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Operations with FractionsREVIEW CONCEPTS
FractionsA number in the form
Numerator
Denominator
OrND
FractionsThe denominator can never be equal to 0.
0
12=
Does not exist!
FractionsA 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 FractionsFour 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.
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
These numbers get pretty big!
56
210Let’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?
Factors A factor is a number that can be divided into another number with no remainder
◦ 8’s 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 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
72
28 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
2872 ÷
÷ 44
==
718
So7228
=7
18
Simplification - Let’s Try It!
3
1
7
2
3
1
63
18=
5
2
114
78=
7
2
19
13
9
3=
84
24=
21
7=
15
6=
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
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.
So let’s go back to our addition 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?
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
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
Putting it All Together
12×14=18
of the project is completed in a quarter of a day.
Putting it All Together
14×13=112
Each piece is of the original sheet of drywall.
Putting it All Together
====
of the project is completed in a quarter of a day.
Putting it All Together
Putting it All Together
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