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Equivalent Fractions
3-8 and Mixed Numbers
Warm Up
Problem of the Day
Lesson Presentation
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
Warm Up
Name a common factor for each pair.
Possible answers:
1. 5 and 10
5
2. 9 and 12
3
3. 20 and 24
4
4. 10 and 14
2
5. 6 and 8
2
6. 8 and 15
1
Course 2
Equivalent Fractions
3-8 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
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
Learn to identify, write, and convert
between equivalent fractions and mixed
numbers.
Course 2
Equivalent Fractions
3-8 and
Insert
Lesson
Title Here
Mixed
Numbers
Vocabulary
equivalent fractions
improper fractions
mixed number
Course 2
Equivalent Fractions
3-8 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
Course 2
=
6
10
=
15
25
Equivalent Fractions
3-8 and Mixed Numbers
6 = 15 . These are called
In the diagram 3
=
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.
3 = 3 · 2= 6
5 5 · 2 10
Course 2
15 = 15 ÷ 5 3
=
25 25 ÷ 5 5
Equivalent Fractions
3-8 and Mixed Numbers
Remember!
3 is in simplest form because the greatest
5
common factor of 3 and 5 is 1.
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
Additional Example 1: Finding Equivalent Fractions
Find a fraction equivalent to the given fraction.
A. 5
7
5 = 5 · 3 = 15
Multiply numerator and
7
7·3
21
denominator by 3.
B. 18
24
18 = 18 ÷ 2 = 9
24
24 ÷ 2 12
Course 2
Divide numerator and
denominator by 2.
Equivalent Fractions
3-8 Insert
Lesson
Title Here
and Mixed
Numbers
Try This: Example 1
Find a fraction equivalent to the given fraction.
A. 3
8
3 = 3·2 = 6
Multiply numerator and
8
8·2
16
denominator by 2.
B.
Course 2
6
12
6 = 6÷3 = 2
12
12 ÷ 3
4
Divide numerator and
denominator by 3.
Equivalent Fractions
3-8 and Mixed Numbers
To determine if two fractions are
equivalent, find a common denominator
and compare the numerators.
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
Additional Example 2A: Determining Whether
Fractions are Equivalent
Write the fractions with a common
denominator. Then determine if they are
equivalent.
A. 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.
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
Additional Example 2B: Determining Whether
Fractions are Equivalent
Write the fractions with a common
denominator. Then determine if they are
equivalent.
B. 6 and 20
10
25
Both fractions can be written with a denominator of 50.
6
6·5
= 30
=
10
10 · 5
50
20 = 20 · 2 = 40
25 · 2
25
50
The numerators are not equal, so the fractions are
not equivalent.
Course 2
Equivalent Fractions
3-8 Insert
Lesson
Title Here
and Mixed
Numbers
Try This: Example 2A
Write the fractions with a common
denominator. Then determine if they are
equivalent.
A. 3 and 6
9
18
Both fractions can be written with a denominator of 3.
3
3÷3
1
=
=
9
9÷3
3
6 = 6÷6 =1
18 ÷ 6
18
3
The numerators are equal, so the fractions are
equivalent.
Course 2
Equivalent Fractions
3-8 Insert
Lesson
Title Here
and Mixed
Numbers
Try This: Example 2B
Write the fractions with a common
denominator. Then determine if they are
equivalent.
B. 4 and 9
12
48
Both fractions can be written with a denominator of 96.
4
4·8
= 32
=
12
12 · 8
96
9 = 9 · 2 = 18
48 · 2
48
96
The numerators are not equal, so the fractions are
not equivalent.
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
8 is an improper
5
fraction. Its
numerator is
greater than its
denominator.
Course 2
8= 13
5
5
3
1 is a mixed
5
number. It
contains both a
whole number
and a fraction.
Equivalent Fractions
3-8 and Mixed Numbers
Additional Example 3: 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
3
·
7
+
2
2
23
=
7 3 =
write the improper
3
3

fraction.
Course 2
Equivalent Fractions
3-8 and Mixed Numbers
Try This: Example 3
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
=
8 3 =
write the improper
3
3

fraction.
Course 2
Equivalent Fractions
3-8 and
Insert
Lesson
Title Here
Mixed
Numbers
Lesson Quiz
1
1. Write a fraction equivalent to 12 .
2
24
2. Write 17 as a mixed number.
21
8
8
3. Write 4 3 as an improper fraction. 31
7
7
4. A carpenter is building a stairway. Each stair
has to be 12 7 in. wide. The carpenter’s ruler is
8
marked in sixteenths. What length should he
measure?
12 14 in.
16
Course 2