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## Fractions Review

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### Fractions Review Fractions A number in the form Fractions The denominator can never be equal to 0. Fractions A fraction with a numerator of 0 equals 0. – PowerPoint PPT presentation

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Title: Fractions Review

1
Fractions Review
2
Fractions
• A number in the form

Numerator
Denominator
Or
N
D
3
Fractions
• The denominator can never be equal to 0.

12
Does not exist!

0
4
Fractions
• A fraction with a numerator of 0 equals 0.

0
0

0

0
156
4
5
Fractions
• If the numerator is larger than the denominator,
it is called an improper fraction.

Find the improper fraction
7
10
56
4
10
11
12
73
9
8
6
Math with Fractions
• Four basic functions
• Multiply
• Divide
• Subtract

7
Multiplication
• Multiply the numerators and put in the numerator
of the result
• Multiply the denominators and put in the
denominator of the result

4
7
7 x 4
28
x

8
9
8 x 9
72
8
Multiplication - Lets Try It!
1
7
9
4
7
36
x
x

9
2
7
11
18
77
7
30
1
7
7
210
x
x

4
14
5
3
15
56
9
These numbers get pretty big!
210
56
What if we needed to multiply again?
Lets make the fraction more simple, so it will
be easier to use in the future.
10
Simplification
• Divide by the Greatest Common Factor

28
But what is a Common Factor?
72
11
Factors
• A factor is a number that can be divided into
another number with no remainder
• 8s factors are
• 1 (8/1 8)
• 2 (8/2 4)
• 4 (8/4 2)
• 8 (8/8 1)
• 3 is NOT a factor of 8, because 8 is not evenly
divisible by 3 (8/3 2 with R3)

12
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 lets go back to our simplification problem
from before
13
Simplification
• Divide both numerator and denominator by the
Greatest Common Factor

28
Factors are 1, 2, 4, 7, 14, 28
Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48,
72
72
Greatest Common Factor is 4
28
7

28
4
7

So

72
18
72

4
18
14
Simplification - Lets Try It!
1
1
18
2
3
7

3
3
63
7
9
21
2
2
78
13
24
6

7
5
114
19
84
15
15
Division
• Just like multiplication with one more step
• Invert the second fraction and multiply

6
1
3
2
3
x

8
8
2
8
1
16
Division - Lets Try It!
1
7
9
4
14
44

9
2
7
11
9
63
1
7
7
20
21
50

5
3
4
10
5
7
17
• To add two fractions, you must make sure they
have a Common Denominator

What is a Common Denominator?
3
5

8
16
18
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 lets go back to our simplification problem
from before
19
• 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 goes into 16 two times
16 goes into 16 one time

5
5
1
6
x

8
16
16
16
1
16
The smallest number that has both of these as
factors is 16
6
5
11

16
16
16
Once you have a common denominator, add the
numerators.
20
1
1
2
4
3
1

4
2
16
8
4
2
2
6
3
13
17
25

8
3
16
4
12
16
21
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 goes into 16 two times
16 goes into 16 one time
-
8
16
6
5
1
The smallest number that has both of these as
factors is 16
-

16
16
16
Once you have a common denominator, subtract the
numerators.
22
Subtraction - Lets Try It!
1
7
3
9
3
3
-
-

8
2
16
8
8
16
1
6
7
5
1
13
-
-

8
2
4
16
4
16
23
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