Fractions

Calculating Percentages and Fractions

Percentage Rise and Fall.

Link between Fraction, Decimals and Percentages

Reminder and Mixed Fractions

Add Subtract basic Fractions

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Add Sub Harder Fractions

Multiplying Fractions

Dividing Fractions

Starter Questions

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Percentages

Learning Intention

Success Criteria

- To understand the process of calculating a

percentage of a quantity.

- To understand how to find a percentage of a

quantity.

- Be able to calculate percentages of a quantity.

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- Show all your working.

Fraction Percentages

Revision Put the fractions in the right box.

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Fraction Percentages

Q. Find 30 of 40

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Step 1 Divide by 10

40 10 4

Step 2 Multiple by 3

4 x 3 12

Fraction Percentages

Q. Find 15 of 300

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Step 1 Divide by 100

300 100 3

Step 2 Multiply by 15

3 x 15 45

Link between Fractions Decimal Percentages

S4 General

Now try Exercise 1A 1B and 2A Ch3 (page 34)

Starter Questions

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PercentageIncrease / Decrease

Learning Intention

Success Criteria

- To understand the process of calculating

percentage increase / decrease.

- To understand how to work out percentage increase

/ decrease.

- Be able to calculate percentage increase /

decrease of a quantity.

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- Show all your working.

Calculating Percentages

S4 General

You need to know the following rule

To calculate the percentage increase or decrease

Calculating Percentages

S4 General

Example 1 Daniel was paid 20 per week. He got

a wage rise to 22 per week. What was his

percentage increase in pay ?

A

Actual Increase 22 - 20 2

increase

B

Calculating Percentages

S4 General

Example 2 A house in Barlanark bought for 40

000 in 2001 was sold last week for 50 000.

Calculate the percentage increase in value?

A

Actual Increase 50 000 - 40 000 10 000

increase

B

Percentage Increase

S4 General

Now try Exercise 2B Ch3 (page 37)

Starter Questions

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Percentages

Learning Intention

Success Criteria

- To be able to convert between fraction decimals

and percentages.

- To understand the connection between Fractions

Decimals and Percentages.

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Fractions, Decimals and Percentages

0.5

0.7

0.8

0.1

0.2

0.3

0.4

0.6

0.9

70

90

20

30

40

50

80

10

60

Just different ways of saying the same thing.

Fractions, Decimals and Percentages

0.8

0.2

0.4

0.6

20

40

80

60

Just different ways of saying the same thing.

0.5

0.3

0.7

10

30

60

80

0.7

0.3

70

30

0.6

0.4

60

40

0.5

0.5

50

50

0.9

0.1

90

10

0.6

0.4

70

30

0.6

0.4

80

20

0.3

0.7

60

40

0.3

0.7

70

30

Link between Fractions Decimal Percentages

S4 General

Now try Exercise 3A 3B Ch3 (page 38)

Starter Questions

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Mixed Fractions

Learning Intention

Success Criteria

- To know what the terms fraction, top-heavy and

mixed fraction are.

- To understand the
- term Fraction and Mixed Fraction.

- Convert between top-heavy and mixed fraction.

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- Solve problems involving fractions.

Fraction Reminder

S4 General

A Fraction consists of 2 parts.

Top number called the NUMERATOR

Bottom number called the DENOMINATOR

Fractions

S4 General

We can sometimes simplify a fraction by

dividing by the HCF of the numerator and

denominator

F15 1 and 15 3 and 5

F27 1 and 27 3 and 9

Fractions

S4 General

Top Heavy to Mixed

S4 General

means seven thirds

Top Heavy to Mixed

S4 General

NUMERATOR ? DENOMINATOR

can be written as 7 ? 3

Top Heavy to Mixed

S4 General

NUMERATOR ? DENOMINATOR

can be written as 17 ? 5

Mixed to Top Heavy

S4 General

WHOLE NUMBER ? DENOMINATOR then add NUMERATOR

Changing a mixed fraction to a top-heavy.

