Transcript Slide 1

4-5 Equivalent Fractions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-5 Equivalent Fractions
Warm Up
List the factors of each number.
1. 8
1, 2, 4, 8
2. 10
1, 2, 5, 10
3. 16
1, 2, 4, 8, 16
4. 20
1, 2, 4, 5, 10, 20
5. 30
1, 2, 3, 5, 6, 10, 15, 30
4-5 Equivalent Fractions
Problem of the Day
John has 3 coins, 2 of which are the
same. Ellen has 1 fewer coin than John,
and Anna has 2 more coins than John.
Each girl has only 1 kind of coin. Who
has coins that could equal the value of a
half dollar?
Ellen and Anna
4-5 Equivalent Fractions
Learn to write equivalent fractions.
4-5 Equivalent Fractions
Vocabulary
equivalent fractions
simplest form
4-5 Equivalent Fractions
Fractions that represent the same value are
equivalent fractions. So
are
equivalent fractions.
1
2
=
2
4
=
4
8
4-5 Equivalent Fractions
Additional Example 1: Finding Equivalent
Fractions
Find two equivalent fractions for
10
___
12
=
15
___
18
=
10
___
.
12
5
__
6
The same area is shaded when the rectangle is divided
into 12 parts, 18 parts, and 6 parts.
10
___
15
___
5
__
So 12 , 18 , and 6 are all equivalent fractions.
4-5 Equivalent Fractions
Check It Out: Example 1
Find two equivalent fractions for
4
__
6
=
8
___
12
=
4
__
6
.
2
__
3
The same area is shaded when the rectangle is divided
into 6 parts, 12 parts, and 3 parts.
4 , ___
8 , and __
2 are all equivalent fractions.
So __
6
12
3
4-5 Equivalent Fractions
Additional Example 2A: Multiplying and
Dividing to Find Equivalent Fractions
Find the missing number that makes the
fractions equivalent.
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
=
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.
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
=
80
___
100
4-5 Equivalent Fractions
Check It Out: Example 2A
Find the missing number that makes the
fraction equivalent.
3
__
9
=
___
27
3•3
______
9
= ____
9• 3
27
3
__
In the denominator, 9 is multiplied by
3 to get 27.
Multiply the numerator, 3, by
the same number, 3.
9
___
So 9 is equivalent to 27 .
3
__
9
=
9
___
27
4-5 Equivalent Fractions
Check It Out: Example 2B
Find the missing number that makes the
fraction equivalent.
2
__
4
=
40
___
2
• 20 ____
40
______
=
4 • 20
80
2
__
In the numerator, 2 is multiplied by
20 to get 40.
Multiply the denominator by
the same number, 20.
40
___
So 4 is equivalent to 80 .
2
__
4
=
40
___
80
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.
4-5 Equivalent Fractions
Additional Example 3A: Writing Fractions in
Simplest Form
Write each fraction in simplest form.
20
___
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 ÷ 4
=
5
__
12
Divide 20 and 48 by their GCF, 4.
4-5 Equivalent Fractions
Additional Example 3A Continued
Method 2: Use prime factorization.
20
___
48
=
2 •2•5
_________________
5
= ___
2 • 2 • 2 •2•3
12
So
20
___
48
Write the prime factors of
20 and 48. Simplify.
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.
4-5 Equivalent Fractions
Additional Example 3B: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
7
___
10
7 is already
The GCF of 7 and 10 is 1 so ___
10
in simplest form.
4-5 Equivalent Fractions
Check It Out: Example 3A
Write each fraction in simplest form.
12
___
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 ÷ 4
=
3
__
4
Divide 12 and 16 by their GCF, 4.
4-5 Equivalent Fractions
Check It Out: Example 3A Continued
Method 2: Use prime factorization.
12
___
16
=
2 •2•3
_____________
2 • 2 • 2 •2
3
= ___
4
Write the prime factors of
12 and 16. Simplify.
12 written in simplest form is ___
3 .
So ___
16
4
4-5 Equivalent Fractions
Check It Out: Example 3B
Write the fraction in simplest form.
3
___
10
3
The GCF of 3 and 10 is 1, so ___ is already in
10
simplest form.
4-5 Equivalent Fractions
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
4-5 Equivalent Fractions
Lesson Quiz
Find 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
1
__
2
7
6. ___
49
1
___
7
4-5 Equivalent Fractions
Lesson Quiz for Student Response Systems
1. Identify two equivalent fractions for
A.
C.
B.
D.
.
4-5 Equivalent Fractions
Lesson Quiz for Student Response Systems
2. Identify two equivalent fractions for
A.
C.
B.
D.
.
4-5 Equivalent Fractions
Lesson Quiz for Student Response Systems
3. Identify the missing number that makes
the given fractions equivalent.
A. 3
C. 6
B. 4
D. 9
4-5 Equivalent Fractions
Lesson Quiz for Student Response Systems
4. Identify the missing number that makes
the given fractions equivalent.
A. 24
C. 40
B. 32
D. 48
4-5 Equivalent Fractions
Lesson Quiz for Student Response Systems
5. Identify the simplest form of the fraction
A.
C.
B.
D.