substitution and Binary operation Review cards

let us review some Algebra

Objectives

At the end of these slides you should remember

1. substitution
2. Binary operations

Substitution

In algebra substitution means putting numbers where the letters are and performing operations to get a single answer. Consider a football team, when a player is being substituted he comes off and another goes onto the field.

Substitution continued

Example: Given that a=5, find the value of 3a,

you replace 'a' with 5... 3(5), but remember a letter beside a number means multiply

so your answer will be 15.

Example

Given that

 $x=3,\ y=4\ and\ z=-2$  
find the value of :
1. xyz
Answer:  (3)(4)(-2) you are multiplying all
            =-24

Example 2

• Given x=3, y=4 and z= -2 find the value of

•  $\frac{2xy}{z^2}$  

• so replace the letters with the numerical values

•  $\frac{2\left(3\right)\left(4\right)}{\left(-2\right)^2}$  

•  $=\frac{24}{4}$  

• =6

Binary operations

Binary operations are operations that associate two things with a third. We are already familiar with binary operations such as addition, subtraction, division and multiplication. E.g. 2 +3 =5, addition is the operation that associates 2 and 3 with 5.

A binary operation is simply a rule for combining two values to create a new value.

Binary Operation

Some binary operations are defined in specific forms and symbols like *, @, ∂ etc.

Operations like a * b = a/b + 2b are called symbolic operations.

Examples

• An operation is defined by x * y = 2x + 3y,  evaluate 3 * 5,

• So, in answering,  consider x * y = 3 *5

• so that means x= 3 and y= 5, first equals first and second  equals second

• Answer:  

• 3 * 5= 2(3) + 3(5)

•          =6+15

•          =21

examples continued

•  $a\ \nabla\ b=\ \sqrt{2a-b}$  

  Given the binary operation above, what is the value of

•  $12\nabla8$  

• so,  $12\nabla8=\sqrt{2\left(12\right)-8}$  

•  $\sqrt{24-8}$  

•  $\sqrt{16}$  

• = 4

more examples

•  $a\Delta b=b-3a$  Given the binary operation, Evaluate  $2\Delta7$  

  
  

• observe that a= 2 and b= 7, first to first, 2nd to 2nd....

• so,  $2\Delta7=7-3\left(2\right)$  

•  $=7-6$  

• = 1

Final example

•  $a\ \delta\ b\ =\ 2a\ +3b$  

  Given the binary operation above, find the value of x for which 

•  $a\ \delta\ 3\ =\ 13$  

•  first identify values for and b and sub as usual

• so, a = ? and b =3,

•  $a\ \delta\ 3=2\left(a\right)+3\left(3\right)$  

•            $=2a+9$  

• so $2a+9=13$  

continued

•  $2a+9=13$   

•   $2a=13-9$  

•  $2a=4$  

•  $\frac{2a}{2}=\frac{4}{2}$  

•  $a=2$  

Quiz time

• find the quiz to see if you are now refreshed on the topic