ch 1 fractions. add, subtract
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matematika ekonomi soalTRANSCRIPT
CHAPTER 1: FRACTIONS. ADD, SUBTRACT.
© John Wiley and Sons 2013www.wiley.com/college/Bradley © John Wiley and Sons 2013
Essential Mathematics for Economics and Business, 4 th Edition
www.wiley.com/college/Bradley © John Wiley and Sons 2013
Fractions
Examples on the following slides:
Addition and subtraction involving fractions:
© John Wiley and Sons 2013
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Fractions
b
aA fraction is written as follows:
Where a and b may be numbers or symbols
The top line is called the ‘numerator’
The bottom line is called the ‘denominator’
numerator
rdenominato
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Addition or subtraction of fractions
5
4
3
2
7
1
Worked Example 1.3:Simplify the following expression
giving your answer as a single fraction
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Add/Subtract Fractions: See text page 5
5
4
3
2
7
1
Terminology: a common denominator:
In this case the common denominator is 7 3 5, which is the product of the denominators from all three individual fractions
A common denominator is a number or expression that is divisible exactly by the denominator of each individual fraction
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Worked example 1.3 Addition and subtraction of fractions:
5
4
3
2
7
1
Then for each fraction in turn….
1. Divide its denominator into the common denominator
2. Then multiply the result by its numerator (top line)
3. Bring down the sign between this and the next fraction
4. Repeat steps 1, 2 and 3 with the next fraction
Start by writing down the common denominator
Method
537
.................
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First fraction
................................
• The result is 3 5• Then multiply the result by its
numerator (top line).
i.e. 3 5 is multiplied by 1
Enter this answer as shown opposite • Bring down the sign ( + in this case)
and continue
7
537
7
1 Numerator
Denominator
Divide its denominator (7) into the common denominator (7 3 5)5
4
3
2
7
1
53
]537[
...............).........53(
]537[
........................)53(
Common denominator
537
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Second fraction
537
.........................)53(5
4
3
2
7
1
• then multiply the result by its numerator (top line) i.e. 7 5 is multiplied by 2. Enter this result as shown opposite.
• Bring down the sign ( - in this case) and continue
3
2 Numerator
Denominator
573
537
Divide its denominator into the common denominator
Method…
537
........)257()53(
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Third fraction
537
)437()257()53(5
4
3
2
7
1
• Then multiply the result by its numerator (top line)
• i.e. 7 3 is multiplied by 4
5
4
375
537
Numerator
Denominator
Common denominator
Divide its denominator into the common denominator
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Simplify
537
4)37(2)57(5)(3
5
4
3
2
7
1
537
847015
105
1
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Add/Subtract Fractions involving x
5
4
3
2
7
xxx
Example: Simplify the following expression, giving your answer as a single fraction
In this case the common denominator is 7 3 5 ..the product of all individual denominators
First take a common denominator.
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To add or subtract fractions: example
5
4
3
2
7
xxx
1. Divide its denominator into the common denominator
2. Then multiply the result by its numerator
3. Bring down the sign between this and the next fraction
4. continue on to the next fraction
continued-
For each ìndividual fraction in following expression….
Method…
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First fraction
]537[
....................................
• The result is 3 5• Then multiply the result by its
numerator (top line).
i.e. 3 5 is multiplied by x• Bring down the sign between this
and the next fraction ( + in this case) and continue
7
537
7
x Numerator
Denominator
Divide its denominator (7) into the common denominator (7 3 5)
5
4
3
2
7
xxx
53
]537[
........................)53(
x
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Second fraction
537
................)53(
5
4
3
2
7
x
xxx
• then multiply the result by its
numerator (top line)
i.e. 7 5 is multiplied by 2x
• Bring down the sign between this
and the next fraction ( - in this case)
and continue
3
2x Numerator
Denominator
573
537
Divide its denominator into the common denominator
537
........)257()53(
xx
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Third fraction
537
........)257()53(5
4
3
2
7
xx
xxx
• Then multiply the result by its numerator (top line)
• i.e. 7 3 is multiplied by 4x
5
4x
375
537
Numerator
Denominator
Divide its denominator into the common denominator
537
)437()257()53(
xxx
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Simplify
105
537
847015
537
)437()257()5(3
5
4
3
2
7
x
xxx
xxxxxx
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Add/Subtract Fractions
xxx 5
4
3
2
7
1
Example: Write the following expression as a single fraction
Take a common denominator
In this case the common denominator is
7 3 5 x
NOTE: this is NOT the product of all denominators
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Add/Subtract Fractions
xxx 5
4
3
2
7
1
1. divide its denominator into the common denominator
2. then multiply the result by its numerator
3. insert sign between this and the next fraction
4. continue on to the next fraction
For each fraction
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First fraction
]537[
........................5
4
3
2
7
1
x
xxx
the result is 3 5
• then multiply the result by its numerator (top line). i.e. 3 5 is multiplied by 1
• bring down the + sign and continue.
x
x
7
537
7x
1 Numerator
Denominator
common denominator
divide its denominator(7x) into the
common denominator:7 3 5 x x
53
]537[
........................)53(
x
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Second fraction
x
xxx
537
.......................)53(5
4
3
2
7
1
• Then multiply the result by its numerator (top line) i.e. 7 5 is multiplied by 2
• Bring down the sign( - in this case) and continue to the next fraction
x3
2 Numerator
Denominator
Common denominator
573
537
x
x
Divide its denominator into the
common denominator
x
537
...)257()53(
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Third fraction
x
xxx
537
)257()53(5
4
3
2
7
1• divide its denominator into
the common denominator
• then multiply the result by its numerator (top line)
• i.e. 7 3 is multiplied by 4
x5
4
375
537
x
x
Numerator
Denominator
Common denominator
x
537
)437()257()53(
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Simplify
x
x
xxxx
105
1
537
847015
537
4)37(2)57(5)(3
5
4
3
2
7
1
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Add/Subtract Fractions
5
4
3
2
7
1
x
x
Example: Simplify the following expression into a single fraction
Take the common denominator.
In this case the common denominator is
7 3 5 x
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Add/Subtract Fractions
5
4
3
2
7
1
x
x
1. divide its denominator into the common denominator
2. then multiply the result by its numerator
3. insert sign between this and the next fraction
4. Continue on to the next fraction
For each separate fraction in question,
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First fraction
]537[
............................................5
4
3
2
7
1
x
x
x
• the result is 3 5• then multiply the result by its
numerator (top line). i.e. 3 5 is multiplied by 1
• insert sign between this and the next fraction ( + in this case)
7x
1 Numerator
Denominator
537
537
x
x
divide its denominator (7) into
the common denominator (7 3 5 x)
]537[
...................................)53(
x
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Second fraction
x
x
x
537
....................................)53(5
4
3
2
7
1
• then multiply the result by its numerator (top line)
i.e. 7 5 × x is multiplied by 2x
• Write in the result and bring down the sign and continue
3
2x Numerator
Denominator
xx
573
537
divide its denominator into the common denominator
]537[
...................)257()53(
x
xx
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Third fraction
x
xxx
x
x
537
)437()257()53(5
4
3
2
7
1
• divide its denominator into the common denominator
• then multiply the result by its numerator (top line)
• i.e. 7 3 x is multiplied by 4
5
4
xx
375
537
Numerator
Denominator
Common denominator
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Simplify
x
xx
x
xx
x
xxxx
x
105
847015
537
847015
537
4)37()257(5)(3
5
4
3
2
7
1
2
2