Download Adding and Subtracting Fractions with Like Denominators

Name
Adding and Subtracting Fractions
with Like Denominators
R 4-1
How to find sums or differences of fractions with like denominators:
Find 2 6 .
14
14
The fractions have like denominators,
so you can just add the numerators.
2
6
8
14
14
14
Write the sum over the common
denominator.
4
8
7
14
Simplify if possible.
Find 5 2 .
7
7
The denominators are the same, so
you can subtract the numerators.
2
3
5
7
7
7
3 cannot be simplified, so
7
2
3
5
7
7
7
Find each sum or difference. Simplify your answer.
1.
1
6
36 2.
9
1
1
14
1 3.
6
7
27 4.
3
1
2
18
2 5.
8
9
59 6.
1
1
0
18
0 7.
4
1
5
8.
16
20
29
0 1115 © Pearson Education, Inc. 6
9. Number Sense Give an example of two fractions whose sum
can be simplified to 12.
10. A quarter has a diameter of 1156 in. A dime has a diameter of
11
13
in., and a nickel has a diameter of in. If you put each coin
16
16
side by side, what is the combined width of the three coins?
Use with Lesson 4-1.
45
Name
Adding and Subtracting Fractions
with Unlike Denominators
R 4-2
If you are adding or subtracting fractions and the denominators are
not the same, the first thing to do is find a common denominator. The
best common denominator to use is the least common multiple of
the two denominators.
Step 1:
Use the LCM to find
a common
denominator.
2
1
.
6
2
The LCM of 2 and 6 is 6.
The least common
denominator (LCD) is 6.
Find
3
1
.
4
3
The LCD of 3 and 4 is 12.
Find
Step 2:
Write equivalent
fractions.
2
2
6
6
1
3
2
6
3
9
4
12
1
4
3
12
Step 3:
Add or subtract.
Simplify if possible.
2
2
6
6
1
3
2
6
5
6
9
3
12
4
1
4
3
12
5
12
Find each sum or difference. Simplify your answer.
3
4
52 2.
11
12
3.
4
1
5
5.
2
3
13 45 4.
5
6
49 17
0 6.
2
5
23 36
0 7. Number Sense The least common denominator for the sum
5
3
8 1
2 is 24. Name another common denominator that you
could use.
8. A recipe calls for 12 cup of milk and 13 cup of water. What is the
total amount of liquid in the recipe?
46
Use with Lesson 4-2.
© Pearson Education, Inc. 6
1.
Name
PROBLEM-SOLVING STRATEGY
R 4-3
Look for a Pattern
Sometimes you can solve a problem by identifying a pattern. Here
are some different types of patterns.
Patterns in sets of numbers
1, 3, 6, 10, 15, 21
Ask yourself: Are the numbers
increasing? Are they decreasing?
Do they change by the same
amount each time?
Patterns in groups of figures
Ask yourself: How is the first
figure modified to make the
second? How is the second
modified to make the third?
Patterns in everyday life
Chris tells three friends a secret.
Each friend tells three more
people, and so on.
Ask yourself: What is happening
at each stage of the activity?
How can I use numbers to help
me understand the pattern?
Name the missing numbers or draw the next three figures. Describe each pattern.
1. 89, 78, 67,
,
,
© Pearson Education, Inc. 6
2.
3.
a
1
2
b
1
4
3
4
5
16
25
6
4. Number Sense Certain cells can reproduce
in only 12 hr. Starting with 1 cell, how many would
there be at the end of 4 hr?
Use with Lesson 4-3.
47
Name
Estimating Sums and Differences
of Fractions and Mixed Numbers
R 4-4
You can use rounding to estimate sums and differences of fractions
and mixed numbers.
How to round fractions:
If the fractional part is greater than or equal to 12, round up to the next
whole number.
Example: Round 3 57 to the nearest whole number.
5
7
is greater than 12, so 3 57 rounds up to 4.
If the fractional part is less than 12, drop the fraction and use the
whole number you already have.
Example: Round 6 13 to the nearest whole number.
1
3
is less than 12, so drop 13 and round down to 6.
How to estimate sums and differences of fractions and mixed
numbers:
Round both numbers to the nearest whole number. Then add or
subtract.
Example: Estimate 4 18 7 23.
4 18 rounds down to 4.
7 23 rounds up to 8.
