(Exponent) Complex Binary Operations with MORE than One Variable

Attendance is taken

Sub-topic: Complex Binary Operations with exponents & More than 1 variable

1] Executing Steps to solve Complex Binary Operations. (Applying)

2. Linking symbols/shapes and four basic operations when evaluating Complex Binary Operations. (Analyzing)

3. Posting the correct answers for given Complex Binary Operations. (Evaluating)

4. Valuing the importance of binding operators to symbols, in order to evaluate Basic and Complex Binary Operation. (Affective domain)

MORE than one variable

Recall order of operations

Recall integer rules

+ or - integers: 1) Signs alike add and keep the sign. 2) Signs different, subtract and take the sign of the larger number

X or ÷ integers: 1) Signs alike: Positive 2) Signs different: Negative

Recall Substitution

Substitution is the process of replacing symbols(letters) with numbers.

Given a = 2b = 4 c = 6

5) bc = 4(6) = 24 6) bc ÷ a = 4(6) ÷ 2 = 12

find: 1) a + b = 2) a – b = 2 + 4 = 6 2 - 4 = - 2 3) 2a = 4) c^2 = 2(2) = 4 6^2 = 36

What Is Binary Operations?

Recall Exponents

Exponent is defined as the method of expressing large numbers in terms of powers.

Class work

If k @ j = k2 – 2j, find: b) 4 @ 1 c) 3 @ 2 d) 10 @ 50

Complex Binary Operations (in front of brackets: left side of bracket)

Complex Binary Operations (behind the brackets: right side of bracket)

MORE than one variable

Given that p * q = p2 + q, find 2 * (3 * 4)

More than one variable

If m # n = m2 – n; find (3 # 2) # 4

What Is Binary Operations?

Left of bracket

Claculation complex Binary Operations

(in front of brackets: left of the bracket)

Given p * q = p2 + q, find 2 * (3 * 4)

32 = 3 x 3 = 9

22 = 2 x 2 = 4

Exponent

p * q = p2 + q2 * (3 * 4) = 2 * (32 + 4) 2 * (3 * 4) = 2 * (9 + 4) 2 * (3 * 4) = 2 * 13

p * q = p2 + q 2 * 13 = 22 + 13 = 4 + 13 2 * (3 * 4) = 17

Claculation complex Binary Operations

(in front of brackets: left of the bracket)

Given p * q = p2 + q, find 2 * (3 * 4)

p * q = p2 + q2 * (3 * 4) = 2 * (32 + 4) 2 * (3 * 4) = 2 * (9 + 4) 2 * (3 * 4) = 2 * 13

Exponent

32 = 3 x 3 = 9

22 = 2 x 2 = 4

p * q = p2 + q = 22 + 13 = 4 + 13 2 * (3 * 4) = 17

Claculation complex Binary Operations

(in front of brackets: left of the bracket)

Given p * q = p2 + q, find 2 * (3 * 4)

Exponent

p * q = p2 + q2 * (3 * 4) = 22 + (32 + 4) 2 * (3 * 4) = 22 + (9 + 4) 2 * (3 * 4) = 22+ 13 2 * (3 * 4) = 4 + 13 2 * (3 * 4) = 17

32 = 3 x 3 = 9

22 = 2 x 2 = 4

Class work

Given that c * d = c + d, find: find: 1b) 2 * (3 * 4)

Extended Activity

Exercise 3f: #2b page 32If p Δ q = 2p – q, find b) 3 Δ (4 Δ 1)

Class work

Given that j ⊕ k = j2 – k, find: find: 3b) 3 ⊕ ( 2 ⊕ 1)

Class work

If r ⌂ s = 3r + s, find: find: 4a) 4 ⌂ ( 2 ⌂ 1) 4c) 3 ⌂ ( 5 ⌂ 3)

🏃🏽Exit Slip🏃🏽‍♀️

Given that j ⊕ k = j2 – k, find: 3 ⊕ ( 2 ⊕ 1)

What Is Binary Operations?

Right of bracket

Claculation complex Binary Operations

(behind the brackets: right of the bracket)

If m # n = m2 – n, find (3 # 2) # 4

32 = 3 x 3 = 9

Exponent

72 = 7 x 7 = 49

m # n = m2 – n(3 # 2) # 4 = (32 – 2) # 4 (3 # 2) # 4 = (9 – 2) # 4 (3 # 2) # 4 = 7 # 4

m # n = m2 – n 7 # 4 = 72 – 4 = 49 – 4 (3 # 2) # 4 = 45

Claculation complex Binary Operations

(behind the brackets: right of the bracket)

If m # n = m2 – n, find (3 # 2) # 4

Exponent

m # n = m2 – n(3 # 2) # 4 = (32 – 2) # 4 (3 # 2) # 4 = (9 – 2) # 4 (3 # 2) # 4 = 7 # 4

32 = 3 x 3 = 9

72 = 7 x 7 = 49

m # n = m2 – n = 72 – 4 = 49 – 4 (3 # 2) # 4 = 45

Claculation complex Binary Operations

(behind the brackets: right of the bracket)

If m # n = m2 – n, find (3 # 2) # 4

Exponent

m # n = m2 – n(3 # 2) # 4 = (32 – 2)2 – 4 (3 # 2) # 4 = (9 – 2)2 – 4 (3 # 2) # 4 = 72 – 4 (3 # 2) # 4 = 49 – 4 (3 # 2) # 4 = 45

32 = 3 x 3 = 9

72 = 7 x 7 = 49

Class work

Given that c * d = c + d, find: find: 1c) (3 * 4) * 2

Extended Activity

Exercise 3f: #2c page 32If p Δ q = 2p – q, find c) (4 Δ 1) Δ 20

🏃🏽Exit Slip🏃🏽‍♀️

Given that j ⊕ k = j2 – k, find: ( 2 ⊕ 1)⊕3

References

1. Juan, K. 2008. Interactive Approach to Mathematics First Form, 3rd Edition pages 37 – 41 2. Juan, K. 2020. Interactive Approach to Mathematics First Form, 4th Edition pages 31 – 33 3. https://www.youtube.com/watch?v=9i3s-wFkL5I Binary Operation (right distributive) 4. https://www.youtube.com/watch?v=KUWJhsrgSBY Binary Operation (left distributive)