1. Using Algebra to Solve Problems
Form 1 Mathematics
Chapter 2 and Chapter 4

2. Reminder WB P.46-47 Open Book Quiz Close Book Quiz
Today!
Open Book Quiz
Close Book Quiz
7 Nov (Wednesday)
You must hand in on time!

3. Operation on Directed numbers
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) 正正得正 負負得正 正負得負 負正得負

4. Addition and Subtraction
(+ A) + (+ B) = A + B
(+ A) + (– B) = A – B
(– A) + (+ B) = – A + B
(– A) + (– B) = – A – B
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
(+ A) – (+ B) = A – B
(+ A) – (– B) = A + B
(– A) – (+ B) = – A – B
(– A) – (– B) = – A + B

5. Multiplication and Division
(+ A)  (+ B) = A  B
(+ A)  (– B) = – (A  B)
(– A)  (+ B) = – (A  B)
(– A)  (– B) = A  B
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
(+ A)  (+ B) = A  B
(+ A)  (– B) = – (A  B)
(– A)  (+ B) = – (A  B)
(– A)  (– B) = A  B

6. Algebraic Expression (代數式)
Pay attention to the followings:
Consider A as a variable (變數)
1  A = A
A + A + A = 3A
A  A  A = A3
3A  4A = 12A2
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7. Like Terms and Unlike Terms
When we work on the followings, we should put together the like terms and then simplify!
For examples:
1. A +2B +3A +4B = A +3A +2B +4B
= 4A + 6B
2. A -2B –3A +4B = A -3A -2B +4B
= (A-3A) + (-2B+4B)
= (-2A) + (2B)
= -2A +2B
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8. Equations If a = b Then a + c = b + c Addition of equality (等量相加)
X – 7 = 2
X = 2 +7
X = 9
X = 2 +7
If a = b
Then a + c = b + c
Ronald HUI

9. Equations If a = b Then a - c = b - c Subtraction of equality (等量相減)
X + 7 = 12
X = 12 -7
X = 5
X = 12 -7
If a = b
Then a - c = b - c
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10. Equations If a = b Then ac = bc Multiplication of equality (等量相乘)
X  5 = 4
X 5  5 = 4  5
X = 20
X = 4  5
If a = b
Then ac = bc
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11. Equations If a = b Then a  c = b  c (but c  0)
Division of equality (等量相除)
5X = 20
5X  5 = 20  5
X = 4
X = 20  5
If a = b
Then a  c = b  c
(but c  0)
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12. Equations a(b + c) = ab + ac (a + b)c = ac + bc Distributive Law (分配律)
5 (X+2) = 20
5 (X) + 5 (2) = 20
5X+10 = 20
5X = 10
X = 2
a(b + c) = ab + ac
(a + b)c = ac + bc
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13. Equations -a(b + c) = -ab - ac -a(b - c) = -ab + ac
Distributive Law (分配律)
-5 (X-2) = 20
(-5) (X) – (-5) (2) = 20
-5X+10 = 20
-5X = 10
X = -2
-a(b + c) = -ab - ac
-a(b - c) = -ab + ac
Ronald HUI

14. Equations If a  c = b  d Then ad = bc (but c0 and d0)
Cross Method (交义相乘)
If a  c = b  d
Then ad = bc
(but c0 and d0)
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15. Forming Equations
Use a letter x to represent unknown number 設 x 為變數 (即想求的答案)
Follow the question and form an equation 根據問題，製造算式
Solve for x 算出 x 的值
Write answer in words (with units!) 寫出答案 (包括單位)
Ronald HUI

16. Forming Equations Page 99 Question 3:
If the sum of two consecutive natural numbers is 37, find the smaller number.
Step 1: Let the smaller number be x.
Step 2: Then, the larger number will be x + 1
So, x + (x + 1) = 37
Step 3: x + x + 1 = 37
2x = 36
x = 18
Step 4: Therefore, the smaller number is 18.
Checking: = 37!
Ronald HUI

17. Forming Equations Page 99 Question 5:
The number of candies Susan has is represented by the algebraic expression x, where x stands for the number of boxes of candies she buys, If Susan has 36 candies after the purchases, find the number of boxes of candies she buys.
Step 1: Given x is the number of boxes.
Step 2: Then, x = 36
Step 3: x = 30
x = 3
Step 4: Therefore, the number of boxes is 3.
or Susan buys 3 boxes of candies.
Ronald HUI

18. Forming Equations Page 99 Question 8:
There are three $100 notes and some $10 coins inside a bag. If there are altogether $460, how many $10 coins are there?
Step 1: Let there are x $10 coins.
Step 2: Then, 3 ($100) + x ($10) = $460
Step 3: x = 460
10x = 160
x = 16
Step 4:  There are 16 $10 coins.
Ronald HUI

19. SHW (II) – Yellow paper!
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20. SHW (II) – Question 1
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21. SHW (II) – Question 2
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22. SHW (II) – Question 3 8 8
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23. SHW (II) – Question 4
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24. SHW (II) – Question 5
Felix
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25. SHW (II) – Question 6
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26. SHW (II) – Question 7 The number of student tickets is = 490 – x
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27. SHW (II) – Question 8
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28. SHW (II) – Question 9
The number of staff who receive a $300 voucher is = 45 – x
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29. SHW (II) – Question 10 The time Simon spends on studying = x/3 hours
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30. Are you ready?
Open Book Quiz
Now!
Close Book Quiz
7 Nov (Wednesday)

31. Good Luck! Enjoy the world of Mathematics!
Ronald HUI