Transcript Fractions - mathtools

Fractions
A quick help for those who have
forgotten how to work with them.
Fraction Operations
•
•
•
•
•
Addition
Subtraction
Multiplication
Division
Exit
Adding Fractions
Adding Fractions
In order to add fractions
you must have common
denominators and for the
sake of this presentation
you must also change all
mixed numbers to
improper fractions.
Adding Fractions
Adding fractions with like
denominators.
When you have like
denominators, you add the
numerators, then reduce.
Adding Fractions
Example 1
1 3
 
8 8
Adding Fractions
Example 1
4 1

8 2
Adding Fractions
When fractions have
uncommon denominators
multiply the denominators
together, then multiply the
numerator by the same
number you multiplied the
denominator by. This will
always give you a
common denominator.
Adding Fractions
Example 2
1 2
 
3 7
Adding Fractions
Example 2
7
7
1 2
 
3 7
3
3
Adding Fractions
Example 2
7
6


21 21
Adding Fractions
Example 2
13
21
Adding Fractions
When you have mixed
numbers change the
mixed number to an
improper fraction then add
as before. However, if you
start out with a mixed
number you need to
convert your answer to a
mixed number as well.
Adding Fractions
Example 3
2
3
1 3 
3
4
Adding Fractions
Example 3
5 15
 
3 4
Adding Fractions
Example 3
5 15
 
4 3
4
4
3
3
Adding Fractions
Example 3
20 45


12 12
Adding Fractions
Example 3
65
5
5
12
12
Adding Fractions
Try these:
3 1
1.  
8 4
5 2
2.
 
12 9
1
1
3. 3  5 
4
6
Adding Fractions
Answers:
5
1.
8
23
2.
36
5
3. 8
12
Fraction Operations
•
•
•
•
•
Addition
Subtraction
Multiplication
Division
Exit
Subtracting Fractions
Subtracting Fractions
In order to subtract
fractions you must have
common denominators
and for the sake of this
presentation you must also
change all mixed numbers
to improper fractions.
Subtracting Fractions
Subtracting fractions with
like denominators.
When you have like
denominators, you
subtract the numerators,
then reduce.
Subtracting Fractions
Example 1
1 3
 
8 8
Subtracting Fractions
Example 1
2
1
 
8
4
Subtracting Fractions
When fractions have
uncommon denominators
multiply the denominators
together, then multiply the
numerator by the same
number you multiplied the
denominator by. This will
always give you a
common denominator
Subtracting Fractions
Example 2
2 2
 
3 7
Subtracting Fractions
Example 2
7
7
2 2
 
3 7
3
3
Subtracting Fractions
Example 2
14 6


21 21
Subtracting Fractions
Example 2
8
21
Subtracting Fractions
When you have mixed
numbers change the
mixed number to an
improper fraction then
subtract as before.
However, if you start out
with a mixed number you
need to convert your
answer to a mixed number
as well.
Subtracting Fractions
Example 3
2
3
1 3 
3
4
Subtracting Fractions
Example 3
5 15
 
3 4
Subtracting Fractions
Example 3
5 15
 
4 3
4
4
3
3
Subtracting Fractions
Example 3
20 45


12 12
Subtracting Fractions
Example 3
 15  5

12
4
Subtracting Fractions
Example 3
5
1
 1
4
4
Subtracting Fractions
Try these:
3 1
1.  
8 4
5 2
2.
 
12 9
1
1
3. 3  5 
4
6
Subtracting Fractions
Answers:
1
1.
8
7
2.
36
11
3 . 1
12
Fraction Operations
•
•
•
•
•
Addition
Subtraction
Multiplication
Division
Exit
Multiplying Fractions
Multiplying Fractions
When multiplying fractions
we don’t care about
having common
denominators. We just
multiply straight across.
Multiplying Fractions
Example 1
1 3
 
8 8
Multiplying Fractions
Example 1
3
64
Multiplying Fractions
Example 2
1 2
 
3 7
Multiplying Fractions
Example 2
2
21
Multiplying Fractions
When you have mixed
numbers change the
mixed number to an
improper fraction, then
multiply as before.
However, if you start out
with a mixed number you
need to convert your
answer to a mixed number
as well.
Multiplying Fractions
Example 3
2
3
1 3 
3
4
Multiplying Fractions
Example 3
5 15
 
3 4
Multiplying Fractions
Example 3
5 15
 
3 4
Multiplying Fractions
Example 3
75 25

12 4
Multiplying Fractions
Example 3
25
1
6
4
4
Multiplying Fractions
Try these:
3 1
1.  
8 4
5 2
2.
 
12 9
1
1
3. 3  5 
4
6
Multiplying Fractions
Answers:
3
1.
32
5
2.
54
19
3. 16
24
Fraction Operations
•
•
•
•
•
Addition
Subtraction
Multiplication
Division
Exit
Division
Dividing Fractions
We never really divide
fractions. We take the first
fraction and multiply it by
the reciprocal of the
second fraction.
Dividing Fractions
Hint for dividing fractions:
To get the right answer, flip
the fraction on the right.
Dividing Fractions
Example 1
1 3
 
8 8
Dividing Fractions
Example 1
1 8
 
8 3
Dividing Fractions
Example 1
8 1

24 3
Dividing Fractions
Example 2
2 2
 
3 7
Dividing Fractions
Example 2
2 7
 
3 2
Dividing Fractions
Example 2
14 7

6 3
Dividing Fractions
When you have mixed
numbers change the
mixed number to an
improper fraction, then
divide as before. However,
if you start out with a mixed
number, you need to
convert your answer to a
mixed number as well.
Dividing Fractions
Example 3
2
3
1 3 
3
4
Dividing Fractions
Example 3
5 15
 
3 4
Dividing Fractions
Example 3
5 4
 
3 15
Dividing Fractions
Example 3
20 4

45 9
Dividing Fractions
Try these:
3 1
1.  
8 4
5 2
2.
 
12 9
1
1
3. 3  5 
4
6
Dividing Fractions
Answers:
3
1.
2
15
2.
8
39
3.
62
Fraction Operations
•
•
•
•
•
Addition
Subtraction
Multiplication
Division
Exit
The End