1 Mixed Numbers & Improper Fractions. OBJECTIVE: 7.1.02 ESSENTIAL QUESTION: How can I translate...

$: 1 Mixed Numbers & Improper Fractions. OBJECTIVE: 7.1.02 ESSENTIAL QUESTION: How can I translate between mixed numbers and improper fractions?$
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Mixed Numbers & Improper Fractions

Mixed Numbers & Improper Fractions

Mixed Numbers & Improper FractionsMixed Numbers & Improper Fractions

OBJECTIVE:7.1.02

ESSENTIAL QUESTION:How can I translate between mixed numbers and 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


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

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


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 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.


3 squares are shaded…1

4

13

4…is the same as saying squares are shaded.


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


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


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


Example 2

Write as a mixed number.59

4


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

1 Mixed Numbers & Improper Fractions. OBJECTIVE: 7.1.02 ESSENTIAL QUESTION: How can I translate...

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