1. Tuesday: January 24, 2012 Warm-Up
What are improper fractions? Give and example.

2. 4-3 Mixed Numbers and Improper Fractions
Vocabulary
A mixed number is the sum of a whole number and a fraction.
Ex: 1 ¼ = 1 + ¼

3. 4-3 Mixed Numbers and Improper Fractions
Vocabulary
A proper fraction is when the numerator is smaller than the denominator.
“Normal” fractions
Ex: ¾, ½

4. 4-3 Mixed Numbers and Improper Fractions
Vocabulary
An improper fraction is when the numerator is bigger than the denominator.
Ex: 5/4, 8/5, 12/7
Improper fractions can be written as mixed numbers.
Ex: 5/4 = 1 ¼

5. 4-3 Mixed Numbers and Improper Fractions
Vocabulary
An improper fraction is when the numerator is bigger than the denominator.
Ex: 5/4, 8/5, 12/7
Improper fractions can be written as mixed numbers.
Ex: 5/4 = 1 ¼

6. 4-3 Mixed Numbers and Improper Fractions
Example 1: Write Mixed Numbers as Improper Fractions
A. 7 ½ = ?
7/1 x 2/2 = 14/2
14/2 + 1/2 = 15/2
B. 4 ¾ = ?
4/1 x 4/4 = 16/4
16/4 + 3/4 = 19/4

7. 4-3 Mixed Numbers and Improper Fractions
Example 2: On Your Own
Write the mixed numbers as improper fractions:
5 3/10
4 2/3
C /7

8. 4-3 Mixed Numbers and Improper Fractions
Example 2: On Your Own
5 3/10
5/1 x 10/10 = 50/10
50/10 + 3/10 = 53/10
4 2/3
4/1 x 3/3 = 12/3
12/3 + 2/3 = 14/3
2 5/7
2/1 x 7/7 = 14/7
14/7 + 5/7 = 19/7

9. 4-3 Mixed Numbers and Improper Fractions
Example 3: Write Improper Fractions as Mixed Numbers
A. 23/6 = ?
Divide 23 by 6 to get 3 R5
The remainder tells you how many 1/6 pieces you have left over.
Answer: 3 5/6

10. 4-3 Mixed Numbers and Improper Fractions
Example 4: On Your Own
Write the improper fractions as mixed numbers:
7/3
26/3

11. 4-3 Mixed Numbers and Improper Fractions
Example 4: On Your Own
7/3
Divide 7 by 3 to get 2 R1
The remainder tells you how many 1/3 pieces you have left over.
Answer: 2 1/3
26/3
Divide 26 by 3 to get 8 R2
The remainder tells you how many 1/3 pieces you have left over. In this case, there are zero
Answer: 8 2/3

12. 4-6 Comparing and Ordering Fractions
In order to compare and order fractions, all fractions HAVE TO HAVE THE SAME DENOMINATOR.
STEPS:
Find the least common denominator (LCD). The least common denominator is the LCM of the denominators.
Write an equivalent fraction for each fraction using the LCD.
Compare the numerators.

13. 4-6 Comparing and Ordering Fractions
Example 5: Compare Fractions and Mixed Numbers
Replace each blank with <, >, or =
5/8 ___ 7/12
Step 1 The LCM of the denominators (8 and 12) is So, the LCD is 24.
Step 2 Write equivalent fractions with a denominator of 24
5/8 x 3/3 = 15/24
7/12 x 2/2 = 14/24
Step 3 15/24 > 14/24 because 15 > 14.
So, 5/8 > 7/12

14. 4-6 Comparing and Ordering Fractions
Example 6: On Your Own
2/3 ___ 4/9
5/12 ___ 7/8
4 1/16 ___ 4 5/8

15. 4-6 Comparing and Ordering Fractions
Example 6: On Your Own
2/3 ___ 4/9
1. The LCM of the denominators (3 and 9) is 18. So, the LCD is 18.
2. Write equivalent fractions with a denominator of 18.
2/3 x 6/6 = 12/ 18
4/9 x 2/2 = 8/18
3. 12/18 > 8/18, because 12 > 8, so 2/3 > 4/9

16. 4-6 Comparing and Ordering Fractions
Example 5: On Your Own
B. 5/12 ___ 7/8
1. The LCM of the denominators (12 and 8) is 24. So, the LCD is 24.
2. Write equivalent fractions with a denominator of 24.
5/12 x 2/2 = 10/24
7/8 x 3/3 = 21/24
3. 10/24 < 21/24, because 10 < 21, so 5/12 < 7/8

17. 4-6 Comparing and Ordering Fractions
Example 5: On Your Own
B. 4 1/6 ___ 4 5/18
1. The LCM of the denominators (6 and 18) is 18. So, the LCD is 18.
2. The whole numbers are the same, so only look at the fractions. Write equivalent fractions with a denominator of 18.
1/6 x 3/3 = 3/18
5/18 stays the same
/18 < 4 5/18, because 3 < 5, so
4 1/6 < 4 5/18

18. 4-6 Comparing and Ordering Fractions
Example 6: Order Fractions
Order the fractions 1/2, 9/14, 3/4, and 5/7 from least to greatest.
The LCD of the fractions is 28. So rewrite each fraction with a denominator of 28.
1/2 x 14/14 = 14/28
3/4 x 7/7 = 21/28
9/14 x 2/2 = 18/28
5/7 x 4/4 = 20/28
Since 14/28 < 18/ 28 < 20/28 < 21/28, the order of the original fractions is 1/2, 9/14, 5/7, 3/4

19. 4-6 Comparing and Ordering Fractions
Example 7: On Your Own
Order the fractions 4/5, 2/5, 3/4, and 1/4 from least to greatest.
The LCD of the fractions is 20. So rewrite each fraction with a denominator of 20.
4/5 x 4/4 = 16/20
2/5 x 4/4= 8/20
3/4 x 5/5 = 15/20
1/4 x 5/5 = 5/20
Since 5/20 < 8/20 < 15/20 < 16/20, the order of the original fractions is 1/4, 2/5, 3/4, 4/5