Introduction to Algebra

MATH: ALGEBRA INTRODUCTION

by MARIA RODRIGUEZ

​CONTENT

​TODAY WE ARE GOING TO REMEMBER

• ​What is algebra

• ​Algebraic expressions

• ​Algebraic language

• ​Evaluating algebraic expressions.

Open Ended

What is algebra? What is it about? What elements are part of algebra?

​Algebra's elements include:

• ​Numbers

• Variables

• ​Operations symbols

• ​Equal signs (in equations)

• ​Solutions

​Algebraic expressions

​Represent information which includes a variable or unknown data.

​DOES NOT have a solution since it is not an equation.

​

​Algebraic language

​We can translate situations or word problems into algebraic expressions.

​As any language we need the vocabulary necessary to do that.

​

• ADDITION: more than, increase, addition, sum of...

• ​SUBTRACTION: difference, subtract from, less than (careful with this one!!)

• ​MULTIPLICATION: times, product, *twice...

• ​DIVISION: quotient, *half...

Multiple Choice

The difference of 3 times a number and 7

• 3 + 7n
• 3n - 7
• 3n + 7 
• 3 / 7n

Multiple Choice

w increased by 5

• w - 5
• 5w
• w + 5
• w / 5

Multiple Choice

The quotient of a number and 8

• 8g
• 8/g
• g+8
• g/8

Multiple Choice

2 times the sum of y and 5 

• 2 + y + 5
• 2y + 5 
• 2(y + 5)
• 2 - y + 5

Multiple Choice

Three times the sum of 2 and e. 

• 3e+2
• 3(e-2)
• 3(e+2)
• 2e+3

Multiple Choice

The product of 7 and j increased by 3.

• 3+7j
• 7j-3
• 7(j+3)
• 3j+7

​Evaluating algebraic expressions

​Evaluate means to give value.

​We will have expressions in which they want to know the value for a given value.

We will SUBSTITUTE the variable by the number we are given and then, we will solve the operation using the correct order of operations!

​

​example: evaluate 2x+6 if x=3

​2(3)+6

​ 18 + 6

​ 24

Multiple Choice

Evaluate the expression below for x=16. $$\frac{x}{2}$$  

• 32

• 8

• 14

• 18

Multiple Choice

Evaluate the expression below for h=7.

3h

• 21

• 37

• 4

• 14

Multiple Choice

Evaluate the expression below for e=81. $$\frac{e}{9}$$  

• 90

• 1/9

• 9

• 72

Multiple Choice

 Evaluate the expression below for c=5. $$8c+25$$

• 17

• 33

• 110

• 65

Multiple Choice

Evaluate the expression below for b=7. $$b-5$$  

• 2

• 75

• -12

• 12

Multiple Choice

Evaluate the expression below for j=6. $$2j-7$$  

• 17

• 5

• -5

• 19

Multiple Choice

Evaluate the expression below for f=8. $$2f+7$$  

• 24

• 23

• 31

• 35

Multiple Choice

Evaluate the expression below for n=7. $$8n-10$$  

• 46

• 5

• 77

• 38

Multiple Choice

Evaluate the expression below for w=4. $$3w+17$$  

• 42

• 29

• 20

• 51

Multiple Choice

Evaluate the expression below for y=6. $$8y-7$$  

• 41

• 47

• 79

• 1

Multiple Choice

If x = 5, what is the value of "Twice a number x decreased by 12"

• 2

• -2

• 10

• 12

Multiple Choice

If y = (-3), what is the value of "The quotient of a number and 9"

• 3

• -3

• 1/3

• -1/3

Multiple Choice

"Ten less than twice a number" is expressed.....

• 10-2x

• 2(10) - x

• 2x - 10

• 2x+10