1. Understand and use fractions, decimals and percentages
GCSE Maths Lesson 4
Understand and use fractions, decimals and percentages

3. What did we do last week?

4. What do these inequalities say
What do these inequalities say? What integer values satisfy the inequality?

5. Have you done your homework?

6. -5 20 -10 -8 6 -16 -23 -14 9 The number in the centre equals = -5 + -3
The number that goes in the top right box is 5 less than -5
The number in the bottom left is -3 x -3
The number in the top left is the number in the centre x -1 add -13
The number in the middle of the bottom row is 6 less than the number above it
There is a number 6 in one of the middle row boxes
There is a number equal to -4 x -5 next to the box containing -5
When you add up the numbers in the right hand column you get -27
The number below -5 is -6-10

7. What are we going to do today?
Catch up with Primes, Factors, Prime Factors etc!!
Fractions
Order fractions
Find a fraction part of a quantity
The four operations: + - x ÷
Percentages
Find a percentage part of a quantity
Write one value as a percentage of another value
Percentage increase and decrease (simple/compound interest)
Reverse percentages
Convert between fractions, decimals and percentages

8. What is a ……..
Factor
Multiple
Prime

9. Prime Numbers A prime number has exactly two factors – one and itself
One is not a prime number because it has only one factor – itself
Two is the first prime number
Two is the only even prime number

10. From these numbers: 1 3 8 12 16 20 13 15 2 17 24 6 Write down
Write down
4 prime numbers
all the factors of 6
any multiples of 4

11. Square numbers √ Square Square root Square Square root Area = 3 x 3
= 3² 3 9 =9
Square root √
Area =
4 x 4
Square
= 4² 4 16
Square root
= 16

12. cube numbers cube cube Cube root Cube root Volume = 3 x 3 x 3 Volume =
= 3³
= 4³
cube
= 27
cube
= 64 4 64 3 27
Cube root
Cube root

13. Can you answer these questions?
What is the square of 5? What is the square root of 36? Is there another one? What is the cube of 2? What is the cube root of 125? What are the powers of 10?

14. From these numbers: 121 49 20 19 800 1000 5 Find two square numbers
Find
two square numbers
a cube number
the square root of 400
the cube root of 125

15. 90 Prime factors Then with powers Over to you – prime factors of 84?
With powers only when in index form

16. 84

17. Fractions Finding a fraction part Equivalent fractions & simplifying
Ordering fractions
Adding and Subtracting fractions
Multiplying and Dividing fractions

18. Finding a fraction part of a number
You need to remember the following:
Divide by the bottom
THEN
Times by the top

19. Example:
What is of 350 ?
First, divide by the bottom: ÷ 7 = 50
Then, times your answer by the top: x 5 = 250
So of 350 is 250.

20. Your Turn…

21. Can you guess which thing One of these things, it doesn’t belong.
3 8 𝑜𝑓 32
1 2 𝑜𝑓 24
Can you guess which thing
One of these things, it doesn’t belong.
Before I finish my soonnnggg.
One of these things is not like the other thing
is not like the other things
2 5 𝑜𝑓 20
6 7 𝑜𝑓 14

22. 3 8 𝑜𝑓 32
1 2 𝑜𝑓 24
2 5 𝑜𝑓 20
6 7 𝑜𝑓 14

23. Simplify the fractions…
Customers have paid the following amounts to begin to pay off their overdraft. Simplify the fractions below.
£300 paid of £450
£50 paid of £600
£400 paid of £1000
£60 paid of £120
£30 paid of £40
£45 paid of £90
£110 paid of £450

24. ½ = 2 4 = 3 6 = 4 8 = 5 10 Equivalent Fractions
Equivalent means equal to, so equivalent fractions are fractions that are the same.
½ = = = = 5 10
(These could all be simplified to ½ therefore they are equivalent)

26. Ordering fractions - together
We use equivalent fractions to put fractions in order: We find the common denominator and use it to place the fractions in order, smallest to largest

27. Your turn
Using the common denominator place the fractions in order, smallest to largest.

28. A fraction problem to solve together
Anna, Bobby and Cheryl order a large 24 piece pizza. Anna eats 1/6 of the pizza. Bobby has 5 pieces and Cheryl eats a quarter. What fraction of the pizza is left?
9/24
3/8
3/8 is the answer

29. Another fraction problem – “The builder’s day”
A builder works for of a day.
If he sleeps 7 ½ hours per day, what fraction of the day does he have left ?
13/48

30. Yet another – “The TV Programme”
A TV programme lasting an hour has ⅖ of it dedicated to adverts.
The rest of the programme is split equally between current affairs and sport.
How long is spent on Sport ?
18 minutes

31. Adding and Subtracting Fractions
To add or subtract fractions, you need to have a common denominator – both fractions need to have the same value on the bottom. =

