Chapter 9: Comparing Quantities1. Watch the videos on the chapter comparing quantities 2. Write the notes in your math notebook with chapter heading and learning objectives 4.Take

Chapter 9: Comparing Quantities

Percentage Percentages are numerators of fractions with denominator 100 and have been used in comparing

results. Per cent is represented by the symbol % and means hundredths too. That is 1% means 1 out of

hundred or one hundredth. It can be written as: 1% = 1

100 = 0.01

Applications Of percentages

In a mathematics test Aisha scored 18 out of 25 and Fathima scored 35 out of 50. Who scored more marks?

Marks obtained by Aisha = 18

25

Instructions General Instructions 1. Watch the videos on the chapter comparing quantities 2. Write the notes in your math notebook with chapter heading and learning objectives 4.Take the snaps and make it as running pdf. 6. Send your work after the completion.

Learning Objectives: • To describe percentages and its applications • To calculate different forms of percentages • How to calculate percentage of a given quantity •

Marks obtained by Fathima = 35

50

Change the denominator into 100 to convert into percentage

18

25 =

18×4

25×4=

72

100 = 72 %

35

50=

35×2

50×2=

70

100 = 70%

So, Aisha scored better than Fathima. Because percentage of Aisha is more than Fathima Different Forms of Percentages

Convert Fraction into Percentage To convert fraction to percentage, multiply it by 100 and insert % symbol.

e.g.: Express 4

5 as a percent

4

5 =

4

5 × 100 =

4×100

5=

400

5= 80%

Convert Decimal into Percentage To convert decimal to percentage, multiply it by 100 and insert % symbol. e.g.: Express 0.21 as a percent 0.21 = 0.21×100=21%

To convert percentage as Fraction or Decimal To convert percentage to fraction or decimal, divide it by 100 and remove the %

symbol. E.g.: Express 62% as a decimal and as a fraction. As a decimal, As a fraction,

62% = 62

100 = 0.62 62% =

62

100=

31

50

1) If in a school, 57% of the children are boys, then how many percentages of them are girls? Number of girls = 100% -57% = 43% 2) A bag contains balls of 3 different colors -red, blue, and yellow. If 50% of the balls are red, 20% of the balls are blue, then what percent of the balls are yellow? 50% + 20% +? % = 100% Therefore, yellow balls = 100% - 70% = 30% 3) I have 8 mangoes 25% of them are rotten. Find the number of rotten mangoes Total mangoes= 8 Number of rotten mangoes = 25% of 8

= 25

100 × 8 =

25×8

100=

200

100= 2

4) Out of 25 children in class VII, 10 are boys. Find the percentage of boys is

Number of boys =10

25 ∴% of boys = 10

25 × 100 =

10×100

25=

1000

25= 40 %

Note: Parts always add to give a whole

5)Suppose 60% of students in a college are girls. If the number of boys is 2,448, find the number of students in a college. If 60% of students are girls, then number of boys = 100% - 60% = 40% Let the total number of students in the college be x. ∴ 40% of x = 2448

40

100 × 𝑥 = 2448

x = 2448 × 100

40= 6120

Thus, number of students in the college is 6120. 6)In a survey of 55 students, 20% of students like to play cricket. What is the total number of students who like to play cricket? Total number of students =55 Number of students who like to play cricket= 20% of 55

∴ 20% of 55 = 20

100 × 55 =

20×55

100=

1100

100= 11

∴ Number of students who like to play cricket = 11

7) In a village, 30% people are women, 40% are men and rest are children. Find the percent of the children in the village? 8) There are 25 bulbs, 16 of them are damaged. Find percentage of damaged bulbs?

Learning Objectives: • To evaluate the increase and decrease percentage of a quantity

1) Amir’s pocket money was AED 40. He spends AED 35. What percent of the pocket money did he save?

Pocket money = AED 40 Money Spent = AED 35 Money Saved = 40 -35 =5

Percent of pocket money saved = 5

40 × 100 =

500

40= 12.5%

2)A book costs AED 10. After 6 months. The cost of the book is expected to be AED 13. What will be the percent increase in price? To find: Increase in price = 13-10 = AED 3

% Increase in price = 3

10 × 100 = 30%

Percentage Increase = 𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆

𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝑽𝒂𝒍𝒖𝒆× 100

3) A book costs AED 10. After 6 months, the cost of the book is expected AED 6. What will be the percent decrease in price? To find: Decrease in price = 10-6 = AED 4

% Increase in price = 4

10 × 100 = 40%

Percentage Decrease = 𝐷𝑒𝑐𝑟𝑒𝑎𝑠𝑒

𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒× 100

4)A businessman’s total earning last year was AED 60,000. There is an increase of 15% in his earning this year. What is his earning this year? Percentage Increase = 100% +15% =115%

Earning this year = 115% of 60,000

=115

100 × 60,000 =

6900000

100= 69,000

Therefore, earning of businessman this year = AED 69,000 5)In a sale, the price of shoes is reduced by 20%. If the reduced price is AED 200. Find its original price. Assume the original price = AED 100 Reduction = 20% of original price

= 20

100 × 100 = 𝐴𝐸𝐷 20 (𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡)

Reduced price = 100 – 20 = AED 80 If reduced price = 80 Original price = 100 If reduced price = 200 Original price = ?

