4-5 Equivalent Fractions
Learn to write equivalent fractions.
Course 1
4-5 Equivalent
Insert Lesson
Title Here
Fractions
Vocabulary
equivalent fractions
simplest form
Course 1
4-5 Equivalent Fractions
Fractions that represent the same value are
1 , __
2 , and __
4 are
equivalent fractions. So __
2
4
8
equivalent fractions.
1
2
Course 1
=
2
4
=
4
8
4-5 Equivalent Fractions
Additional Example 1: Finding Equivalent
Fractions
10
___
Find two equivalent fractions for 12 .
10
___
12
10
___
15
___
=
5
__
15
___
18
=
5
__
6
So 12 , 18 , and 6 are all equivalent fractions.
Course 1
4-5 Equivalent Fractions
Try This: Example 1
Find two equivalent fractions for
4
__
6
=
8
___
12
=
4
__
6
.
2
__
3
4 , ___
8 , and __
2 are all equivalent fractions.
So __
6
12
3
Course 1
4-5 Equivalent Fractions
Additional Example 2A: Multiplying and
Dividing to Find Equivalent Fractions
Find the missing number that makes the
fractions equivalent.
A.
3
__
5
=
___
20
3•4
______
12
= ____
5• 4
20
3
__
In the denominator, 5 is multiplied
by 4 to get 20.
Multiply the numerator, 3, by
the same number, 4.
12
___
So 5 is equivalent to 20 .
3
__
5
Course 1
=
12
___
20
4-5 Equivalent Fractions
Additional Example 2B: Multiplying and
Dividing to Find Equivalent Fractions
Find the missing number that makes the
fractions equivalent.
B.
4
__
5
=
80
___
4
• 20 ____
80
______
=
5 • 20 100
4
__
In the numerator, 4 is multiplied by
20 to get 80.
Multiply the denominator by
the same number, 20.
80
___
So 5 is equivalent to 100 .
4
__
5
Course 1
=
80
___
100
4-5 Equivalent Fractions
Every fraction has one equivalent fraction
that is called the simplest form of the
fraction. A fraction is in simplest form
when the GCF of the numerator and the
denominator is 1.
Example 3 shows two methods for writing
a fraction in simplest form.
Course 1
4-5 Equivalent Fractions
Additional Example 3A: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
20
___
A. 48
20
___
The GCF of 20 and 48 is 4, so 48 is not
in simplest form.
Method 1: Use the GCF.
20 4
_______
48
Course 1
4
=
5
__
12
Divide 20 and 48 by their GCF, 4.
4-5 Equivalent Fractions
Additional Example 3A: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
Method 2: Use a ladder diagram.
2 20/48
2
10/24
5/12
Use a ladder. Divide 20 and 48 by any
common factor (except 1) until you cannot
divide anymore
So
20
___
48
5
___
written in simplest form is 12 .
Helpful Hint
Method 2 is useful when you know that the numerator and
denominator have common factors, but you are not sure
what the GCF is.
Course 1
4-5 Equivalent Fractions
Additional Example 3B: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
B.
7
___
10
7 is already
The GCF of 7 and 10 is 1 so ___
10
in simplest form.
Course 1
4-5 Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
12
___
A. 16
12
___
The GCF of 12 and 16 is 4, so 16 is not
in simplest form.
Method 1: Use the GCF.
12 4
_______
16
Course 1
4
=
3
__
4
Divide 12 and 16 by their GCF, 4.
4-5 Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
Method 2: Use a ladder diagram.
2 12/16
2
6/8
3/4
12
___
Use a ladder. Divide 20 and 48 by any
common factor (except 1) until you cannot
divide anymore
3
___
So 16 written in simplest form is
.
4
Course 1
4-5 Equivalent
Insert Lesson
Fractions
Title Here
Lesson Quiz
Write two equivalent fractions for each
given fraction. Possible answers
8
2 , ___
___
4
1. ___
5
10
20
7
2. ___
14
1 , ___
14
___
2
28
Find the missing number that makes the
fractions equivalent.
2
3. __ =
7
___
21
6
4
20
4. __ = ___
15
75
Write each fraction in simplest form.
4
__
5. 8
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1
__
2
7
___
6. 49
1
___
7