Transcript Document

Adding and Subtracting
Rational Numbers
Rational Numbers
• The term, Rational Numbers, refers to any number that can
be written as a fraction.
• This includes fractions that are reduced, fractions that can
be reduced, mixed numbers, improper fractions, and even
integers and whole numbers.
• An integer, like 4, can be written as a fraction by putting the
number 1 under it.
4
4
1
Types of Rational Numbers
• Reduced Fractions:
2
3
4
• Not Reduced Fractions:
6
1
• Mixed Numbers: 5
4
• Improper Fractions: 6
4
6
• Integers and Whole Numbers:
1
Simplifying Fractions
• Simplifying fractions by dividing the numerator (top
number) and denominator (bottom number) by the
same value.
• Repeat this until there are no more numbers that
divide into both the numerator & denominator.
• Example:
• Example:
• Example:
4 2 2

6 2 3
15 5 3

10 5 2
36 6 6

42 6 7
Simplifying Fractions
• Example: 15 is already simplified.
14
• Example: 3 2  35  2  17 is already simplified.
5
5
5
(Rewrite mixed numbers as improper fractions before
you simplify.)
36 2 18 3 6


• Example:
42 2 21 3 7
(If after you divide, the fraction can still be
simplified, keep going.)
Adding Fractions
• To add fractions, they must have a common
denominator.
• If the denominators are the same, add the numerators,
and put the result over the denominator.
• If the answer can be simplified, then simplify it.
2 9 2  9 11
 

5 5
5
5
• Example: 2  8  2 8  10 5  2  2
5 5
5
5 5 1
• Example:
Getting a Common Denominator
• Use this formula to get two fractions to have a
common denominator:
2 4

3 5
Common Denominator = 3•5=15.
2 4 2 5  4 3 Cross Multiply & Add.
 
3 5
15
2 4 2 5  4 3 22
 

Simplify if possible.
3 5
15
15
More Examples
Cross Multiply & Add.
{
3 1 3 6 1 4 22 22 2 11
1)  



4 6
4 6
24 24 2 12
Common Denominator
Divide to Simplify.
5 3 5 2  38 34 34 2 17
2)  



8 2
8 2
16 16 2 8
More Examples
6 10 6 10 Change Subtraction to Addition.
3) 
 
(Keep-Change_Change.)
5 3
5
3
6 3  (10)  5 18 50 32



5 3
15
15
Note: A fraction with a negative numerator
or denominator is a negative fraction.
32 32
32


15 15
15
More Examples
Change Subtraction to Addition
(Keep-Change_Change.).
1
5
3 4 1 1 6  5 13 11


4)  3 1  

4
6
4
6
4
6
Change Mixed Numbers to Improper Fractions.
13 11 (13) 6  (11) 4 122 61
61





4
6
4 6
24
12
12
Get Common Denominator, Cross Multiply & Add.
Simplify.
You Try It!
Find each sum or difference.
3 4
1) 
5 3
1 7
2) 
8 10
2
1
3) 5  2
5
4
1 1
4) - 3 
2 5
Solutions
3 4 3 3  4 5 29
1)  

5 3
5 3
15
1 7 1 7 110 (7) 8 46
23
2)   



8 10 8 10
8 10
80
40
2
1 27 9 27 4  9  5 153
3) 5  2 
 

5
4 5 4
5 4
20
1 1
7 1 7 1 (7)5  (1)2
37
4) - 3     



2 5
2 5 2
5
2 5
10