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Equivalent Fractions
2-9 and Mixed Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
Objective: Students identify, write, and convert
between equivalent fractions and mixed numbers
Equivalent Fractions
2-9 and Mixed Numbers
Warm Up
Name a common factor for each pair.
Possible answers:
1. 5 and 10
2. 9 and 12
5
3
3. 20 and 24
4
4. 10 and 14
2
5. 6 and 8
2
6. 8 and 15
1
Equivalent Fractions
2-9 and Mixed Numbers
Problem of the Day
Find a number less than 100 for which all
three statements are true:
• Divide by 3. Remainder of 2.
• Divide by 4. Remainder of 3.
• Divide by 5. Remainder of 4.
59
Equivalent Fractions
2-9 and Mixed Numbers
Learn to identify, write, and convert
between equivalent fractions and mixed
numbers.
Equivalent Fractions
2-9 and Mixed Numbers
Vocabulary
equivalent fractions
relatively prime
Equivalent Fractions
2-9 and Mixed Numbers
In some recipes the amounts of ingredients
are given as fractions, and sometimes those
fractions do not equal the fractions on a
measuring cup. Knowing how fractions relate
to each other can be very helpful.
Different fractions can name the same number.
3
5
=
6
10
=
15
25
Equivalent Fractions
2-9 and Mixed Numbers
In the diagram 3 = 6 = 15 . These are called
5 10 25
equivalent fractions because they are
different expressions for the same nonzero
number.
To create fractions equivalent to a given
fraction, multiply or divide the numerator and
denominator by the same number.
Equivalent Fractions
2-9 and Mixed Numbers
Additional Example 1: Finding Equivalent Fractions
Find two fractions equivalent to 5
7.
5 · 2 = 10
7·2
14
Multiply numerator and
denominator by 2.
5·3
7·3
Multiply numerator and
denominator by 3.
= 15
21
Equivalent Fractions
2-9 and Mixed Numbers
Check It Out: Example 1
Find two fractions equivalent to
6 .
12
6 · 2 = 12
12 · 2
24
Multiply numerator and
denominator by 2.
6÷2
3
=
12 ÷ 2
6
Divide numerator and
denominator by 2.
Equivalent Fractions
2-9 and Mixed Numbers
A fraction is in simplest form when the
numerat or and denominator are relatively
prime. Relatively prime numbers have no
common factors other than 1.
Equivalent Fractions
2-9 and Mixed Numbers
Additional Example 2: Writing Fractions in
Simplest Form
18
Write the fraction 24 in simplest form.
Find the GCF of 18 and 24.
18 = 2
•
3
•
3
24 = 2
•
2
•
2
The GCF is 6 = 2
•
•
3.
3
18 = 18 ÷ 6 = 3
24
24 ÷ 6
4
Divide the numerator and
denominator by 6.
Equivalent Fractions
2-9 and Mixed Numbers
Check It Out: Example 2
15
Write the fraction 45 in simplest form.
Find the GCF of 15 and 45.
15 = 3
•
5
45 = 3
•
3
The GCF is 15 = 3
•
•
5.
5
15 = 15 ÷ 15 = 1
45 45 ÷ 15
3
Divide the numerator and
denominator by 15.
Equivalent Fractions
2-9 and Mixed Numbers
Additional Example 3A: Determining Whether
Fractions are Equivalent
Determine whether the fractions in each pair
are equivalent.
4 and 28
6
42
Both fractions can be written with a denominator of 3.
4
4÷2
2
=
=
6
6÷2
3
28 = 28 ÷ 14 = 2
42 ÷ 14 3
42
The numerators are equal, so the fractions are
equivalent.
Equivalent Fractions
2-9 and Mixed Numbers
Additional Example 3B: Determining Whether
Fractions are Equivalent
Determine whether the fractions in each pair
are equivalent.
6 and 20
10
25
Both fractions can be written with a denominator
of 50.
6 = 6 · 5 = 30
10 · 5
10
50
20 = 20 · 2 = 40
25 · 2
25
50
The numerators are not equal, so the fractions are
not equivalent.
Equivalent Fractions
2-9 and Mixed Numbers
8 is an improper
5
fraction. Its
numerator is
greater than its
denominator.
8= 13
5
5
3
1 is a mixed
5
number. It
contains both a
whole number
and a fraction.
Remember!
An improper fraction is a fraction where the
numerator is than or equal to the denominator.
Equivalent Fractions
2-9 and Mixed Numbers
Additional Example 4: Converting Between Improper
Fractions and Mixed Numbers
A. Write 13
5 as a mixed number.
First divide the numerator by the denominator.
13 = 2 3
5
5
Use the quotient and remainder to
write a mixed number.
B. Write 7 2
as an improper fraction.
3
First multiply the denominator and whole number,
and then add the numerator.
+
Use the result to
2 = 3 · 7 + 2 = 23
write the improper
3
3
3

fraction.
Equivalent Fractions
2-9 and Mixed Numbers
Check It Out: Example 4
A. Write 15
6 as a mixed number.
First divide the numerator by the denominator.
15 = 2 3 = 2 1 Use the quotient and remainder to
2 write a mixed number.
6
6
B. Write 8 1
as an improper fraction.
3
First multiply the denominator and whole number,
and then add the numerator.
+
Use the result to
3
·
8
+
1
1
25
=
83 =
write the improper
3
3

fraction.
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quiz
12
1. Write two fractions equivalent to 24 .
1 3
2, 6
2. Determine if 5 and 4 are equivalent.
12
10
16
3. Write the fraction 48 in simplest form.
no
4. Write 17 as a mixed number.
8
21
8
5. Write 4 3
7 as an improper fraction.
31
7
1
3
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quiz for Student Response Systems
1. Identify two fractions equivalent to 12 .
60
3
1
A. Possible answer: ,
5 15
B. Possible answer: 1 , 3
5 5
C. Possible answer: 1 , 3
6 18
D. Possible answer: 1 , 3
10 30
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quiz for Student Response Systems
2. Identify the fractions that are not
equivalent.
7 , 14
10 20
A. 3 , 6
16 32
C.
B. 3 , 7
16 10
D. 3 , 15
7 35
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quiz for Student Response Systems
3. Which of the following represents the
fraction 15 in simplest form?
30
1
A.
C. 1
3
5
B. 1
4
D. 1
2
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quiz for Student Response Systems
4. Which of the following represents 19 as a
6
mixed number?
A. 5 1
C. 3 1
6
6
B. 4 1
6
D. 2 1
6
Equivalent Fractions
2-9 and Mixed Numbers
Lesson Quiz for Student Response Systems
5. Which of the following represents the
fraction 4 5 as an improper fraction?
6
A. 29
C. 27
6
6
B. 28
6
D. 25
6