020, 1211, 1002, 1202, 1200
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
57. Multiple Choice Two boards are nailed together. One board is
3
5
inch thick. The other board is inch thick. What is their
4
6
combined thickness in inches?
7
10
A. inch
4
5
B. inch
7
12
C. 1 inches
3
4
D. 1 inches
2
58. Short Response You put ounce of lemon juice in a measuring
3
7
cup. After you add some water, the cup measures ounce.
8
How much water did you add? Show how you found the answer.
Lesson 6.3
Fractions with Different Denominators
281
Page 6 of 7
6.1TO
6. 3
Notebook Review
Check Your Definitions
Review the
vocabulary
definitions in
your notebook.
Copy the review
examples in your
notebook. Then
complete the
exercises.
mixed number, p. 244
improper fraction, p. 244
round, p. 686
fraction , p. 228
least common
denominator (LCD),
p. 239
Use Your Vocabulary
1
1. Writing Explain how to round 3 to the nearest whole number.
2
3
1
2. Copy and complete: The LCD of and is _?_.
8
6
6.1 Can you estimate with fractions and mixed numbers?
EXAMPLE Estimate the sum or difference.
4
7
1
a. 5 12 ≈ 1 2
5
1
b. 4 6 1 4 ≈ 5 1
1
2
1 4
✓ Estimate the sum or difference.
9
2
3. 10
9
5
7
4. 12
8
1
5
5. 6 4 5
8
3
1
6. 3 2 4
6
6.2 Can you add and subtract fractions with common denominators?
EXAMPLE Find the sum or difference.
3
1
4
a. 10 10 10
11
5
6
b. 12 12 12
2
5
1
2
✓ Find the sum or difference.
2
4
7. 9
9
282
Chapter 6
3
3
8. 4
4
Addition and Subtraction of Fractions
4
2
9. 5
5
7
11
10. 16
16
Page 7 of 7
6.3 Can you add and subtract fractions with different denominators?
EXAMPLE Find the sum or difference.
a.
4
22
2
14
72
7
1
1
1
14
14
14
5
14
b.
3
33
5
53
1
15
3
35
9
15
5
15
4
15
✓ Find the sum or difference.
1
4
11. 10
5
5
1
12. 8
2
3
2
13. 4
7
8
5
14. 9
6
about Lessons 6.1–6.3
15. Estimation Do you get a closer estimate if you round a
mixed number to the nearest half or to the nearest whole
number? Explain.
16. Critical Thinking When you add or subtract fractions
with different denominators, do you have to use the LCD?
Explain.
Review Quiz 1
Estimate the sum or difference.
9
1
1. 10
6
2
4
2. 11
7
2
11
3. 7 4 15
16
5
7
4. 3 1 8
9
8
3
7. 13
13
2
11
8. 15
15
Find the sum or difference.
7
5
5. 8
8
5
4
9. 18
9
7
1
6. 10
10
2
3
10. 3
4
2
1
11. 11
2
13. Geometry Estimate the perimeter
of the figure at the right.
3
3
12. 10
4
35 yd
14 6 yd
5
12 4 yd
3
32 4 yd
1
Lessons 6.1–6.3
Notebook Review
283