ch 1 fractions. add, subtract

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

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Fractions

Examples on the following slides:

Addition and subtraction involving fractions:

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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