Original Price = 100×200

80 20000

80= 250

6)A person’s salary was reduced by 20%. What percentage should be added to get back his original salary? Let his original salary be AED 100

To find: 20% of his original salary = 20

100 × 100 = 𝐴𝐸𝐷 20

After 20% reduction, Salary =100 -20 =AED 80 Current salary = AED 80 Original Salary =AED 100 Increase in salary =20

Percentage increase =𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑒

𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑆𝑎𝑙𝑎𝑟𝑦× 100 =

20

80× 100 =

2000

80=

25% 7) The price of a can of cooking oil is increased by 20%. The new price is AED 48. What was the price of the cooking oil before the increase? a. AED 20 b. AED 28 c. AED38.40 d. AED 40

Learning Objectives: To calculate the selling price of articles when discount is offered or goods and Sales Tax (VAT) is imposed

1. A pair of jeans has a marked price of Rs. 1500. During sale, a discount of 30% is given on the marked price. Find the selling price. Solution: Marked Price = 1500

Discount Offered = (30

100 × 1500)

=Rs. 450 So, the selling price = 1500-450=1050

2. Mr. Bose bought a mobile phone for Rs. 30,000 after a discount of 20%. Find the marked price of the mobile phone Solution: Let the marked price (MP)= x Selling price of the phone (SP) = 30,000 Discount = 20%

Discount = 20

100

SP = MP- Discount

30,000 = x – 20

100 × x

30,000= 80

100 x

x= 30,000×100

80 = 37,500 ∴ Marked price = Rs. 37,500

3.

4.

MP = 600 SP =450 SP =MP – Discount Discount = MP-SP = 600 – 450 = 150

Discount Percentage = 150

600 × 100 =

150

6= 25%

MP = 6500 Discount % = 8 %

Discount = 8

100 × 6500 = 520

SP= MP – Discount = 6500-520 = 5980 VAT % = 8%

VAT = 8

100 × 5980 =

47840

100 = 478.4

SP after adding VAT = 5980 + 478.4 = 6458.4

Chapter 16 : Data Handling Topics: Organizing and grouping data Learning Objective: To describe basic terms related to statistics To arrange the raw or ungrouped data in the form of a frequency distribution table

Tally Marks

A survey was conducted on the favorite sport of the students

Sports Tally Marks Frequency

Group the following data in frequency distribution table

18

Group the following data in grouped frequency distribution table

1 -5 (including 1 and including 5) and 1 and 5 are called class limits

And 1 is called the lower-class limit and 5 is called the upper-class limit.

Prepare a continuous frequency distribution table

Range of the data = Highest – Lowest

Class limits = The highest and lowest numbers in a class interval

Upper class limit= the highest number in a class interval

Lower class limit= the lowest number in a class interval

Class width or class size=the difference b/w upper class limit and lower-class limit

Class mark= the midpoint of the class interval i.e. sums of upper-class limit and lower-class limit divided by 2

Learning Objective:

To describe, interpret and construct bar graph

This is a data showing the favorite sport liked by the students at a particular school

Construct a bar graph to represent this data

Note: All numbers are represented in equal intervals

1) Which is the hottest city among these? City F 2)If the temperature above 25 is warm cities, then which all cities are warm cities. Cities B, C and F 3)What is the difference between temperature of hottest and coldest cities Hottest city temp = 50 coldest city temp = 10 Difference = 50-10 =40

Areas Of Countries

Learning Objective: To describe, interpret and construct double bar graph Construct a double bar graph to represent the data

Construct a histogram to represent the data

Learning Objective: To describe , construct and interpret pie charts.

𝑇𝑜𝑡𝑎𝑙 𝑎𝑛𝑔𝑙𝑒

𝑡𝑜𝑡𝑎𝑙=

360

1200 =

360÷10

1200÷10=

36

120=

36 ÷ 12

120 ÷ 12=

3

10= 0.3

𝑇𝑜𝑡𝑎𝑙 𝑎𝑛𝑔𝑙𝑒

𝑡𝑜𝑡𝑎𝑙=

360

40 =

360÷10

40÷10=

36

4= 9

The given pie chart shows the percentages of blood types for a group of 200 people.

a) How many people in this group have blood type A? b) How many people in this group do not have blood type o? c) How many people in this group have blood types A and B?

360

200=

36

20=

18

10= 1.8

a) A type blood =90

1.8= 50

b) O type blood = 72

1.8= 40

People who do not have o type blood = 200-40 = 160

c) B type blood = 144

1.8= 80

Total number of A and B type blood = 50+80=130

Learning Objective:

To describe terms related to probability

To evaluate the probability of simple events

Sample Space All Possible Outcomes Sample Point One Possible Outcome

Event One or more Possible Outcomes

ZZZZZZZZZ

Learning Objective:

To evaluate the sample space and probability of tossing 2 coins and

throwing 2 dice

1. a) Probability of picking a red sweet = 3

5

Probability of not picking a red sweet = 1 - 3

5 =

2

5

b) P(Raining tomorrow) = 0.6 P (not raining tomorrow) = 1-0.6 =0.4

Sample space when 2 coins are tossed

Sample space when 2 dice are thrown

3 1 4 1 5 1 3 2 4 2 5 2 3 3 4 3 5 3 3 4 4 4 5 4 3 5 4 5 5 5 3 6 4 6 5 6

Sample space (2 coins tossed) = { HH, HT, TH,TT}

a)Probability( exactly one head )= 2

4=

1

2

b) Probability (no heads) = 1

4

c) Probability (both heads) = 1

4

Sample space = {3 white discs, 5 black discs}

a)Probability( white disc )= 3

8

b) Probability (black discs) = 5

8