3-4
Equivalent Fractions and Mixed Numbers
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
3-4
Equivalent Fractions 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
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
California
Standards
NS2.4 Determine the least common
multiple and the greatest common divisor of
whole numbers; use them to solve problems
with fractions (e.g. to find a common
denominator to add two fractions or to find the
reduced form of a fraction).
Also covered:
NS1.1
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Vocabulary
equivalent fractions
improper fraction
mixed number
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Different fractions can name the same number.
3
5
Holt CA Course 1
=
6
10
=
15
25
3-4
Equivalent Fractions 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 nonzero number.
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
8 is an improper
5
fraction. Its
numerator is
greater than its
denominator.
Holt CA Course 1
3
is a mixed
5
number. It
contains both a
whole number
and a fraction.
1
8 = 13
5
5
3-4
Equivalent Fractions and Mixed Numbers
To determine if two fractions are equivalent,
simplify the fractions.
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Additional Example 1: Finding Equivalent Fractions
Find two fractions equivalent to 5
7.
5  2 = 10
72
14
Multiply the numerator and
denominator by 2.
53
73
Multiply the numerator and
denominator by 3.
= 15
21
Remember!
A fraction with the same numerator and
2
denominator, such as is equal to 1.
2
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
10 , and 15 are equivalent,
The fractions 5
,
21
7 14
but only 5 is in simplest form. A fraction is in
7
simplest form when the greatest common divisor
of its numerator and denominator is 1.
Holt CA Course 1
3-4
Equivalent Fractions 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
Simplify both fractions and compare.
4
4÷2
2
=
=
6
6÷2
3
28 = 28 ÷ 14 = 2
42 ÷ 14 3
42
4 and 28 are equivalent because both are equal to 2 .
6
42
3
Holt CA Course 1
3-4
Equivalent Fractions 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
Simplify both fractions and compare.
6 = 6÷2 = 3
10 ÷ 2
10
5
20 = 20 ÷ 5 = 4
25 ÷ 5
25
5
6 and 20 are not equivalent because their simplest
10
25
forms are not equal.
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Additional Example 4: Converting Between Improper
Fractions and Mixed Numbers
A. Write 13 as a mixed number.
5
First divide the numerator by the denominator.
13 = 2 3
5
5
Use the quotient and remainder to
write the mixed number.
B. Write 7 2
as an improper fraction.
3
First multiply the denominator and whole number,
and then add the numerator.
+
2 = 3  7 + 2 = 23 Use the result to
write the improper
3
3
3

fraction.
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Check It Out! Example 1
Find two fractions equivalent to 6 .
12
6  2 = 12
12  2
24
Multiply the numerator and
denominator by 2.
6 ÷2
3
=
12 ÷ 2
6
Divide the numerator and
denominator by 2.
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Check It Out! Example 2
15
Write the fraction 45 in simplest form.
Find the GCD of 15 and 45.
15 = 3
•
5
45 = 3
•
3
The GCD is 15 = 3
•
5.
5
15 = 15 ÷ 15 = 1
45 45 ÷ 15
3
Holt CA Course 1
•
Divide the numerator and
denominator by 15.
3-4
Equivalent Fractions and Mixed Numbers
Check It Out! Example 3A
Determine whether the fractions in each pair
are equivalent.
3 and 6
9
18
Simplify both fractions and compare.
3
3÷3
1
=
=
9
9÷3
3
6 = 6 ÷6 = 1
18 ÷ 6
18
3
3 and 6 are equivalent because both are equal to 1 .
9
18
3
Holt CA Course 1
3-4
Equivalent Fractions 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
2
6
6
Use the quotient and remainder
to write the mixed number.
B. Write 8 1
3 as an improper fraction.
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.
Holt CA Course 1
3-4
Equivalent Fractions and Mixed Numbers
Lesson Quiz
12 1 , 3
1. Write two fractions equivalent to 24 . 2 6
2. Determine if 5 and 4 are equivalent. no
12
10
3. Write the fraction 16 in simplest form. 1
48
3
4. Write 17 as a mixed number. 2 1
8
8
31
5. Write 4 3
as
an
improper
fraction.
7
7
Holt CA Course 1