University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

26

Pages:

3
Author:

anon

Evaluate the following expressions and hand in your solutions. (−20) 10 + 8 (−2) a) (2)(5)(7) b) c) -1-5+9-2+3 d) (-4+6)(3-7) e) (-8)+(-7)+(+14)-(-1) Order of Operations with Integers What do we use to remember the correct order of operations? B - brackets E - exponents D – division are performed in the order they appear from left to right M - multiplication A – addition are performed in the order they appear from left to right S – Subtraction What does it mean to simplify? To simplify, it means to find an equivalent expression that it simpler than the original. It usually is a smaller expression than the original. Example 1: Simplify. a) 7(7 - 2) - 5(-3 - 8)+ 19 ←evaluate brackets =7(5)-5(-11)+19 ← multiply =35 +55 +19 ← add =109 b) 5(-4) - [(-6) + (-3) - 4(2(-4) -7)] +3(-8) =5(-4)-[(-6)+(-3)-4(-8-7)+3(-8) =-20-L-6-3-4 (-15)] -24 =-20-(-6-3 +60) - 24 =-20-(-9+60) - 24 =-20-(51) -24 =-20-51-24 =-95 c) 5(−3−4)−(−6)(13−6) (−1)(11−4) = 5(−7)−(−6)(7) (−1)(7) = −35−(42) (−7) = −35+42 −7 = 7 −7 ← 𝑏𝑟𝑎𝑐𝑘𝑒𝑡𝑠 ← 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦 (𝑟𝑒𝑚𝑒𝑚𝑏𝑒𝑟 𝑡𝑜 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑑𝑜𝑢𝑏𝑙𝑒 𝑠𝑖𝑔𝑛𝑠) ← 𝑎𝑑𝑑 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡 ← 𝑑𝑖𝑣𝑖𝑑𝑒 =− 1 2 2 Is there a difference between (− 3) and − 3 ? 2 (− 3) = (− 3)(− 3) =9 2 − 3 =− (3 × 3) =− 9 2 Yes, there is a difference between (− 3) and − 3? 2 (− 3) the square applies to the negative sign and 3. 2 -3 - the square applies to the 3 only Example 2: Evaluate, 2 2(− 3) –7. 2 Sol: 2(− 3) − 7 = 2(− 3)(− 3) − 7 ← brackets and exponent = 2(+ 9) − 7← multiplication = 18-7 ← subtraction =11 Substitution means that you replace the variables in the expression by their actual values. Example 3: Evaluate. a) 7x - 9 when x = -1 7x-9 =7(-1)-9 ← substitute x = - 1 =-7-9 ← multiply =-16 ←subtract b) - 2x + 3y - z when x = 3 y = - 4 and z = -7 - 2x + 3y - z = - 2(3) + 3(- 4) - (- 7) =-6-12 +7 =-18+7 =-11 c) xy + 2yz - xz when x = - 1 y = - 5 and z = 3 xy+2yz-xz = (- 1)(- 5) + 2(- 5)(3) - (- 1)(3) = 5-30+3 =5+3-10 =8-30 =-22