4 8 12
So, 4 18 7 23 is about 12.
1. 8 67
2. 14 29
3. 42 47
51
4. 6 10
0
5. 29 45
6. 88 24
7. 19 43
4
8. 63 441
9
Estimate each sum or difference.
9. 7 25 8 19
10. 13 58 2 17
0
11. 2 14 5 12 10 34
12. 11 35 4 11
2
13. 8 4 1114 5 19
14. 15 67 12 12
0
48
Use with Lesson 4-4.
© Pearson Education, Inc. 6
Round to the nearest whole number.
Name
Adding Mixed Numbers
R 4-5
To add mixed numbers, you can add the fractional parts to the whole
number parts, and then simplify.
2
1
3 .
4
4
The fractions have a
common denominator.
Add the fractions. Then
add the whole numbers.
Find 2
2
2
4
1
3
4
3
5
4
2
1
4 .
3
9
Write equivalent fractions
with the LCD.
Find 3
2
6
3
3
9
1
1
4
4
9
9
3
Add the whole numbers.
Add the fractions.
Simplify if possible.
3
Find 4 3 .
5
Add the whole numbers;
then add the fraction.
4
3
5
3
7
5
3
6
9
1
4
9
7
7
9
3
Find each sum. Simplify your answer.
1. 2 15 2 35 2. 4 23 1 16 3. 5 35 13
0 4. 8 58 1 15
2 5. 6 14 11 38 6. 7 8 13 © Pearson Education, Inc. 6
7. In 2001, the men’s indoor pole vault record was 20 16 ft.
The women’s record for the indoor pole vault was 15 15
2 ft.
What is the combined height of the two records?
8. Writing in Math How high is a stack of library books if one book
is 138 in. high, the second book is 1 56 in. high, and the third is
2 13 in. high? Explain how you solved this problem.
Use with Lesson 4-5.
49
Name
Subtracting Mixed Numbers
R 4-6
To subtract mixed numbers, the fractional parts must have the same denominator.
Step 1
Find 9
1
5
4 .
12
8
Step 2
Estimate.
945
Write equivalent
fractions for the LCD.
1
2
9
12
24
5
15
4
4
8
24
9
2
Find 10 4 .
5
There is no fraction
from which to
2
subtract .
5
Step 3
Before you can subtract,
2
rename 9
to show
24
more twenty-fourths.
Subtract and
simplify if
possible.
2
24
2
26
8
8
9
24
24 24
24
15
15
4
4
24
24
Rename 10 to show fifths.
10 9 26
24
15
4
24
11
4
24
8
Subtract.
Simplify if
possible.
5
5
9
5
5
5
5
2
4
5
3
5
5
9
3
1. 5 19
0 2 5 3
2. 11 17
6 8 8 3. 9 23 9 16 4. 4 23 2 5. 4 14 17
2 6. 5 67 2 1134 7. Number Sense How do you know if you need to rename the
first number in a subtraction problem involving mixed numbers?
50
Use with Lesson 4-6.
© Pearson Education, Inc. 6
Find each difference. Simplify if possible.
Name
Choose a Computation Method
R 4-7
Depending on the type of problem, you can use different methods to
find the solution. Your goal should be to use the most accurate and
efficient method. The different choices are:
Mental Math Think: Are the numbers easy to work with? If there are
fractions, is there already a common denominator? Will an estimate
solve the problem?
Example: Find 4 15 2 25.
Paper and Pencil Think: Can I easily convert the fractions to a
common denominator? Are the calculations fairly straightforward?
Example: Find 6 14 2 12.
Calculator Think: Are there many steps needed to find the solution?
Would using pencil and paper take too long? Would the numbers be
too cumbersome?
1
3
2
Example: Find 3 12
2 4 3 9 4 7 6.
Find each sum or difference. Tell which computation method
you used.
1. 8 45 1 25 2.
11
16
4 135
2 3. 14 12 59 23 4. 3 19
6 2
5. 7 13 7 18
4 © Pearson Education, Inc. 6
6. 2 19 2 19 7. A dog had three puppies. One puppy weighed 2 18 lb, one
weighed 2 34 lb, and the third weighed 3 lb. What is the combined
weight of the puppies? What method did you use?
8. Writing in Math Why would it be faster to use mental math
2
rather than a calculator to find 4 11
4 2 7? Explain.
Use with Lesson 4-7.
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