Multi-Part Lesson
6-1
Fractions
PART
Main Idea
I will write a fraction in
simplest form.
Review Vocabulary
factor
A
C
B
Simplest Form
Among the equivalent fractions _ , _ , and _ , the fraction _ is
3 6
3
12
in simplest form because its numerator and denominator have
no common factor other than 1.
Fractions in
Simplest Form
simplest form
1
_
2
macmillanmh.com
8
2 4
New Vocabulary
greatest common
factor
D
2
_
3
_
3
Fractions NOT in
Simplest Form
3
_
4
2
5
_
7
2
_
4
_
4
8
8
_
6
8
_
10
16
_
24
12
To change a fraction into its simplest form, you can divide both
the numerator and the denominator by the greatest common
factor. A greatest common factor is the greatest of the
common factors of two or more numbers.
Simplest Form
QUIZ There are 12 questions on a quiz.
8
Esteban got 8 out of 12 or
of the
12
questions correct. Two fractions
8
4
2
equivalent to
are and .
3
6
12
8
Write
in simplest form.
_
_
_
_
Factors of 8:
1, 2, 4, 8
Factors of 12:
1, 2, 3, 4, 6, C
12
Blue
9.
10.
4.
5.
13-
11.
12.
085
int (
A-1
057
11.a
hano
The numbers 2 and 3 have
ndw
r
common factor other than 1.
8
2
_
So,
in simplest form is _ .
3
12
286
8.
3.
Divide by the greatest common
prfactor, 4.
8 ÷4
2
_
=_
3
12 ÷ 4
7.
2.
6.
Find the common factors of
8 and 12.
Common factors: 1, 2 and 4
Step 2
1.
_
12
Step 1
Name:
i
b
itten e
)
Chapter 6 Relate Decimals and Fractions
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7/20/09 1:24:05 AM
To write a fraction in simplest form, you can also divide by
common factors.
ANIMALS Koala bears sleep
up to 18 hours each day. What
part of a day do koalas sleep?
Write the fraction in simplest
form.
Step 1
Write a fraction.
18
_
24
Step 2
Divide by common factors.
18 ÷ 2
18
9
_
=_=_
A common factor of
18 and 24 is 2.
9 ÷ 3
9
3
_
=_=_
A common factor of
9 and 12 is 3.
24
Divide until the
numerator and the
denominator have no
common factor other
hours sleep each day
total hours in a day
24 ÷ 2
12
4
12 ÷ 3
18
3
3
So, _ simplifies to _. Koalas sleep up to _ of a day.
4
4
24
12
than 1.
Simplest Form
One Way
Divide the numerator and denominator by
the greatest common factor.
Another Way
Divide the numerator and denominator by
common factors until the only common
factor is 1.
Write each fraction in simplest form. If it is in simplest form,
write simplest form. See Example 1 (p. 286)
6 3
5
2 1
1. _
2. _
3. _ simplest form
4 2
6
10 5
_
_
5. Daniela read for 24 minutes. What
fraction of an hour did she read?
Write as a fraction in simplest form.
See Example 2 (p. 287) 2
5
_
6.
_
18 3
4. _
30 5
How do you
4
know that _ is in simplest form?
5
Lesson 6-1 Fractions 287
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EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
See page R17.
Write each fraction in simplest form. If it is in simplest form,
write simplest form. See Example 1 (p. 286)
3 1
6 2
2 1
7
7. _
8. _
9. _
10. _
20
10 5
12 4
9 3
_
10 2
12. _ _
_
18 2
13. _ _
27 3
15 3
_
32 16
15. _ _
_
24 3
14. _
40 5
11.
16.
42 21
_1
3
42 _
_
56
4
_
16 4
4
Measurement What part of one day is each amount of time?
Write as a fraction in simplest form. See Example 2 (p. 287)
3
2
17. 9 hours
18. 16 hours
8
3
_
_
19. 20 hours
_5
Algebra Find the value of x to simplify each fraction.
16
4
21. _ = _
x
28
15
x
20. _ = _ 1
45
3
20
x
22. _ = _
36
9
Write as a fraction in simplest form.
23. Six of the 16 marbles in a bag are
yellow. What fraction of the marbles
3
is yellow?
8
24. Adina read 12 out of 36 pages in a
comic book. What fraction of the pages
1
did she read?
3
_
_
Measurement The table lists the length of
some objects in a classroom. What part of
a foot is each object? Write as a fraction in
simplest form. See Example 2 (p. 287)
1
1
25. pencil
ft
26. crayon
ft
4
2
3
2
27. scissors
ft
28. pencil box
ft
4
3
_
_
_
_
29. OPEN ENDED Write three fractions that are in simplest form.
30. WHICH ONE DOESN’T BELONG? Identify the fraction that does
not belong with the other three. Explain your reasoning.
_2
3
31.
288
_6
_1
2
15
_
11
12
The simplest form of _ is _ . How can you
5
15
use multiplication to show that they name the same number?
6
2
Chapter 6 Relate Decimals and Fractions
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