Algebraic Expressions incl. Simplifying

Algebraic Expressions including Simplifying

Learning Goals

• To review the definitions and conventions of algebra

• To be able to substitute values for pronumerals in expressions and evaluate

• To review the conventions and processes for multiplication and division of algebraic terms

• To understand what is meant by ‘like terms’ and that only like terms can be collected under addition and subtraction

• To be able to simplify algebraic expressions using addition and subtraction

Match

Match the following

• Product

• Sum

• Difference

• Quotient

Multiplication

Addition

Subtraction

Division

• Multiplication

• Addition

• Subtraction

• Division

Key Ideas

• In algebra, letters are used to represent numbers. These letters are called pronumerals or variables.
  

• An expression is a combination of numbers and pronumerals connected by any of the four operations +, −, × and ÷. Brackets can also be used.

Key Ideas

• A term is a combination of numbers and variables connected with only multiplication and division. Terms are separated with the operations + and −.

• Coefficients are the numbers being multiplied by pronumerals.

• Constant terms consist of a number only.

• Expressions can be evaluated by substituting a number for a pronumeral.

Multiple Choice

State the number of terms in this expression: $$5x+2y$$

• 1

• 2

• 3

• 4

Multiple Choice

State the number of terms in this expression: $$1+2a^2$$

• 1

• 2

• 3

• 4

Multiple Choice

State the number of terms in this expression: $$b^2+ca-1$$

• 1

• 2

• 3

• 4

Multiple Choice

State the number of terms in this expression: $$\frac{x^2}{2}$$

• 1

• 2

• 3

• 4

Math Response

State the coefficient of $$5xy$$

Type answer here

Correct Answer: 5

Deg^°

Rad

Math Response

State the coefficient of $$-2a^2$$

Type answer here

Correct Answer: -2

Deg^°

Rad

Math Response

State the coefficient of $$\frac{x}{3}$$

Type answer here

Correct Answer: \frac{1}{3}

Deg^°

Rad

Math Response

State the coefficient of $$-\frac{2x}{5}$$

Type answer here

Correct Answer: -\frac{2}{5}

Deg^°

Rad

Order of Operations

Order of operations should be following when evaluating expressions:

1. Brackets

2. Powers

3. Multiplication and division

4. Addition and subtraction

​Example 1: Writing algebraic expressions from words

Write an algebraic expression for:
a) the number of tickets needed for 3 boys and r girls

Math Response

Write an algebraic expression for: the number of seats needed for a adults and 7 children

Type answer here

Correct Answer: a+7

Deg^°

Rad

​Example 1: Writing algebraic expressions from words

Write an algebraic expression for:
b) the cost of P pies at $3 each

Math Response

Write an algebraic expression for: the cost of a apples at $1.20 each

Type answer here

Correct Answer: 1.2a

Deg^°

Rad

​Example 1: Writing algebraic expressions from words

Write an algebraic expression for:
c) the number of grams of peanuts for one child when 300g of peanuts is shared equally among C children

Math Response

Write an algebraic expression for: the number of pieces of chocolate for one person when 60 pieces is equally shared among b people

Type answer here

Correct Answer: \frac{60}{b}

Deg^°

Rad

​Example 2: Converting words to expressions

Write an algebraic expression for:
a) five less than x




b) three more than twice x

Drag and Drop

The algebraic expression for six more than x is ​

Placeholder

Drag these tiles and drop them in the correct blank above

x+6

6-x

x-6

6x

Drag and Drop

The algebraic expression for one less than three times is ​

Placeholder

Drag these tiles and drop them in the correct blank above

3x-1

1-3x

3x-x

3x+1

​Example 2: Converting words to expressions

Write an algebraic expression for:
c) the sum of a and b is divided by 4




d) the square of the sum of x and y

Math Response

What is the algebraic expression for the following: two less than a is divided by 3

Type answer here

Correct Answer: \frac{a-2}{3}

Deg^°

Rad

Draw

What is the algebraic expression for the following: the square root of the sum of a and b

​Example 3: Substituting values into expressions

​Example 3: Substituting values into expressions

Math Response

Evaluate the following when $$a=3,\ b=-1\ and\ c=-2$$

$$3\left(a-b\right)\ +2c$$

Type answer here

Correct Answer: 8

Deg^°

Rad

Math Response

Evaluate the following when $$a=3,\ b=-1\ and\ c=-2$$

$$c^2-3ab$$

Type answer here

Correct Answer: 13

Deg^°

Rad

Miss B

" What you do to one side, do to the other" 

​Time to do MathsOnline - you have homework

MO Task 1 - Due Monday