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&RPSDUHWZRIUDFWLRQVZLWKGLIIHUHQWQXPHUDWRUVDQGGLIIHUHQW
Readiness:
GHQRPLQDWRUVHJE\FUHDWLQJFRPPRQGHQRPLQDWRUVRUQXPHUDWRUVRUE\FRPSDULQJWR
NS 2.3
Solve simple problems, including ones arising in concrete
DEHQFKPDUNIUDFWLRQVXFKDV5HFRJQL]HWKDWFRPSDULVRQVDUHYDOLGRQO\ZKHQWKH
situations involving the addition and subtraction of fractions and
WZRIUDFWLRQVUHIHUWRWKHVDPHZKROH5HFRUGWKHUHVXOWVRIFRPSDULVRQVZLWKV\PEROV!
mixed numbers (like and unlike denominators of 20 or less), and
RUDQGMXVWLI\WKHFRQFOXVLRQVHJE\XVLQJDYLVXDOIUDFWLRQPRGHO
UNDERLYING SKILLS AND CONCEPTS:
understand numerator and
denominator;
use numbers less than 1;
write equivalent fractions
express answers in the simplest form.
Compare and Order Fractions
To compare fractions, rewrite them all with the same denominator.
Then, when they all have the same denominator, compare the
numerators.
• The greatest fraction is the one with the greatest numerator.
• The least fraction is the one with the least numerator.
E x am p l E s
1
7
3
7
4
7
5
7
The order of fractions from least to greatest is:
1 3 4 5
!, !, !, !.
7 7 7 7
Write these fractions in order from greatest to least:
3 1 1
!, !, !
4 4 2
Notice that the fractions have different denominators.
Recall how many fourths are in one half.
1 2
Another way to write !2 is !4 .
Notice that the circle is divided into 4 equal sections.
3 1 1
From greatest to least, they are: !4 , !2 , !4 .
more
3
4
1
4
1
2
3
4
1
4
1 #2
2
4
3
4
1# 2
2 4
1
4
less
1
1
Which is greater, !3 or !4 ? Rewrite both as equivalent fractions with same denominator:
4
1
4
!" ! #!
3
12
4
page 176
3
1
3
!" ! #!
4
12
3
4
3
!
!
12 $ 12
1
1
So, !3 $ !4
Chapter 15 – Lesson 4
E – © CSL Associates, Inc. All rights reserved.
Notice that each rectangle is divided into 7 sections, because the denominator is 7.
more
Write these fractions in order from least to greatest:
4 5 3 1
!, !, !, !
7 7 7 7
You can use a picture to help you order the fractions.
less
4
7
5
7
3
7
1
7
Name
P RAC T I C E
Compare the fractions. Use , , or . Explain your reasoning.
2
1. 3
3
2
< 4 because 3 Compare the fractions. Use , , or .
1
2
1
3
3. 2. 4 < 2
3 > 5
3
7. 4
3
3
8. 4
> 5
3
3
9
and 4 3
12
8
4
4
12
4
> 6
5
4. 7
< 4
6
9. 9
> 7
8
and 12
<
9
12
3
7
5. 9
> 3
2
5
6. 14
4
3
10. 10
< 3
1
3
11. 15
1
> 3
21
= 105
Write these fractions or mixed numbers in order from least to greatest.
1 3 2
12. 3 , 3, 3
1 2 3
, , 3 3 3
1 1 3 2
13. 1 5, 25, 15, 15
2 4 5 1 1
14. 6, 6, 6, 6, 2
1 2 1 4 5
, , , , 6 6 2 6 6
3
1 1 1 1 1
1
3
, 9 , 9 9 , 9 , 10 , 10 15. 10 ,
10
4
4 2 4 4 2
4
4
1 2 3 1
, 1, 1, 2
15
5 5 5
E – © CSL Associates, Inc. All rights reserved.
Answer each question.
1
2
1
16. Last week-end, Suzanne completed 3 , Vanessa 3 , and Lee 2 of their research
project. Which student completed the largest portion of their project?
1
2
1
is greater than or .
Vanessa; 3
2
3
1
1
1
17. 3 of the students at Lee Middle School play after-school sports. 5 play music and 4
of them belong to the art club. Which activity has the greatest number of students?
1
1
1
is greater than or .
Sports; 3
5
4
Math
Reasoning
Logical Thinking
MR 3.3
18. How can the following picture help you compare the following fractions without
rewriting them to all the same denominator:
1
,
2
1
,
3
1
,
4
1
,
5
1
,
6
1
,
7
1
,
8
I can see that 1 part out of 2 is bigger than 1 part out of 3,
which is bigger than 1 part out of 4, ....
Chapter 15 – Lesson 4
page 177
MCX94.HW.CL.G5.FM&Lesson.v211
8/2/04
18:03
Page 120
Name
…at home!
P RAC T I C E
Compare the fractions. Use , , or . Explain your reasoning.
2
1. 3
3
2
5
10
because 5
3
5
15
Compare the fractions. Use , , or .
1
2
1
3
2. 3. 3
2
3
8
3
7. 4
3
8. 4
3
6
5
6
3
3
9
and 5 3
15
10
and 15
9
15
5
4. 7
3
4
7
5. 8
2
3
3
6. 15
1
3
6
9. 8
4
7
7
10. 10
1
7
3
11. 12
1
4
Write these fractions or mixed numbers in order from least to greatest.
