ALGEBRA
Name
Lesson 6.10
Use Properties of Addition
Essential Question How can properties help you add fractions with
unlike denominators?
connect You can use properties of addition to help you add
fractions with unlike denominators.
Number and Operations—
Fractions—5.NF.A.1
MATHEMATICAL PRACTICES
MP2, MP7, MP8
Commutative Property: 1_2 + 3_ = 3_ + 1_
5
5
2
(2_9 + 1_8) + 3_8 = 2_9 + (1_8 + 3_8)
Associative Property:
Parentheses ( ) tell which
operation to do first.
Unlock
Unlock the
the Problem
Problem
Jane and her family are driving to Big Lagoon State
Park. On the first day, they travel 1_3 of the total
distance. On the second day, they travel
1_
3 of the total distance in the morning and then
_1
6
of the total distance in the afternoon. How much
of the total distance has Jane’s family driven by the
end of the second day?
Use the Associative Property.
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Day 1 + Day 2
(
) (
1
__
__
__
+ 1
+1
=
3 3 6
+
)+
Write the number sentence to represent the
problem. Use the Associative Property to group
fractions with like denominators together.
=
+
Use mental math to add the fractions with
like denominators.
=
+
Write equivalent fractions with like
denominators. Then add.
=
So, Jane’s family has driven _ of the total distance by
the end of the second day.
Math
Talk
MATHEMATICAL PRACTICES 8
Generalize Explain why
grouping the fractions
differently makes it easier to
find the sum.
Chapter 6
407
Example
(
)
__ + 12
__ + 11
__
Add. 25
8
3
8
Use the Commutative Property and the Associative Property.
(25__8 + 12__3) + 11__8 = (
+
(
Use the Commutative Property to
put fractions with like denominators
next to each other.
)+
Use the Associative Property to
group fractions with like
denominators together.
)
=
+
=
+
Use mental math to add the fractions
with like denominators.
=
+
Write equivalent fractions with
like denominators.
Then add.
=
=
+
Rename and simplify.
Try This! Use properties to solve. Show each step and name
the property used.
B
3 + 2_
(1_5 + __
10) 5
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5
A 51_ + (3_ + 1__
4
12)
4
408
Name
Share
hhow
Share and
and Show
Sh
MATH
M
BOARD
B
Use the properties and mental math to solve. Write your answer in
simplest form.
1. 25_ 1 5_ 1 11_
( 8 6)
8
5 1 __
5 1 3_
2. __
12
12 4
(
3. 31_4 1 25_ 1 13_4
6
)
(
Math
Talk
)
MATHEMATICAL PRACTICES 7
Identify Relationships
How is solving Exercise 3
different from solving
Exercise 1?
On
On Your
Your Own
Own
Use the properties and mental math to solve. Write your answer in
simplest form.
(7 3)
6. _1 1 3_7 1 2_7
6
(
5. _1 1 1_ 1 2_
5 1 41
_ 11
_
7. 2__
4
4
12
8. 11_ 1 51_ 1 23_
(
© Houghton Mifflin Harcourt Publishing Company
(5 2)
4. 2_ 1 1_ 1 2_
10.
3
)
8
(2
5
)
8
)
(9 5)
9. 5_ 1 _1 1 4_
9
DEEPER
Tina used 10 1_2 yards of yarn to make three yarn dolls.
yards of yarn for the first doll and 21_ yards for the
5
second doll. How much yarn did Tina use for the third doll?
She used 4 _12
Chapter 6 • Lesson 10 409
MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&
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Use the map to solve 11–12.
11.
DEEPER
Julie rides her bike from the sports
complex to the school. Then she rides from the school
to the mall, and then on to the library. Kyle rides his
bike from his house to the mall, and then to the library.
Who rides farther? How many miles farther?
Sports
Complex
School
2
3 mile
Park
Mall
2
3 mile
12.
13.
SMARTER
On one afternoon,
Mario walks from his house to the
library. That evening, Mario walks from
the library to the mall, and then to Kyle’s
house. Describe how you can use the
properties to find how far Mario walks.
Library
2
5 mile
4
5 mile
1 31 miles
Kyle’s
House
Mario’s
House
1 53 miles
4 Write an Expression Kyle is adding the distances between the school
and the mall, the mall and the park, and the mall and his house. He writes 2_ + 2_ + 4_ .
MATHEMATICAL
PRACTICE
5
3
5
Rewrite Kyle’s expression using properties so the fractions are easier to add.
SMARTER
For 14a–14c, tell whether the Commutative Property or the Associative
Property can be used to show each equation is true without calculating. Choose the
correct property of addition.
14a.
Associative Property
3
9
9 + ( __
3 ) + 5_
__
+ 5_ ) = ( __ + __
10
10
10
6
10
6
Commutative Property
Associative Property
3
14b. ( _4 + 1_ )+ 1_4 = ( 1_5 + 3_4 ) + 1_4
5
14c.
410
Commutative Property
( 31_ + 21_ ) + 15_ = 31_ + ( 21_ + 15_ )
2
8
8
2
8
8
Associative Property
Commutative Property
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14.
Practice and Homework
Name
Lesson 6.10
Use Properties of Addition
COMMON CORE STANDARD—5.NF.A.1
Use equivalent fractions as a strategy to add
and subtract fractions.
Use the properties and mental math to solve. Write your
answer in simplest form.
1. 21_ + 12_ + 32_
(3
)
5
(5
3
3
2. 81_ + 42_ + 3__
3. 23_ + 13_ + 57_
__
__
5. 31_ + 31_ + 51_
)
6. 11_ + 32_ + 53_
__
__
5
(5
)
(8
10
)
4
8
)
_ + 21
_ + 32
_
= 12
3
3
2
2
1
_
_
= 1 + 2_ + 3
3
5
3
2
= 1_ + 6
5
_
= 72
5
__
(
)
1
9
4. 2__
+ 12_ + 4__
10
(7
10
)
__
4
(4
5
4
(3
4
)
Problem
Problem Solving
Solving
7. Elizabeth rode her bike 6 1_2 miles from her house
to the library and then another 2 2_5 miles to her
friend Milo’s house. If Carson’s house is 2 1_2 miles
beyond Milo’s house, how far would she travel
from her house to Carson’s house?
© Houghton Mifflin Harcourt Publishing Company
______
9.
WRITE
8. Hassan made a vegetable salad with 2 3_8 pounds
of tomatoes, 1 1_4 pounds of asparagus, and
2 7_8 pounds of potatoes. How many pounds of
vegetables did he use altogether?
______
Math Write Commutative Property and Associative
Property at the top of the page. Underneath the name of each property,
write its definition and three examples of its use.
Chapter 6
411
Lesson Check (5.NF.A.1)
1. What is the sum of 2 1_3 , 3 5_6 , and 6 2_3 ?
2. Letitia has 7 1_6 yards of yellow ribbon, 5 1_4 yards of
orange ribbon, and 5 1_6 yards of brown ribbon.
How much ribbon does she have altogether?
Spiral Review (5.OA.A.1, 5.NBT.B.6, 5.NBT.B.7, 5.NF.A.1)
3. Juanita wrote 3 3 47 as 3 3 40 1 3 3 7. What
property did she use to rewrite the expression?
4. What is the value of the expression?
5. Evan spent $15.89 on 7 pounds of birdseed.
How much did the birdseed cost per pound?
6. Cade rode 1 3_5 miles on Saturday and 1 3_4 miles on
Sunday. How far did he ride on the two days?
FOR MORE PRACTICE
GO TO THE
412
Personal Math Trainer
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18 2 2 3 (4 1 3)