21-Aug-14 Compiled by Mr. Lafferty Maths Dept. Fractions Simplifying Fractions Fractions of a quantity Finding (Simple) Percentages

11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.

FractionsFractionsw

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Simplifying Fractions

Fractions of a quantity

Finding (Simple) Percentages

More Simple Percentages

Reminder of Mixed Fractions

Add & Subtract Fractions

Multiplying Fractions

General


1. Find the missing value

2. I f you know the length of the side of a square describe in words how to calculate the perimeter.

3. 4x + 10 = 46

3 ?=4 20

Starter Starter QuestionsQuestions

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General


FractionsFractionsw

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1.1. To know what the terms To know what the terms fraction.fraction.

1. To understand theterm Fraction and be able to simplify fraction.

2.2. Be able to simply fractions.Be able to simply fractions.

General

11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww

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Top number is called the numerator

Bottom number is called the denominator

FractionsFractions

The denominator tells us the type of fraction we have

The numerator tells us the how many we have

General


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Write down the fraction that is shaded in light blue.

24

36

FractionsFractionsGeneral


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fraction that you have by multiplying the numeratorand the denominator by any number.

24

15

Find a fraction equivalent to :

x3

x3

612

210

x2

x2



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between the numerator and denominator.

24

312

Simplify the fractions below :

÷2

÷2

12

14

÷3

÷3



Now try Ex 1Ch11(page 126)

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2. Simplify

3. 8.52 + 4.6

4.

25150

1 of 2355

6cm

10cm

General


Fractions of a Fractions of a quantityquantity

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1.1. To know the 2 step for To know the 2 step for finding a fraction of a finding a fraction of a quantity.quantity.

1. To explain the 2 step process of finding a fraction of a quantity.

2.2. Be able to calculate the Be able to calculate the fraction of a quantity.fraction of a quantity.

General


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12


of 12014

of 120

Simply divide by the bottom number

602 120

304 120

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23


of 24

Simply divide by the bottom numberThen multiply the answer by top number

83 24 8 x 2 = 16Step 1: Step 2:

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58


of 360

Simply divide by the bottom numberThen multiply the answer by top number

458 360 45 x 5 = 225Step 1: Step 2:

General


Now try Ex 2Ch11 (page 126)

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General



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of 120

1. Find the LCM of 2 and 3

2. Find HCF of 4 and 1

3. Find

4. Simplify

45

85200

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1.1. Calculate basic simple Calculate basic simple percentages.percentages.

1. To understand how to calculate simple percentages without a calculator. 2.2. Show all working.Show all working.

Simple Simple PercentagesPercentages

General


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Copy down and learn the following basic percentages

Simple Simple PercentagesPercentages

100% 50%1

33 %3 25% 20% 10% 5% 1%

112

13

14

15

110

120

1100

General


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Q. Find 25% of £40

PercentagesPercentages

1 40

4

40 ÷4 =10

General


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Q. Find 5% of £300


1 300

20

300 ÷20 =15

General



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General



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75200

1. Calculate 1200 300

2. Simplify

3. Find 10% of 65

4. Find LCM and HCF for 7 and 35

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1.1. To know the basic To know the basic percentages.percentages.

1. To explain some more basic percentages.

2.2. Calculate basic percentage Calculate basic percentage without a calculator.without a calculator.

Extended Extended PercentagesPercentages

General


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Copy down and learn the following basic percentages

100% 50%1

33 %3

266 %

3 20% 40%60% 80%

112

13

23

15

25

35

45

10% 30%70% 90%

110

310

710

910


General


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Q. Find 30% of £40

3 40

10

40 ÷10 x 3 =12


General


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Q. Find 75% of £600

3 600

4

600 ÷4 x 3 =450


General



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General



1. Solve the inequality 4x+5>29

2. Calculate 3+(- 10)+(- 7)

3. Simplify the fraction 4

200

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General


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1.1. To know that to add and To know that to add and subtract fractions the subtract fractions the denominators must be denominators must be the same.the same.

1. To understand how toadd and subtract basic fractions.

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

Add / Sub FractionsGeneral

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w.m

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35

Top number is called the numerator

Bottom number is called the denominator

FractionsFractions

The denominator tells us the type of fraction we have

The numerator tells us the how many we have

General

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FractionsFractions

A fraction, like, where the numerator is bigger

than the denominator is called a ‘Top-Heavy’ fraction.

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A number like, consisting of

a ‘whole number’ part and a ‘fraction’ part is called a Mixed fraction

35

4

General

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Top Heavy to Top Heavy to MixedMixed

means seven thirds73

7 1 1 1 1 1 1 13 3 3 3 3 3 3 3

7 3 3 13 3 3 3

7 12

3 3

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NUMERATOR DENOMINATOR


can be written as 7 373

23 7

remainder 1

12

3

General

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NUMERATOR DENOMINATOR


can be written as 17 5175

35 17

remainder 2

23

5

General

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Changing a mixed fraction to a top-heavy.

