1 mixed numbers & improper fractions. objective: 7.1.02 essential question: how can i translate...
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Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
OBJECTIVE:7.1.02
ESSENTIAL QUESTION:How can I translate between mixed numbers and improper fractions?
Mixed Numbers & Improper FractionsMixed Numbers & 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.
With improper fractions, the numerator is bigger than or equal to the denominator.
4
210
8
7
3
16
43
1
Improper Fractions
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
Some examples of improper fractions include:
(five-halves) circles are shaded.5
2
(four-thirds) triangles are shaded.4
3
(six-sixths) of a hexagon is shaded.6
6
Mixed Numbers & Improper FractionsMixed 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:
3 (three and one-quarter) squares are shaded. 1
4
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
There are 2 (two and one‑third) glasses of water.1
3
1 (one and one-eighth) large cubes are shaded.1
8
Mixed Numbers & Improper FractionsMixed 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:
shaded circles is the same as saying 2 shaded circles.5
2
1
2
2 whole circles and one half-circle are shaded.
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
3 squares are shaded…1
4
13
4…is the same as saying squares are shaded.
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
Practice
Represent the shaded fraction of these groups of shapes using a mixed number and an improper fraction.
1.
2.
4
53 or, of the stars are shaded.
19
5
1
61 or, of the hexagons are shaded.
7
6
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
Converting Mixed Numbers to Improper Fractions
You could draw a diagram.
Suppose you need to convert 2 to an improper fraction. 1
4
The mixed number 2 can be represented by this diagram:1
4
This shows that 2 consists of a total of 9 quarters, or .1
4
9
4
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
Example 1
Solution
Write 4 as an improper fraction.5
6
12
Improper FractionsImproper Fractions
Write the following mixed numbers as improper fractions.
3. 5 4. 4
5. 1 6. 10
7. 8 8. 7
9. 2 10. 9
1
4
1
10
3
5
3
8
2
3
3
7
4
5
7
8
(5 × 4) + 1
4
21
4=
(1 × 8) + 3
8
11
8=
(8 × 3) + 2
3
26
3=
(2 × 7) + 3
7
17
7=
(4 × 5) + 3
5
23
5=
(10 × 10) + 1
10
101
10=
(7 × 5) + 4
5
39
5=
(9 × 8) + 7
8
79
8=
Practice
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
Example 2
Write as a mixed number.59
4
Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions
Write the following improper fractions as mixed numbers.
11. 12.
13. 14.
15. 16.
17. 18.
8
5
12
11
9
4
11
8
21
216
13
91
8
23
7
8 ÷ 5 = 1 R 33
51
11 ÷ 8 = 1 R 33
81
23 ÷ 7 = 3 R 22
73
16 ÷ 13 = 1 R 3 13
13
12 ÷ 11 = 1 R 1 11
11
9 ÷ 4 = 2 R 11
42
91 ÷ 8 = 11 R 33
811
21 ÷ 2 = 10 R 1 101
2
Practice