Improper Fractions and Mixed Numbers
-
Definitions of Improper Fractions and Mixed Numbers
In your pocket, you have five quarters. Their are two ways of
mentioning your cash. The first way is five quarters or 5/4
dollars. The second way is one dollar and a quarter or 1¼
dollars. Both of these represent the same amount of money, however
they are written in very different ways. We define
A proper fraction is
a fraction smaller than one (the denominator is larger than the numerator)
2
5
7
3 5
,
,
,
,
are all proper fractions
9 10
32
4 7
An improper
fraction is a fraction greater than or
equal to one (the numerator is larger or the same as than the denominator
12
8
16
21 1
,
,
,
,
are all improper fractions
5
8
13
2 1
A mixed
fraction is the sum of a whole number
greater than zero and a proper fraction
1
4
2
7
11
6
, 4
, 1
, 7
, 2
are all mixed fractions
4
7
13
8 12
-
Changing an Improper Fraction to a Mixed Fraction
We have already learned how to do all of the work in changing an
improper fraction to a mixed fraction when we learned how to perform long
division with a remainder. Now we just need to learn how to write down
the answer.
Example
Convert
22
7
into a mixed number
Solution
We divide
3
7 |
22
21
1
The result is 3R1.
Now to write this as a mixed number, the whole number part is 3 the
numerator is 1 and the denominator is the original denominator 7
22
1
= 3
7
7
Exercises
Convert the following improper fractions to mixed numbers
-
53
6
Hold mouse over the yellow rectangle for the
solution
-
92
63
Hold mouse over the yellow rectangle for the
solution
-
9321
32
Hold mouse over the yellow rectangle for the
solution
-
Changing a Mixed Fraction to an Improper Fraction
Warm up problem
Write the number 4 as an improper fraction with
denominator 3.
Solution
We write
4 x
3
12
4 =
=
3
3
To change a mixed fraction to an improper
fraction we write the whole number as a fraction with the given denominator
and then add the numerators.
Example
Write the mixed fraction
3¾
as an improper fraction
Solution
Write
3 3 x
4 3
3
=
+
4
4
4
12 + 3 15
=
=
4
4
Exercises
Convert the following mixed fractions to
improper fractions
-
5
7
6
Hold mouse over the yellow rectangle for the
solution
-
1
2
16
Hold mouse over the yellow rectangle for the
solution
-
12
5
13
Hold mouse over the yellow rectangle for the
solution
-
Reducing Improper Fractions and
Mixed Numbers
To reduce a mixed fraction, we need only reduce
the fractional part of the mixed fraction by pulling out the common factor.
Example
Reduce
9
18
30
Solution
We have
9
3 x
3
3
=
=
30 2 x 3 x
5 10
So
9
3
18
= 18
30
10
To reduce an improper fraction, we can cancel
common factors just as we did with proper fractions.
Example
Reduce
102
68
Solution
102
2 x 51 2 x
3 x 17
=
=
68
2 x 34 2 x
2 x 17
3
=
2
For an improper fraction with a large
numerator, it is easier to first convert the fraction to a mixed fraction
then reduce.
Example
Reduce
35682
15
Solution
Divide first
2378
15|
35682
-
30
56
- 45
118
- 105
132
- 120
12
Hence
35682
12
= 2378
15
15
Now reduce the fractional part
12
2 x 2 x 3 4
=
=
15
3 x
5 5
Putting the two results together gives
35682
12
4
= 2378
= 2378
15
15
5
Exercises
Reduce the following. Write your answer
as a mixed fraction.
-
24
4
64
Hold mouse over the yellow rectangle for the
solution
-
42
36
Hold mouse over the yellow rectangle for the
solution
-
26234
18
Hold mouse over the yellow rectangle for the
solution
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