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Fractions Review
Fractions
A number in the form
Numerator
Denominator
Or
N
D
Fractions
The denominator can never be equal to 0.
12
0
Does not
=
exist!
Fractions
A fraction with a numerator of 0 equals 0.
0
4
= 0
0
156
= 0
Fractions
• If the numerator is larger than the denominator,
it is called an improper fraction.
Find the improper fraction
7
10
4
56
10
11
8
9
73
12
Math with Fractions
Four basic functions
• Multiply
• Divide
• Add
• Subtract
Multiplication
• Multiply the numerators and put in
the numerator of the result
• Multiply the denominators and put
in the denominator of the result
7
8
x
4
9
=
7x4
8x9
=
28
72
Multiplication - Let’s Try It!
7
x
1
9
2
7
1
5
x
3
=
=
7
4
18
7
11
7
30
7
15
4
x
x
9
14
=
=
36
77
210
56
210
56
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
28
72
But what is a
Common Factor?
Factors
• A factor is a number that can be divided
into another number with no remainder
– 8’s factors are:
•
•
•
•
1
2
4
8
(8/1 =8)
(8/2 = 4)
(8/4 = 2)
(8/8 = 1)
– 3 is NOT a factor of 8, because 8 is not
evenly divisible by 3 (8/3 = 2 with R=3)
Common Factors
• A common factor is a factor that
two numbers have in common
– For example, 7 is a factor of both 21 and 105,
so it is a common factor of the two.
– The greatest common factor is the largest
factor that the two number share
So let’s go back to our simplification
problem from before…
Simplification
• Divide both numerator and denominator by
the Greatest Common Factor
28
72
Factors are 1, 2, 4, 7, 14, 28
Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72
Greatest Common Factor is 4
28 ÷ 4 = 7
72 ÷ 4 = 18
28
7
So
=
72
18
Simplification - Let’s Try It!
3
1
=
9
3
7
1
=
21
3
18
2
=
63
7
24
2
=
84
7
6
2
=
15
5
78
13
=
114 19
Division
• Just like multiplication with one more step
• Invert the second fraction and multiply
3
8
÷
1
2
=
3
8
x
2
1
=
6
8
Division - Let’s Try It!
7
1
÷
9
2
7
5
÷
1
3
14
=
9
=
4
9
44
÷
=
7
11
63
21
20
5
4
÷
7
10
=
50
7
Addition
• To add two fractions, you must make
sure they have a Common Denominator
3
8
+
5
16
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.
So let’s go back to our simplification
problem from before…
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?
3
5
+
8
16
8 goes into 16 two times
3 x 2
6
8 2 = 16
The smallest number that has
both of these as factors is 16
Once you have a common
denominator, add the numerators.
16 goes into 16 one time
5 x 1
5
16 1 = 16
6
5
11
+
=
16
16
16
Addition - Let’s Try It!
1
1
+
4
2
6
8
+
2
3
=
=
3
4
4
2
1
+
=
16
8
2
17
13
12
16
+
3
4
=
25
16
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?
3 - 5
8
16
8 goes into 16 two times
3 x 2
6
8 2 = 16
The smallest number that has
both of these as factors is 16
16 goes into 16 one time
5 x 1
5
16 1 = 16
6
5
1
=
Once you have a common
16
16
16
denominator, subtract the numerators.
Subtraction - Let’s Try It!
7
8
-
1
2
6
1
8
2
=
3
9
8
16
1
=
4
-
3
8
=
3
16
5
7
13
=
4
16
16
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