8-Jun-15Compiled by Mr. Lafferty Maths Dept. Fractions What is a Fraction Fractions of origin amount Percentage (Fraction by another

18 Apr 202318 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.

FractionsFractionsw

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What is a Fraction

Fractions of origin amount

Percentage (Fraction by another name)

Conversion between F, D ,%

Equivalent Fractions

Using Percentages

Proper Fractions and mixed numbers

Ratios


Level E Starter QuestionsLevel E Starter Questionsw

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with length 3 cm.

2. 4.56 + 2.36 - 1.2

3. Find an equivalent fraction

with denominator 100 for .1

20


PercentagesPercentagesw

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1.1. To understand the term To understand the term percentage.percentage.

1. We are learning what the term percentage means and how it is connected to fractions.

2.2. Understand connection Understand connection between percentages, and between percentages, and fractions.fractions.

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PercentagesPercentages

It is common to express fractions using a denominator of a 100

31100

means 7 % 7

100

31 out of a 100

7 out of a 100

means 31 %

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Q. Write down the following as a fraction and a decimal.

27%


27100

27 100 0.27

15%15100

15 100 0.15

2%2

100 2 100 0.02

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Covert these percentages to fraction and simply.


15

20100

20%

34

75100

75%

35

60100

60%

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Covert these fractions to percentages


110

1 10 100 10%

320

3 20 100 15%

45

4 5 100 80%

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Sandra got 15 out of 20 in an maths exam.What percentage is this.


1520

15 20 100 75%

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Franchesca got 45 out of Sandra 60 mathsand Drew got 21 out of 30 in an English exam.Who got the best result.


4560 45 60 100 75%2130 21 30 100 70%

Franchesca has the best

result.

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Now try Ex 1Page 41

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15

100

1. Calculate 45.6 x 7

2. Simplify

3. Change 20% to a fraction

4. Find highest number divides both 4 and 20 without leaving a remainder

18 Apr 202318 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww

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1.1. Learn rules for Learn rules for converting between converting between percentages fractions percentages fractions and decimals.and decimals.

1. To understand how to convert between percentages, fractions and decimals.

Fractions Fractions Percentages Percentages

DecimalsDecimals

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Copy triangle and use it to convert between fraction decimals and percentages


DecimalsDecimals

100

Percentage (P%)Common Fraction a

b

Decimal Fraction

a b

%100P

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Now try Ex 6.1Page 341

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DecimalsDecimals



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75200

1. Calculate 1200 300

2. Simplify

3. Find of 65

4. Find highest number that divides both 14 and 35 without leaving a remainder.

110


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1.1. To know the fractions of To know the fractions of basic simple percentages.basic simple percentages.

1. To explain some simple percentages.

2.2. Calculate simple Calculate simple percentage mentally.percentage mentally.

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Copy down and learn the following basic percentages


= one half

= one tenth

= half of 10%

50%

10%

5%

2

10

10 then 2

= one hundredth1% 100

= half of 1 %0.5% 100 then 2

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Q. Find 16% of £40


10%

5%

40 10 4.00

= 4 2 2.00

1% 40 100 0.40

16% £ 6.40

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Remember money 2 decimal places

Q. Find 17% of £450

PercentagesPercentagesof means MULTIPLY

Calculator Keys

1 1 x 4 = 76.57 0 0 5 0

17450

100

17 100 450

£ 76.50

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Remember money 2 decimal places

Q. Find 4% of £70

PercentagesPercentagesof means

times

Calculator Keys

1 x 7 = 2.84 0 0 0

470

100

4 100 70

£ 2.80

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Now try Ex8.1

Page 345


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Q. Find 17.5% of £1200


10%

5%

1200 10 120

= 120 2 60

2.5% 60 2 30

17.5% £ 210

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Now try Ex 8.2

Page 346




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65

100

1. Calculate 11% of 150

2. Simplify

3. Find of 64

4. Find highest number that divides both 10 and 45 without leaving a remainder.

34


Proper Fractions Proper Fractions and Mixed Numbersand Mixed Numbers

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1.1. To know To know the terms proper fraction, mixed number and improper fraction.

1. To explain the terms proper fraction, mixed number and improper fraction and convert between them.

2.2. Convert between improper Convert between improper fraction and mixed fraction and mixed number.number.

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How many halves are there in 1

22

=

52

12

2 =

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Is called a proper fraction. ( Numerator is less than denominator )

12

52

12

2Is called a mixed fraction. ( whole number and a fraction )

Is called a improper fraction. ( Numerator bigger than denominator )

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Converting mixed fractions to improper fractions

32 =

44 2 + 3

4 11

= 4

71 =8

1 8 + 78

15=

8

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Other way round improper fractions to mixed fractions

7=

2

3 12 7 and lef t over

2

1= 3

2

11=

5

2 15 11 and lef t over

5

1= 2

5

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Now try Ex 9.1

Ch15 page 348




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45

100

1. Change to mixed number

2. Simplify

3. Find of 35

4. Change to a improper fraction 4

174

25

37



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1.1. Convert between decimal Convert between decimal fractions and mixed fractions and mixed numbers.numbers.

1. To explain how to convert between decimal fractions and mixed numbers.

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Mixed number to decimal fraction

34

= 0.75

6.75

36

4

Just convert fraction part to

decimal

12

= 0.5

4.5

14

2

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Decimal fraction to mixed number

0.55

= 101

32

3.5

0.1515

= 1003

720

7.15

1=

23

= 20

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Now try Ex 9.2

Ch15 page 349



Starter QuestionsStarter Questionsw

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2. Calculate 20% of 220

(a) 123 (b) 250 (c) 59

1. Find x when x + 5 = 17

3. Round to the nearest 100

4. Convert 0.05 to a percentage and then to a fraction

Level E

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RatiosRatios

Ratios can be used to compare different quantitiesRatios can be used to compare different quantities

What is a ratio ?

Example : There are 2 triangles and 3 rectangles.

The ratio of triangles to rectangles is said to be 2 : 3

Note: The ratio of rectangles to triangles is said to be 3 : 2

Level E

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RatiosRatios

Simplifying a ratio is like simplifying fractionsSimplifying a ratio is like simplifying fractions

Simplifying a ratio ?

Fraction :÷2

÷2

6 6 3= =

8 8 4

Ratio : ÷2 ÷26 : 8 = 6 : 8 = 3 : 4

Level E

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Now try Ex 10.1

Page 351

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RatiosRatiosSimplifying a ratio ?Level E


Starter QuestionsStarter Questionsw

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2. Write 0.12 as a percentage

1230

(a) 0.13 (b) 0.02 (c) 1.09

1. 15% of 50

3. Round to 1 decimal place

4. Simplify fraction

Level E


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1.1. Use tabulating method Use tabulating method to work out ratios.to work out ratios.

1. To show how to do ratio calculations.

RatiosRatios

2.2. Show appropriate Show appropriate working.working.

Ratio CalculationsLevel E

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RatiosRatiosRatio Calculations

Example : The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there.

boys girls

4 5

16 20x 4 x 4

Level E

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RatiosRatiosRatio Calculations

Example : The ratio of cars to buses is 3:7. If there are 49 buses, how many cars are there.

cars buses

3 7

21 49x 7 x 7

Level E

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Now try Ex 11.1

Page 352

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RatiosRatiosRatio CalculationsLevel E

Documents

8-Jun-15Compiled by Mr. Lafferty Maths Dept. Fractions What is a Fraction Fractions of origin amount Percentage (Fraction by another