Fractions

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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
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Starter Questions
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Percentages
Learning Intention
Success Criteria

1. To understand the process of calculating a
   percentage of a quantity.

1. To understand how to find a percentage of a
   quantity.

1. Be able to calculate percentages of a quantity.

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1. Show all your working.

4
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
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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
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Link between Fractions Decimal Percentages
S4 General
Now try Exercise 1A 1B and 2A Ch3 (page 34)
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Starter Questions
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PercentageIncrease / Decrease
Learning Intention
Success Criteria

1. To understand the process of calculating
   percentage increase / decrease.

1. To understand how to work out percentage increase
   / decrease.

1. Be able to calculate percentage increase /
   decrease of a quantity.

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1. Show all your working.

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Calculating Percentages
S4 General
You need to know the following rule
To calculate the percentage increase or decrease
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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
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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
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Percentage Increase
S4 General
Now try Exercise 2B Ch3 (page 37)
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Starter Questions
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Percentages
Learning Intention
Success Criteria

1. To be able to convert between fraction decimals
   and percentages.

1. 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.
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Fractions, Decimals and Percentages
0.8
0.2
0.4
0.6
20
40
80
60
Just different ways of saying the same thing.
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0.5
0.3
0.7
10
30
60
80
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0.7
0.3
70
30
20
0.6
0.4
60
40
21
0.5
0.5
50
50
22
0.9
0.1
90
10
23
0.6
0.4
70
30
24
0.6
0.4
80
20
25
0.3
0.7
60
40
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0.3
0.7
70
30
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Link between Fractions Decimal Percentages
S4 General
Now try Exercise 3A 3B Ch3 (page 38)
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Starter Questions
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Mixed Fractions
Learning Intention
Success Criteria

1. To know what the terms fraction, top-heavy and
   mixed fraction are.

• To understand the
• term Fraction and Mixed Fraction.

1. Convert between top-heavy and mixed fraction.

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1. Solve problems involving fractions.

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Fraction Reminder
S4 General
A Fraction consists of 2 parts.
Top number called the NUMERATOR
Bottom number called the DENOMINATOR
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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
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Fractions
S4 General
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Top Heavy to Mixed
S4 General
means seven thirds
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Top Heavy to Mixed
S4 General
NUMERATOR ? DENOMINATOR
can be written as 7 ? 3
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Top Heavy to Mixed
S4 General
NUMERATOR ? DENOMINATOR
can be written as 17 ? 5
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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
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Mixed Fractions
S4 General
Now try Exercise 4 Ch3 (page 39)
38
Starter Questions
5cm
7cm
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Add / Sub Fractions
Learning Intention
Success Criteria

1. 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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1. To be able to do simple fraction calculations.

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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
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Add Fractions
S4 General
When dealing with mixed fractions deal with
whole part first then the fraction part
Change to mixed fraction
42
Subtract Fractions
S4 General
When dealing with mixed fractions deal with
whole part first then the fraction part
simplify fraction
43
Add / Sub Fractions
S4 General
Now try Ex 5A Ch3 (page 40)
44
Starter Questions
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45
Harder Fractions
Learning Intention
Success Criteria

1. Find the LCM of two denominators.

1. To understand how to add and subtract fractions
   with different denominators.

1. Convert fractions to equivalent fractions.

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1. Add / Sub fractions.

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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
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Harder Fractions
S4 General
Example 1
M2 2,4
M4 4
LCM 4
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Harder Fractions
S4 General
Example 2
LCM 30
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Harder Fractions
S4 General
Example 3
LCM 12
Change to mixed fraction
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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
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Harder Fractions
S4 General
Example 1
Change to mixed fraction
LCM 6
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Harder Fractions
S4 General
Example 2
LCM 24
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Harder Fractions
S4 General
Example 3
LCM 12
Change to mixed fraction
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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
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Harder Fractions
S4 General
LCM 12
We cannot subtract
write 4 as
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Harder Fractions
S4 General
LCM 15
We cannot subtract
write 6 as
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Harder Fractions
S4 General
Now try Ex 5B Ch3 (page 41)
58
Starter Questions
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Multiplying Fractions
Learning Intention
Success Criteria

1. To know the simply rules for multiplying basic
   and mixed fractions.

1. To show how to multiply basic and mixed
fractions.

1. Calculate fractions.

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60
Multiplying Fractions
S4 General
Multiply basic fractions
1. Multiply the numerators
2. Multiply the denominators
Example 1
Example 2
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Multiplying Fractions
S4 General
Now try Ex 6A Ch3 (page 42)
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Multiplying Fractions
S4 General
Multiplying Mixed Fractions

1. Make fractions top-heavy

2. Multiply the numerators
3. Multiply the denominators
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Multiplying Fractions
S4 General
Example 1
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Multiplying Fractions
S4 General
Example 2
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Multiplying Fractions
S4 General
Now try Ex 6B Ch3 (page 43)
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Starter Questions
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Dividing Fractions
Learning Intention
Success Criteria

1. To know the simply rules for dividing basic and
   mixed fractions.

1. To show how to divide basic and mixed
fractions.

1. Calculate fractions.

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68
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
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Dividing Fractions
S4 General
Easy rule to remember is
Example 1
Example 2
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Dividing Mixed Fractions
S4 General
For mixed fractions YOU MUST make them top-heavy
first !!
Example 1
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Dividing Fractions
S4 General
Example 2
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Dividing Fractions
S4 General
Now try Exercise 7B Ch3 (page 44)