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4-6 Mixed Numbers and Improper Fractions
Learn to convert between mixed numbers
and improper fractions.
4-6 Mixed Numbers and Improper Fractions
Vocabulary
improper fraction
proper fraction
4-6 Mixed Numbers and Improper Fractions
An improper fraction is a fraction in which the
numerator is greater than or equal to the
__ .
denominator such as 11
4
Reading Math
11
___
is read as “eleven-fourths.”
4
4-6 Mixed Numbers and Improper Fractions
Whole numbers can be written as improper
fractions. The whole number is the numerator,
7
and the denominator is 1. For example, 7 = __
.
1
When the numerator is less than the denominator,
the fraction is called a proper fraction.
4-6 Mixed Numbers and Improper Fractions
You can write an improper fraction as a mixed
number.
4-6 Mixed Numbers and Improper Fractions
Additional Example 1: Application
9
__
4
Ella hiked for
hours yesterday. Write
as a mixed number.
9
__
4
Method 1: Use a model.
Draw squares divided into fourth sections. Shade 9 of
the fourth sections.
1
4
1
4
1
4
1
4
1
1
4
1
4
1
4
1
4
2
1
4
1
4
1
__
4
1
4
1
4
1
There are 2 whole squares and 1 fourth square, or 2 __
4
squares, shaded.
4-6 Mixed Numbers and Improper Fractions
Additional Example 1 Continued
Method 2: Use division.
1
__
24
4 9
-8
1
Divide the numerator by the denominator.
To form the fraction part of the quotient,
use the remainder as the numerator and
the divisor as the denominator.
Ella hiked for
1
__
24
hours.
4-6 Mixed Numbers and Improper Fractions
Check It Out: Example 1
7
4
Arnold biked for __ hours yesterday. Write
7
__
4
as a mixed number.
Method 1: Use a model.
Draw squares divided into fourth sections. Shade 7 of the
fourth sections.
1 1
1 1
4
1
4
4
1
4
1
4
1
4
4
1
4
3
__
4
There is 1 whole square and 3 fourth squares, or
squares, shaded.
3
__
14
4-6 Mixed Numbers and Improper Fractions
Check It Out: Example 1 Continued
Method 2: Use division.
3
__
14
4 7
-4
3
Divide the numerator by the denominator.
To form the fraction part of the quotient,
use the remainder as the numerator and
the divisor as the denominator.
3
Arnold biked for 1 __
hours.
4
4-6 Mixed Numbers and Improper Fractions
Additional Example 2: Writing Mixed Numbers
as Improper Fractions
Write 3
2
__
3 as
an improper fraction.
Method 1: Use a model.
You can draw a diagram to illustrate the whole and
fractional parts.
11
__
There are 11 thirds or
.
3
Count the thirds in the diagram.
4-6 Mixed Numbers and Improper Fractions
Additional Example 2 Continued
Method 2: Use multiplication and addition.
When you are changing a mixed number to an improper
fraction, spiral clockwise as shown in the picture. The order
of operations will help you remember to multiply before you
add.
2
(3 • 3) + 2
__
= __________
3
3
9+2
_____
=
=
3
3
11
__
3
Multiply the whole number
by the denominator and
add the numerator.
Keep the same
denominator.
Then add.
2
33
First Multiply.
4-6 Mixed Numbers and Improper Fractions
Check It Out: Example 2
Write 4
1
__
as
3
an improper fraction.
Method 1: Use a model.
You can draw a diagram to illustrate the whole and
fractional parts.
13
__
There are 13 thirds, or
.
3
Count the thirds in the diagram.
4-6 Mixed Numbers and Improper Fractions
Check It Out: Example 2 Continued
Method 2: Use multiplication and addition.
When you are changing a mixed number to an improper
fraction, spiral clockwise as shown in the picture. The order
of operations will help you remember to multiply before you
add.
1
(3 • 4) + 1
__
= __________
3
3
12 + 1
______
3
=
=
4
13
__
3
Multiply the whole number
by the denominator and
add the numerator.
Keep the same
denominator.
Then add.
1
__
43
Multiply.