WHOLE NUMBER DENOMINATORthen add NUMERATOR

5 4 3

7 5 2

Mixed to Top Mixed to Top HeavyHeavy

35

4

27

5

234

375

23 quarters

37 fifths

General

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Examples

1 37 7

47

General

8 79 9

19

3 15 3

7 7

48

7

3 115 4

7 7

211

7

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Examples

6 37 7

97

General

9 715

11 11

1615

11

217

516

11

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Add / Sub Fractions

You can only add or subtract fractions if:

DENOMINATORS ARE THE SAME NUMBER

Example 1 Example 2

3 27 7

7 18 8

57

68

34

General

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Add Fractions

When dealing with mixed fractions deal with ‘whole’ part first then the fraction part

3 42 1

5 5

3 42 1

5 5

73

5

24

5

General

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Subtract Fractions


5 1

7 46 6

5 1

7 4 6 6

43

6

23

3

General

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Now tryExtension BookletEx 5E (page 46)

Mixed FractionsMixed FractionsGeneral

Starter QuestionsStarter Questions


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2. Simplify ?

3. Write 2% as a decimal

4. List the prime numbers between 20 and 30

5. Calculate

1284

7 5+2 2

5cm

7cm

General



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(2 3 4)

4 149 9

y y x

1. Calculate

2. Expand

3. Write 72% as a decimal

4. Find the LCM of 2 and 3

5. 2.5% of £600

General

Harder FractionsHarder Fractions


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1.1. Apply ‘ rules for adding and Apply ‘ rules for adding and subtracting fractions.subtracting fractions.

1. To understand how to add and subtract fractions with different denominators. 2.2. Simplify fractions.Simplify fractions.

General

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MTH 3-07bMTH 3-07cMTH 4-07b



How can we add or subtract fractions that have different denominators

Step 1 : Find the LCM for the denominators

Step 2 : Convert to equivalent fractions

Step 3 : Add or Subtract the numerator and simplify

Before we can add or subtract they MUST

have the same denominator

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2 4



Example 1

Step 1 : Find LCM

Step 2 : Equivalent Fractions

Step 3 : Add/Subtract the numerator

and simplify


LCM of 2 and 4

4

4 4+2 1

43

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1225

5 26 5



Example 1

Step 1 : Find LCM



and simplify


LCM of 5 and 6

30

30 30-

1330

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1820

5 36 4



Example 1

Step 1 : Find LCM



and simplify


LCM of 4 and 6

24

24 24+

3824

1912

= =7

121

112 19 R7

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How can we add /subtract mixed fractions that have different denominators


Simple !

General

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1 22 3

2 3

1 22 3


5

43

1 22 3

6 6+

16

1

16

1= 5 +

16

= 6 76

=

LCM of 2 and 3

61

6 7 R1

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7 2

7 48 3

7 28 3


3

1621

7 28 3

24 24-

524

524

= 3 +

524

= 3 =

LCM of 8 and 3

24

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3 5

44 6

3 54 6


4

109

3 54 6

12 12+

712

1

712

1= 4 +

712

= 5 1912

=

LCM of 4 and 6

121

12 19 R7

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Most Difficult Most Difficult FractionsFractions

1 2

6 24 3

1 24 3


4

83

1 24 3

12 12-= 4 +

712

= 3 =

LCM of 4 and 3

12

512

-

512

-

= 45

12-

Adding a negative is the

same as subtracting

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Most Difficult Most Difficult FractionsFractions

1 2

7 15 3

1 25 3


6

103

1 25 3

15 15-= 6 +

815

= 5 =

LCM of 5 and 3

15

715

-

715

-

= 67

15-

Adding a negative is the

same as subtracting

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Now try Extension Booklet

Ex 6E (page 48)

Multiplying Multiplying FractionsFractions

General

Starter QuestionsStarter Questions


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4 , 3 2

5

3 14 3

2

56

1. Calculate

2. I f . Find

3. Calculate 60% of £360

4. Make the following top- heavy

x y and z z xy

General



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1.1. To know the simply rule To know the simply rule for multiplying basic for multiplying basic fractions.fractions.

1. To show how to multiply basic fractions.

2.2. Apply fraction rules Apply fraction rules correctly.correctly.

General

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Example 1 Example 2

Multiply basic fractions

3 34 5

9

20

4 55 6

2030

23

1. Multiply the numerators

2. Multiply the denominators


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Example 3 Example 4

Multiplying basic fractions

32

5

2 31 5

65

4 21 3

2

43

83

2

23

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1. Make fractions top-heavy

Multiplying Mixed Fractions




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1 13 1

2 3

7 42 3

286

4

46

Example


2

23




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3 1

4 14 5

19 64 5

11420

14

520

Example


7

510




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Now try Extension Booklet

Ex 7E (page 50)


General

Documents

21-Aug-14 Compiled by Mr. Lafferty Maths Dept. Fractions Simplifying Fractions Fractions of a quantity Finding (Simple) Percentages