Transcript Mixed Numbers & Improper Fractions

Mixed
Numbers &
Improper
Fractions
1
Mixed Numbers & Improper Fractions
OBJECTIVE:
7.1.02
ESSENTIAL QUESTION:
How can I translate
between mixed numbers
and improper fractions?
Mixed Numbers & Improper Fractions
Improper Fractions
In previous lessons we learned and reviewed how to
simplify, compare, and order fractions when the numerator
was smaller than the denominator but now we are going to
look at fractions with numerators larger than the
denominator as well as mixed numbers.
16
4
7
3
3
1
4
2
10
8
With improper fractions,
the numerator is bigger
than or equal to the
denominator.
Mixed Numbers & Improper Fractions
Some examples of improper fractions include:
5
(five-halves) circles are shaded.
2
4
(four-thirds) triangles are shaded.
3
6
(six-sixths) of a hexagon is shaded.
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Mixed Numbers & Improper Fractions
Mixed Numbers
A mixed number is one that shows the
sum of a whole number and a fraction.
Examples of mixed numbers include:
1
3 (three and one-quarter) squares are shaded.
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Mixed Numbers & Improper Fractions
1
There are 2 (two and one-third) glasses of water.
3
1
1 (one and one-eighth) large cubes are shaded.
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Mixed Numbers & Improper Fractions
Mixed Numbers Have Equivalent Improper Fractions
The diagrams shown previously can all be represented
by both mixed numbers and improper fractions.
For example:
5
1
shaded circles is the same as saying 2 shaded circles.
2
2
2 whole circles and one
half-circle are shaded.
Mixed Numbers & Improper Fractions
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3 squares are shaded…
4
13
…is the same as saying
squares are shaded.
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Mixed Numbers & Improper Fractions
Practice
Represent the shaded fraction of these groups of shapes
using a mixed number and an improper fraction.
1.
3
19
4
or,
of the stars are shaded.
5
5
1
1
7
or, of the hexagons are shaded.
6
6
2.
Mixed Numbers & Improper Fractions
Converting Mixed Numbers to Improper Fractions
1
Suppose you need to convert 2 to an improper fraction.
4
You could draw a diagram.
1
The mixed number 2 can be represented by this diagram:
4
1
9
This shows that 2 consists of a total of 9 quarters, or .
4
4
Mixed Numbers & Improper Fractions
Example
1
5
Write 4 as an improper fraction.
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Solution
Improper Fractions
Practice
Write the following mixed numbers as improper fractions.
1 (5 × 4) + 1 21
3
(4 × 5) + 3 23
3. 5
4. 4
=
=
4
4
5
5
4
5
3
5. 1
8
(1 × 8) + 3 11
=
8
8
1
6. 10
10
2
7. 8
3
(8 × 3) + 2 26
=
3
3
4
8. 7
5
(7 × 5) + 4 39
=
5
5
3
9. 2
7
(2 × 7) + 3 17
=
7
7
7
10. 9
8
(9 × 8) + 7 79
=
8
8
(10 × 10) + 1 101
=
10
10
12
Mixed Numbers & Improper Fractions
Example
2
59
Write
as a mixed number.
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Mixed Numbers & Improper Fractions
Practice
Write the following improper fractions as mixed numbers.
11. 8 8 ÷ 5 = 1 R 3 1 3
12. 9 9 ÷ 4 = 2 R 1 2 1
5
4
4
5
13. 11
8
11 ÷ 8 = 1 R 3
15. 16
13
16 ÷ 13 = 1 R 3
1
23 ÷ 7 = 3 R 2
2
3
7
17. 23
7
3
1
8
3
13
14. 12
11
12 ÷ 11 = 1 R 1
1
16. 21
2
21 ÷ 2 = 10 R 1
10
1
2
18. 91
8
91 ÷ 8 = 11 R 3
11
3
8
1
11