32. Or you can use the “kiss & smile” method to add and subtract fractions

33. Your turn

34. Multiplying Fractions
Multiplying fractions is nice and easy – you just multiply across!
3 7 x =

35. Your turn

36. Dividing Fractions
To divide fractions, you first need to flip the second fraction and multiply them.
5 8 ÷ 2 3 =

37. Your turn

38. Percentages Finding a percentage part without a calculator
Finding a percentage part with a calculator
Writing one number as a percentage of the other

39. Without a calculator
Remember how to find the following amounts and you can then work out any percentage:
50% = divide by 2
25% = divide by 2 again
75%?
10% = divide by 10
20%?
5%?
15%?
1% = divide by 100

41. Without a calculator 5% of 350 = 25% of 550 = 40% of 800 =

42. How do you find a percentage with a calculator?
What is 34% of 812?

43. How do you find a percentage with a calculator?
What is 27% of 540?

44. Make some up

45. Writing one number as a percentage of the other
First write it as a fraction and then multiply it by 100 to turn it into a percentage.
Freddie scored 25 out of 40 on his Maths test. What percentage did he get right?

46. Example:
A DVD contains a film and some extra clips. The film lasts 120 mins.
The clips after the main film last an extra 30 mins.
What % of the DVD is taken up with:
(a) the film (b) the clips?

47. Your turn
60/150 x 100 = 40%
= /200 x 100 = 16%
= = /480 x 100 = 33.3%

48. Percentage Increase and Decrease

49. BRITISH GAS INCREASE PRICES BY 15%
Mr and Mrs Jones,
BILL
3 months = £150
BRITISH GAS INCREASE PRICES BY 15%

50. Complete the missing figures
Account holder
Amount from 2013
Increase in profit (%)
Amount in 2014
Person
£5,102
10%
B. Anks
£80, 980
30%
V. Rich
£32, 654 5%
M. Oney
£10, 809 2%
E. Gold
£200, 902
L. Cheque
£4, 598
50%
H. Penny
£17, 858
25%

51. Percentage Profit/Loss
If a value has increased or decreased by an amount and the question asks what this would be as a percentage, this is how you would work it out:
actual increase/decrease x 100
original amount

52. Example:

53. Your turn

54. So how do we convert between fractions, decimals and percentages?
Fractions to decimals? Top of fraction divided by bottom Decimals to percentages? x 100 Fractions to percentages Both of the above, one after the other Decimals to fractions 1 decimal place – over 10 2 decimal places – over 100 etc Percentages to decimals ÷ 100 Percentages to fractions a fraction of 100 and cancel if you can MAKE YOUR OWN NOTES ON THE HOMEWORK SHEET

55. Please can you complete the equivalencies table showing the fraction, decimal and percentage for each amount.

56. Reverse Percentages

57. There is a 20% sale on in Topshop. The bag I want is now £60.
What was the original cost of my bag? % 60

58. In a sale, everything is reduced by 30%
In a sale, everything is reduced by 30%. If an armchair costs £175 in the sale, how much did it cost before the sale? %
175

59. A mouse increases its body weight by 15%
A mouse increases its body weight by 15%. If it now weighs 368g, what was the mouse’s original weight? %
368

60. Compound Interest

61. Definition

62. £2000 earning Compound Interest at 5% per year for 3 years
Original Amount = 100%
Compound Interest = 5%
100% + 5% = 105% = 1.05 3
£2000 x
105%
1.05
= £
This is the total amount including interest: £

64. Mathswatch clip 137
This is based on the method on the previous slide

65. Compound Interest Questions
£10,000 earning Compound Interest at 1% per year for 3 years
£8,650 earning Compound Interest at 2% per year for 5 years
£5,000 earning Compound Interest at 0.5% per year for 4 years
£10,000 earning Compound Interest at 1.5% per year for 6 years
£8,000 earning Compound Interest at 3% per year for 7 years

66. The formula to calculate compound interest is:
A = P x (1 + i)n

67. Help is at hand
Website of the week

68. All working must be shown
It’s Quiz Time!
Teams of 2 or 3 please
All working must be shown
The round/question will tell you whether or not a calculator is permitted
Any team caught using a calculator on a non-calculator question/round will be deducted 5 points

69. Fractions
13 marks available

70. Question 1

71. Question 2

72. Question 3

73. Question 4

74. Question 5

76. Percentages
17 marks available

77. Question 1

78. Question 2

79. Question 3
(3 marks)

80. Question 4

81. Question 5

83. Miscellanous
13 marks available

84. Question 1
A box of 8 calligraphy pens was bought for £ How much did each pen cost?
(2 marks)

85. Question 2

86. Question 3

87. Question 4
(2 marks)

88. Question 5