Algebraic

"Making sense

of algebra"​

​by: Mr. Agung Prasetiyo, S.Pd

​Parts of algebraic expression

​

• Variables: the variables of an algebraic expression are letters that represent numbers.

• Coefficients: the coefficients of an algebraic expression are the numbers that multiply the variables.

• Constant: a constant of an algebraic expression is a number that is not multiplied by any variable.

• Term: a term can be a variable, a constant or the product of a number and a variable (or variables).

• Degree: the degree of an algebraic expression is the highest degree of its terms.

Multiple Choice

$$3x+2y=0$$  

• one variable

• two variables

• three variables

• four variables

Multiple Choice

$$-2x+3x-5=4$$  

• one variable

• two variables

• three variables

• four variables

Multiple Choice

$$x^2+3x-5y+z=4$$  

• one variable

• two variables

• three variables

• four variables

Open Ended

Write down part of "terms" from this expressions: $$4a^2-5a+2ab-3c+6c$$  

Open Ended

Write down part of "cofficients" from this expressions: $$4a^2-5a+2ab-3c+6c$$  

2.1 Using letters to represent unknown value

Some examples of algebraic word

• change

• the difference of ...

• less than ...

• younger than ...

• decreased

• etc

​Substraction (-)

• ... and ...

• the sum of ...

• more than ...

• older than ...

• increased

• etc

​Adding (+)

2.1 Using letters to represent unknown value

Some examples of algebraic word

• divided

• etc

​Division (÷) or (∕)

• product

• times by ...

• twice of ...

• multiplied ...

• etc

Multiply (x) or (.)

Multiple Choice

The sum of two different numbers is 50

• x + y = 50

• $$x^2=50$$  

• 2x = 50

• x = 50

Multiple Choice

John has y stickers. His friend gives him another 20 stickers.

How many stickers does he have altogether?

• 20y

• 2 + 20y

• y + 20

• y + y

Multiple Choice

John bought z hamburgers at $3 each and paid with a 20 dollar

note. How much change did he get?

• 3 - 20z

• 20 - 3z

• 20 + z

• 3z + 20

Multiple Choice

Burgers (B) for $3 and Pepsi (P) for $2.

Find the total cost!

• 2B + 3P

• 3B + 2P

• 3B - 2P

• 3B + 3P

Multiple Choice

A boy is n years old. His Dad is twice his age.

How old is his Dad?

• $$\frac{2}{n}$$  

• $$\frac{n}{2}$$  

• 2 + n

• 2n

​2.2 Substitution

Expressions have different values depending on what numbers you substitute for the variables.

For example, let’s say casual waiters get paid $5 per hour. You can write an expression to represent everyone’s wages like this: 5h, where h is the number of hours worked.

• If you work 1 hour, then you get paid 5 × 1 = $5.

  So the expression 5h has a value of $5 in this case.

• If you work 6 hours, you get paid 5 × 6 = $30.

  So the expression 5h has a value of $30 in this case.

Subject | Subject

Some text here about the topic of discussion

​

​2.2 Substitution

Some text here about the topic of discussion

​Example:

If it is known​ the value of a = 3, b = 5, c = -2, find the value of: 4a -5b + 3c

​

= 4a -5b + 3c​

= 4(3) - 5(5) + 3(-2)

= 12 - 10 - 6

= - 4​

​Terms: [4a], [-5b], [3c]

• 4a with a = 3 --> 4a = 4(3) = 12

• -5b with b = 5 --> -5b = -5(5) = -10

• 3c with c = -2 --> 3c = 3(-2) = -6​

Multiple Choice

Pencils (P) for $2 and Books (B) for $4.

Find the total cost if Bobby buys 5 pencils and 2 books!

• 2P+4B = 2(2)+4(5)

• 2B+4B = 2(2)+4(2)

• 2P+4B = 2(5)+4(2)

• 2B+4P = 2(2)+4(5)

Multiple Choice

Jon buys 3 mangoes (x) and 2 apples (y) for IDR 11000. If the price of one apple is IDR 1000, then what does the price of one mango cost?

• IDR 5000

• IDR 3000

• IDR 8000

• IDR 1000

Multiple Choice

What is the correct value of k if the following algebraic expression is known:

$$-5k\ +\ 6\ =-4\$$  

• k = 3

• k = 5

• k = 9

• k = 2

Multiple Choice

If its known the perimeter of the following square is 24 cm

Find the value of x

• x = 2

• x = 3

• x = -2

• x = 8

​2.3 Simplifying expressions

Adding or subtracting like terms

Examples:

• 3x + 2x = 5x

• 5a - 2a = 3a

• ​2m + 5n - 3m - 2n = [2m - 3m] + [5n - 2n] = -1m + 3n = -m + 3n

• 2x + 6xy - 7y + 2x - 4xy = [2x + 2x] + [6xy - 4xy] - 7y = 4x + ​2xy - 7y

Simplifying expressions - adding or subtracting rules

Multiple Choice

Simplify: $$3a-3b+3a-2b$$  

• a + b

• 6a - 7b

• 5a + 5b

• 6a - 5b

Multiple Choice

Simplify: $$-2x^2+4x+3x^2-7y+8xy-2x$$  

• x² + 2x + 8xy - 7y

• 5x² + x + 2xy - 7y

• x² + 6x - 7y

• x² + 2x + 15y

Multiple Choice

Find the perimeter of the following figure!

• 10x

• 7x + 2

• 9x + 1

• 4x - 2

Multiple Choice

Find the perimeter of the following figure!

• 18x

• 18x - 1

• 20x + 2

• 17x + 3

​2.3 Simplifying expressions

Simplifying expressions - adding or subtracting rules

Multiplying and dividing in expressions

Examples:

• ​x . x . x . x = x⁴

• y⁸ ​÷ y² = y⁶

• 3x . 2x = 3 . 2 . x . x = 6 . x² = 6x²

• 10a² ÷ 2a = [10 ÷ 2] [a² ÷ a] = 5a

• 4ab . 2bc = 4 . 2 . a . b . b . c = 8 . a . b² . c = 8ab²c

• ​7x . 4yz . 3 = 7 . 4 . 3 . x . y . z = 84xyz

Multiple Choice

Simplify: $$12a^2.\ 3b\ .\ ab\ .\ a^2b$$  

• $$36a^5b^3$$  

• $$15a^2b^3$$  

• $$36a^3b^4$$  

• $$24ab^4$$  

Multiple Choice

Simplify: $$\frac{18x^2y}{6x^2}$$  

• $$3xy$$  

• $$2x^4y^{ }$$  

• $$3y$$  

• $$5xy^2$$  

Poll

Simplify: $$\frac{200a^4b^2c}{50a^2b^2}$$  

• $$4a^2b^2c$$  

• $$10a^4b^4c$$  

• $$4a^6bc$$  

• $$4a^2c$$