Algebraic Techniques and Simplifying Expressions

Algebra

Mathematical language using operations for problem-solving.

Pronumeral

Letter or symbol representing numerical values.

Variable

Pronumeral representing multiple numerical values.

Term

Single mathematical expression, e.g., 3x.

Coefficient

Number in front of a variable in a term.

Constant

Numerical value without variables.

Expression

Mathematical sentence made of terms.

Simplifying Expressions

Combining like terms to reduce complexity.

Like Terms

Terms with identical variable parts.

Evaluating Expressions

Finding numerical value by substituting variables.

Expanding Brackets

Distributing terms across parentheses.

Multiplying Terms

Combining coefficients and variables in multiplication.

Dividing Terms

Separating coefficients and variables in division.

Number Laws

Rules governing arithmetic operations with numbers.

Census

Systematic collection of demographic data.

Statistical Interpretation

Using algebra to analyze data for insights.

Consecutive Numbers

Numbers that follow one after another.

Doubling an Expression

Multiplying the entire expression by two.

Perimeter of Rectangle

Sum of all sides, P = 2(length + width).

Algebraic Techniques

Methods for manipulating algebraic expressions.

Worked Example

Illustrative problem-solving demonstration.

MC Questions

Multiple-choice questions for assessing understanding.

Differentiated Questions

Tailored questions for varied student needs.

Interactivities

Engaging activities to reinforce learning.

JacPLUS

Online platform for additional learning resources.

Algebraic Terminology

Specific vocabulary used in algebra.

Collecting Like Terms

Combining terms with the same variable.

Expression Evaluation

Calculating values based on variable substitutions.

Algebraic Expressions

Combinations of numbers and pronumerals.

5 × y

5y

An expression with '5 times'

means 'multiply by 5'.

An expression with '2 less'

means 'subtract 2'.

y − 2

represents the expression with '2 less'.

An expression with '8 more'

means 'add 8'.

y + 8

represents the expression with '8 more'.

An expression with 'divided by 4'

means 'write as a quotient (fraction)'.

An expression with 'the next consecutive number'

means 'add 1 to the number'.

If three dogs find homes

write an expression to represent the total number of dogs at the lost dogs' home.

The original number of dogs (d) is decreased by three.

d − 3

The number of dogs left at the lost dogs' home is doubled.

2 × (d − 3)

The dogs are divided into 10 pens.

2 × (d − 3) ÷ 10 or 2d − 6

There are two jars of lollies and three loose lollies.

2 × l + 3 = 2l + 3

There are three jars of lollies, four packets of lollipops and four loose lollies.

3 × l + 4 × p + 4 = 3l + 4p + 4

The number of pairs of shoes you own

Let s be the number of pairs of shoes you own.

The number of pairs of shoes your friend owns

s + 5

The number of pairs of shoes your sister owns

s − 3

The number of pairs of shoes your brother owns

s + 5 − 4 = s + 1

The total number of coins in a piggy bank

Use c to represent the number of coins in a piggy bank.

The total number of coins Christie and Jane had

2 × (c + 17)

The number of mice in a cage

If the number of mice doubles each month.

1 month from now

2n

2 months from now

4n

3 months from now

8n

six more than the number

6 + m

a fifth of the number

m ÷ 5

the number just before that number

m − 1

eight more than the product of that number and 10

10m + 8

Unknown Whole Number

Represented by variable m in expressions.

Equation

A mathematical statement asserting equality between expressions.

Substitution

Replacing a variable with its numerical value.

Algebraic Expression

A mathematical phrase combining numbers, variables, and operations.

Cost of Bus Fare

Expression for weekly bus fare: 3d.

Total Earnings

Expression for Ali and Halit's earnings: x + 7.

Temperature Conversion

Formula to convert Fahrenheit to Celsius: C = 5/9(F - 32).

Handshakes Calculation

Total handshakes for 10 couples: 90.

Combined Money Expression

Expression for total money: 10 + 20c.

Number Pattern

Sequence generated by substituting values into expressions.

Algebraic Rule

Guideline for calculating total costs in expressions.

Two Terms

Expression g + 2t has two distinct components.

Expression Comparison

x + 1/3 vs. x/3 + 1 shows different values.

Birthday Difference

Frank's age expression: 2x + 3.

Weekly Spending

Total cost for bus fare: 40d.

Fahrenheit to Celsius Example

Hawaii temperature: 31.1 °C from 88 °F.

Expression for Apples

Friend's apples before pie: a + 6.

Expression for Apples After Pie

Friend's apples after pie: a - 2.

Weekly Bus Fare Calculation

Total weekly fare: 3d.

Total Age Expression

Sasha and Kapila's age: 3x.

Combined Age Expression

James and Frank's age: 2x + 3.

Expression for 3 Days

Adult bus fare: 3(d + 1.5).

BIDMAS

Order of operations: Brackets, Indices, Division, Multiplication, Addition, Subtraction.

Formula

An equation that expresses a mathematical relationship.

Area of Triangle

A = 1/2 × base × height.

Perimeter

Total distance around a shape.

Kilometres to Miles

M = 0.62K converts km to miles.

Goals in Football

A goal scores 6 points in Australian rules.

Behind in Football

A behind scores 1 point in Australian rules.

Total Score Formula

S = 6g + b calculates total score.

Natural Numbers Sum

S = n(n + 1)/2 sums first n numbers.

Unlike Terms

Terms with different pronumerals cannot be combined.

Equivalent Expressions

Different forms representing the same value.

Constant Term

A term without a variable.

Height and Width

Dimensions that determine area of a triangle.

Scoring Shots

Total attempts to score in a game.

Combined Terms

Result of adding or subtracting like terms.

Term Order

Order of pronumerals in a term does not matter.

Mathematical Reasoning

Logical thinking applied to solve problems.

Collaborative Task

Group activity to simplify algebraic expressions.

Coefficient Addition

Adding coefficients of like terms.

Simplification Process

Steps taken to reduce an expression.

Algebraic Terms

Parts of an expression separated by + or -.