1. Mixed Numbers & Improper Fractions

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

3. Mixed 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. 4 2 10 8 7 3 16 1
With improper fractions, the numerator is bigger than or equal to the denominator.

4. Mixed 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

5. Mixed Numbers & Improper Fractions
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

6. Mixed Numbers & Improper Fractions
There are (two and one‑third) glasses of water. 1 3
1 (one and one-eighth) large cubes are shaded. 1 8

7. 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:
shaded circles is the same as saying 2 shaded circles. 5 2 1
2 whole circles and one half-circle are shaded.

8. Mixed Numbers & Improper Fractions
3 squares are shaded… 1 4 13 4
…is the same as saying squares are shaded.

9. Mixed Numbers & Improper Fractions
Practice
Represent the shaded fraction of these groups of shapes using a mixed number and an improper fraction. 1. 2. 4 5
3 or, of the stars are shaded. 19 1 6
1 or, of the hexagons are shaded. 7

10. Mixed Numbers & Improper Fractions
Converting Mixed Numbers to Improper Fractions
Suppose you need to convert to an improper fraction. 1 4
You could draw a diagram.
The mixed number can be represented by this diagram: 1 4
This shows that consists of a total of 9 quarters, or . 1 4 9

11. Mixed Numbers & Improper Fractions
Example 1
Write as an improper fraction. 5 6
Solution

12. Improper Fractions
Practice
Write the following mixed numbers as improper fractions. 1 4 10 3 5 8 2 7
(5 × 4) + 1 4 21 =
(4 × 5) + 3 5 23 =
(1 × 8) + 3 8 11 =
(10 × 10) + 1 10
101 =
(8 × 3) + 2 3 26 =
(7 × 5) + 4 5 39 =
(2 × 7) + 3 7 17 =
(9 × 8) + 7 8 79 =

13. Mixed Numbers & Improper Fractions
Example 2
Write as a mixed number. 59 4

14. Mixed Numbers & Improper Fractions
Practice
Write the following improper fractions as mixed numbers. 8 5 9 4
8 ÷ 5 = 1 R 3 3 5 1
9 ÷ 4 = 2 R 1 1 4 2 11 8 12 11
11 ÷ 8 = 1 R 3 3 8 1
12 ÷ 11 = 1 R 1 1 11 16 13 21 2
16 ÷ 13 = 1 R 3 1 3 13
21 ÷ 2 = 10 R 1 10 1 2 23 7 91 8
23 ÷ 7 = 3 R 2 2 7 3
91 ÷ 8 = 11 R 3 3 8 11