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

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!

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

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

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

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 Ronald HUI

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 Ronald HUI

Equations If a = b Then a + c = b + c Addition of equality (等量相加) X – 7 = 2 X -7 +7 = 2 +7 X = 9 X = 2 +7 If a = b Then a + c = b + c Ronald HUI

Equations If a = b Then a - c = b - c Subtraction of equality (等量相減) X + 7 = 12 X +7 - 7 = 12 -7 X = 5 X = 12 -7 If a = b Then a - c = b - c Ronald HUI

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 Ronald HUI

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) Ronald HUI

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 Ronald HUI

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

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) Ronald HUI

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

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: 18 + 19 = 37! Ronald HUI

Forming Equations Page 99 Question 5: The number of candies Susan has is represented by the algebraic expression 6 + 10x, 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, 6 + 10x = 36 Step 3: 10x = 30 x = 3 Step 4: Therefore, the number of boxes is 3. or Susan buys 3 boxes of candies. Ronald HUI

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: 300 + 10x = 460 10x = 160 x = 16 Step 4:  There are 16 $10 coins. Ronald HUI

SHW (II) – Yellow paper! Ronald HUI

SHW (II) – Question 1 Ronald HUI

SHW (II) – Question 2 Ronald HUI

SHW (II) – Question 3 8 8 Ronald HUI

SHW (II) – Question 4 Ronald HUI

SHW (II) – Question 5 Felix Ronald HUI

SHW (II) – Question 6 Ronald HUI

SHW (II) – Question 7 The number of student tickets is = 490 – x Ronald HUI

SHW (II) – Question 8 Ronald HUI

SHW (II) – Question 9 The number of staff who receive a $300 voucher is = 45 – x Ronald HUI

SHW (II) – Question 10 The time Simon spends on studying = x/3 hours Ronald HUI

Are you ready? Open Book Quiz Now! Close Book Quiz 7 Nov (Wednesday)

Good Luck! Enjoy the world of Mathematics! Ronald HUI