1 5 2 3 4
12. , , , , 5 5 5 5 5
2
14. ,
8
6
,
8
5
,
8
1
,
8
1
,
2
1 2 3 4 5
, , , , 5 5 5 5 5
1 1 5 5
13. 1 , 2 , 1 , 2 6 6 6 6
1 5 1 5
, 1, 2, 2
16
6 6 6
3 7 1 2 3 1 5 6 7
3 1 1 1
, , , , , , , 15. 8 , 8 , 7 , 7 8 8 8 8 8 2 8 8 8
4 4 2 4
1
1 1 3
, 7, 8, 8
74
2 4 4
1
2
1
16. Last week-end, Magda completed 2 , Julia 5 , and Heather 3 of their research
project. Which student completed the largest portion of their project?
1
1
2
is greater than or .
Magda; 2
5
3
1
1
1
17. of the students at Martin Middle School play after-school sports. play music and 4
6
5
of them belong to the art club. Which activity has the greatest number of students?
1
1
1
is greater than or .
Sports; 4
5
6
Math
Reasoning
Logical Thinking
MR 3.3
18. How can the following picture help you compare the following fractions without
rewriting them to all the same denominator:
2 2 2 2 2 2 2
, , , , , , ,
2 3 4 5 6 7 8
The picture helps us compare the amount of the same
whole circle that the fractions represent.
page 120
Home Resource and Homework
Chapter 15 Lesson 4
E – © CSL Associates, Inc. All rights reserved.
Answer each question.
MCX94TEG5CH01_32.v7.4.2 2/24/01 19:46 Page 327
Name
P RAC T I C E
Compare the fractions. Use , , or . Explain your reasoning.
2
1. 3
3
2
< 4 because 3 4
8
4
12
Compare the fractions. Use , , or .
1
2
1
3
2. < 3. > 4
2
3
5
3
7. 4
3
> 5
3
8. 4
4
> 6
3
3
9
and 4 3
12
5
4. 7
< 4
6
9. 9
> 7
8
and 12
<
9
12
3
7
5. 9
> 3
2
5
6. 14
4
3
10. 10
< 3
1
3
11. 15
1
> 3
21
= 105
Write these fractions or mixed numbers in order from least to greatest.
1 3 2
12. , , 3 3 3
2
14. ,
6
4
,
6
5
,
6
1 1
, 6 2
1 2 3
, , 3 3 3
1 1 3 2
13. 1 , 2 , 1 , 1 5 5 5 5
1 2 3 1
, 1, 1, 2
15
5 5 5
1 2 1 4 5
, , , , 6 6 2 6 6
3
1 1 1 1 1
1
3
15. 10 , 10 , 9 , 9 9 , 9 , 10 , 10 4
4 2 4 4 2
4
4
E – © CSL Associates, Inc. All rights reserved.
Answer each question.
1
2
1
16. Last week-end, Suzanne completed 3 , Vanessa 3 , and Lee 2 of their research
project. Which student completed the largest portion of their project?
1
2
1
is greater than or .
Vanessa; 3
2
3
1
1
1
17. of the students at Lee Middle School play after-school sports. play music and 3
5
4
of them belong to the art club. Which activity has the greatest number of students?
1
1
1
is greater than or .
Sports; 3
5
4
Math
Reasoning
Logical Thinking
MR 3.3
18. How can the following picture help you compare the following fractions without
rewriting them to all the same denominator:
1 1 1 1 1 1 1
, , , , , , ,
2 3 4 5 6 7 8
I can see that 1 part out of 2 is bigger than 1 part out of 3,
which is bigger than 1 part out of 4, ....
Chapter 15 – Lesson 4
Student Book Page
page 177
Name
…at home!
P RAC T I C E
Compare the fractions. Use , , or . Explain your reasoning.
2
1. 3
3
2
10
5
because 5
3
5
15
Compare the fractions. Use , , or .
1
2
1
3
2. 3. 3 2
3 8
3
7. 4
3
8. 4
3
6
5
6
3
3
9
and 5 3
15
10
and 15
9
15
5
4. 7
3
4
7
5. 8
2
3
3
6. 15
1
3
6
9. 8
4
7
7
10. 10
1
7
3
11. 12
1
4
Write these fractions or mixed numbers in order from least to greatest.
1 5
12. 5 , 5,
2
,
5
3 4
, 5 5
1 1 5 5
13. 1 6, 26, 16, 26
1 5 1 5
, 1, 2, 2
16
6 6 6
2 6 5 1 1 3 7 1 2 3 1 5 6 7
3 1 1 1
, , , , , , , , , , , 15. 8 , 8 , 7 , 7 14. ,
8 8 8 8 2 8 8 8 8 8 2 8 8 8
4 4 2 4
1
1 1 3
, 7, 8, 8
74
2 4 4
1 2 3 4 5
, , , , 5 5 5 5 5
1
2
1
16. Last week-end, Magda completed 2 , Julia 5 , and Heather 3 of their research
project. Which student completed the largest portion of their project?
1
1
2
is greater than or .
Magda; 2
5
3
1
1
1
17. 4 of the students at Martin Middle School play after-school sports. 6 play music and 5
of them belong to the art club. Which activity has the greatest number of students?
1
1
1
is greater than or .
Sports; 4
5
6
Math
Reasoning
Logical Thinking
MR 3.3
18. How can the following picture help you compare the following fractions without
rewriting them to all the same denominator:
2
,
2
2
,
3
2
,
4
2
,
5
2
,
6
2
,
7
2
,
8
The picture helps us compare the amount of the same
whole circle that the fractions represent.
page 120
Home Resource and Homework
Chapter 15 Lesson 4
E – © CSL Associates, Inc. All rights reserved.
Answer each question.