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Fractions Continued
Fractions
A number in the form
Numerator
Denominator
OrND
Fractions
The denominator can never be equal to 0.
0
12=
Does not exist!
Fractions
A fraction with a numerator of 0 equals 0.
156
0= 0
4
0= 0
Fractions
• If the numerator is larger than the denominator, it is called an improper fraction.
Find the improper fraction
11
7
12
10
73
56
9
4
8
10
Math with Fractions
Four basic functions
• Add
• Subtract
• Multiply
• Divide
Addition• To add two fractions, you must make
sure they have a Common Denominator
8
3
16
5+
What is a Common Denominator?
Common Denominator
• A common denominator is a number with which both of the denominators share at least one factor that is not the number 1
– For example, if the denominators are 4 and 7, then a common denominator is 28.
– 28 shares the factors 1, 2 and 4 with the number 4, and the factors 1 and 7 with the number 7.
Addition• To add two fractions, you must make sure
they have a Common Denominator• What can you multiply each fraction by to give the
smallest common denominator?
83
165+
The smallest number that has both of these as factors is 16
8 goes into 16 two times 16 goes into 16 one time
166
83
22x = 16
5165
11x =
166
165+ =
1611
Once you have a common denominator, add the numerators.
Addition - Let’s Try It!
4 211
=+
=8 3
26+
16 824
=+
=16 4
3 13+
43
12
17
21
16
25
Subtraction• To subtract two fractions, they also must
have a Common Denominator• What can you multiply each fraction by to
give the smallest common denominator?
8
3
16
5-
The smallest number that has both of these as factors is 16
8 goes into 16 two times 16 goes into 16 one time
166
=83
22x
165
=165
11x
166
165- =
161
Once you have a common denominator, subtract the numerators.
Subtraction - Let’s Try It!
=8 2
17-
8 2
16=-
=16 8
39-
4 16
75=-
8
3
4
1
16
3
16
13
Multiplication
• Multiply the numerators and put in the numerator of the result
• Multiply the denominators and put in the denominator of the result
8 9 8 x 9 72
47 7 x 4 28= =x
Multiplication - Let’s Try It!
9 2
17=x
5 3
17=x
7 11
94=x
4 14
730=x
18
7
15
7
77
36
56
210
56
210 These numbers get pretty big!
What if we needed to multiply again?
Let’s make the fraction more simple, so it will be easier to use in the future.
Simplification
• Divide by the Greatest Common Factor
72
28But what is a Common Factor?
Division
• Just like multiplication with one more step• Invert the second fraction and multiply
8 2
13=÷
8 1
23x =
8
6
Division - Let’s Try It!
9 217
=÷
=5 3
17÷
7 1194
=÷
=4 10
720÷
914
5
21
6344
7
50
Review
• A fraction has a numerator and a denominator
• The denominator can never be 0
• You can multiply, divide, add and subtract fractions
• A common factor is a number that both denominators are evenly divisible by
• A common denominator is a number that both denominators share a factor with
