Percentages I Form 1 Mathematics Chapter 3

Percentages (I) Form 1 Mathematics Chapter 3

Reminder • Standard Homework (III), (IV) and (V) ▫ • 30 Nov (Fri) Extra Tutorial ▫ ▫ ▫ • Tuesday’s last CTP MUST: 1, 10, 11, 12, 14, 16, 26, 30, 36 Mon & Tue after-school – Consultation on G/F Open Book Quiz ▫ • 30 Nov (Fri) Close Book Quiz ▫ 5 Dec (Wed)

What is Percentage? (p. 110) • • “%” is the symbol of percentage. Per cent means “per one hundred”. e. g.

Simple Percentage Problems • P. 116 Q 2(c): 125% of $365. 2 • P. 117 Q 10(c): 132 g is 88% of t g • Remark: same units!

Simple Percentage Problems • P. 118 Q 14. 1100 boys and 700 girls took an examination. 15% of boys and 5% of girls failed. Find the total number of students passed. • • • Number of boys failed = 1100 15% = 165 Number of girls failed = 700 5% = 35 Number of students failed = 165+35 = 200 Number of students = 1100+700 = 1800 Number of students passed = 1800 -200 = 1600

Simple Percentage Problems • P. 118 Q 14. 1100 boys and 700 girls took an examination. 15% of boys and 5% of girls failed. Find the total number of students passed. • Number of boys passed = 1100 (1 – 15%) = 1100 (85%) = 935 • Number of girls passed = 700 (1 – 5%) = 700 (95%) = 665 • Number of students passed = 935 -665 = 1600

Time for Practice • Page 117 of Textbook 1 A ▫ Questions 3 - 13 • Pages 54 - 55 of WB 1 A ▫ Questions 4 - 9

Percentage Increase (p. 119) • New value > Original value • Last year, Andy was 150 cm tall. His height is increased by 20% this year. His height now is

Percentage Decrease (p. 122) • New value < Original value • The price of a car was $160, 000 last month. If it is reduced by 15% this month, the new price

Percentage Change (p. 126) • We can summarize the two formulae into one and call percentage change. • • New value > Original value + (increase) New value < Original value – (decrease) • The temperature was dropped from 30 C to 27 C in the evening. The percentage change is

Percentage Change • P. 130 Q 19. James had $5000 in his savings account last year. This year, he has $10000. • Change % • James then takes out 40% of his savings. The amount now is = $10000 (1 – 40%) = $6000 • New change %

Time for Practice • Page 127 of Textbook 1 A ▫ Class Practice • Page 129 of Textbook 1 A ▫ Questions 6 – 14 • Pages 57 - 58 of WB 1 A ▫ Questions 3 - 9

Profit (盈利, p. 131) • Selling Price (售價) > Cost Price (成本價)

Loss (虧蝕, p. 134) • Selling Price (售價) < Cost Price (成本價)

Profit and Loss • A shop sold a car at the profit % of 20%. If the profit was $32000, what was the cost of the car? What was the selling price? • Profit or Loss? • Let n be the Cost Price. Then, • So, the Selling Price is

Profit and Loss • P. 138 Q 22. A merchant bought a chair for $500 and a desk for $750. He sold the chair at a loss of 30% and the desk at a profit of 24%. • • • Selling price of chair Selling price of desk Total selling prices = $350 + $930 = $1280 Total cost prices = $500 + $750 = $1250 So, the profit % is

Time for Practice • Pages 134 - 135 of Textbook 1 A ▫ Class Practice • Page 137 of Textbook 1 A ▫ Questions 7 – 19 • Pages 61 - 62 of WB 1 A ▫ Questions 7 - 10

Discount (折扣, p. 138) • Western style vs. Chinese style • 10% discount • 20% discount • 70% discount 9折 8折 3折 • 12% discount • 25% discount • 5% discount 88折 75折 95折

Discount • Marked Price > Selling Price

Discount • A pair of scorer shoes is sold at 25% discount at a marked price of $650. Can Vincent buy the shoes if he has $500? • Marked price = $650 • Selling price of the shoes • Since Vincent got $500, he can buy the shoes.

Discount • A golden ring is sold at 30% discount with a selling price of $441. What is the marked price? • Selling price = $441. • Let n be Marked price. Then, • So, the Marked price is $630.

Discount • P. 142 Q 10. In shop A, the marked price of a MD is $1920 and the selling price is $1248. In shop B, the prices are $1760 and $1320 respectively. • A’s discount % • B’s discount % • So, B’s discount is smaller.

Time for Practice • Page 141 of Textbook 1 A ▫ Class Practice • Page 142 of Textbook 1 A ▫ Questions 3 – 10 • Pages 65 - 66 of WB 1 A ▫ Questions 7 - 10

Simple Interest (單利息, p. 144) • Amount(A) = Principal(P) + Interest(I) • Interest(I) = Principal(P) Interest rate(r%) Time(T) • Formula:

Simple Interest • If $40000 is deposited in a bank for 5 years at 3%p. a. , find the simple interest and the amount. • P=$40000 r=3 T=5 (years) • Simple interest (I) is • So, the amount (A) is

Simple Interest • How long will $20000 amount to $30000 at 5%p. a. simple interest? • P=$20000 r=5 A=30000 • I = $30000 -$20000=$10000 • Let T be the time. Then, • The time required is 10 years.

Simple Interest • P. 151 Q 14. Judy borrows $1000000 for 10 years. Bank A’s interest is 5% p. a. and B is 4. 5% p. a. • A’s interest • B’s interest • The difference is $50000. • She pays $50000 less in Bank B from in Bank A.

Time for Practice • Page 149 of Textbook 1 A ▫ Class Practice • Page 150 of Textbook 1 A ▫ Questions 1 – 13 • Pages 69 - 70 of WB 1 A ▫ Questions 4 - 7

Reminder • Term 1 Examination Syllabus (p. 1 -185) ▫ ▫ ▫ • Chapter 0: Basic Mathematics Chapter 1: Directed Numbers Chapter 2: Using Algebra to Solve Problems (I) Chapter 3: Percentages (I) Chapter 4: Using Algebra to Solve Problems (II) Date of Term 1 Examination ▫ ▫ ▫ 12 -12 -12 (Wed) 8: 30 am – 9: 30 am (1 hour) Room 104

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