5 ? 4 ? 3

? 23 quarters

7 ? 5 ? 2

? 37 fifths

Mixed Fractions

S4 General

Now try Exercise 4 Ch3 (page 39)

Starter Questions

5cm

7cm

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Add / Sub Fractions

Learning Intention

Success Criteria

- To know that to add and subtract fractions the

denominators must be the same.

- To understand how to
- add and subtract basic fractions.

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- To be able to do simple fraction calculations.

Add / Sub Fractions

S4 General

You can only add or subtract fractions if

DENOMINATORS ARE THE SAME NUMBER

THEN ADD THE NUMERATORS

Example 1

Example 2

Add Fractions

S4 General

When dealing with mixed fractions deal with

whole part first then the fraction part

Change to mixed fraction

Subtract Fractions

S4 General

When dealing with mixed fractions deal with

whole part first then the fraction part

simplify fraction

Add / Sub Fractions

S4 General

Now try Ex 5A Ch3 (page 40)

Starter Questions

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Harder Fractions

Learning Intention

Success Criteria

- Find the LCM of two denominators.

- To understand how to add and subtract fractions

with different denominators.

- Convert fractions to equivalent fractions.

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- Add / Sub fractions.

Harder Fractions

S4 General

How can we add /subtract fractions that have

different denominators

Step 1 Find the LCM of the denominators

Step 2 Change denominators to LCM

Step 3 Add/Subtract the numerators

Harder Fractions

S4 General

Example 1

M2 2,4

M4 4

LCM 4

Harder Fractions

S4 General

Example 2

LCM 30

Harder Fractions

S4 General

Example 3

LCM 12

Change to mixed fraction

Harder Fractions

S4 General

How can we add /subtract mixed fractions that

have different denominators

Step 1 Add/Subtract whole numbers

Step 2 Find the LCM.

Step 3 Change denominators to LCM

Step 4 Add/Subtract the numerators

Harder Fractions

S4 General

Example 1

Change to mixed fraction

LCM 6

Harder Fractions

S4 General

Example 2

LCM 24

Harder Fractions

S4 General

Example 3

LCM 12

Change to mixed fraction

Harder Fractions

S4 General

Step 1 Subtract whole numbers

Step 2 Find the LCM

Step 3 Change denominators to LCM

Step 4 Subtract the numerators

Harder Fractions

S4 General

LCM 12

We cannot subtract

write 4 as

Harder Fractions

S4 General

LCM 15

We cannot subtract

write 6 as

Harder Fractions

S4 General

Now try Ex 5B Ch3 (page 41)

Starter Questions

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Multiplying Fractions

Learning Intention

Success Criteria

- To know the simply rules for multiplying basic

and mixed fractions.

1. To show how to multiply basic and mixed

fractions.

- Calculate fractions.

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Multiplying Fractions

S4 General

Multiply basic fractions

1. Multiply the numerators

2. Multiply the denominators

Example 1

Example 2

Multiplying Fractions

S4 General

Now try Ex 6A Ch3 (page 42)

Multiplying Fractions

S4 General

Multiplying Mixed Fractions

- Make fractions top-heavy

2. Multiply the numerators

3. Multiply the denominators

Multiplying Fractions

S4 General

Example 1

Multiplying Fractions

S4 General

Example 2

Multiplying Fractions

S4 General

Now try Ex 6B Ch3 (page 43)

Starter Questions

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Dividing Fractions

Learning Intention

Success Criteria

- To know the simply rules for dividing basic and

mixed fractions.

1. To show how to divide basic and mixed

fractions.

- Calculate fractions.

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Dividing Fractions

S4 General

It is almost impossible to divide fractions like

by actually dividing.

Instead we change it into a multiplication by

Always 1

Dividing Fractions

S4 General

Easy rule to remember is

Example 1

Example 2

Dividing Mixed Fractions

S4 General

For mixed fractions YOU MUST make them top-heavy

first !!

Example 1

Dividing Fractions

S4 General

Example 2

Dividing Fractions

S4 General

Now try Exercise 7B Ch3 (page 44)