PSLE Algebra: The Complete Guide for P6 Students

Algebra might look intimidating with all those letters, but it’s really just math with mystery boxes! Learn how to write, simplify, and solve algebraic expressions step by step.

Why Algebra Matters for PSLE

Algebra is one of the most important topics in P6 Mathematics. It appears in both Paper 1 (multiple choice and short answer) and Paper 2 (word problems). Once you understand the basics, you’ll see that algebra is a powerful tool that makes solving problems easier, not harder!

What Is a Variable?

A variable is a letter (like $x$ , $y$ , $n$ , or $p$ ) that represents an unknown number. Think of it as a mystery box that could contain any number!

Example: “Maya has some stickers. We use x to represent the number of stickers.”

Here, x could be 5, or 10, or 100 - we don’t know yet!

💡 Remember

Variables are letters that represent unknown numbers. Common variables in PSLE are: $n$ , $x$ , $y$ , $p$ , $m$ , $k$

Writing Algebraic Expressions

An algebraic expression combines variables, numbers, and operations (+, -, ×, ÷).

Addition Expressions

When we add a number to a variable:

Example: Addition

Problem:

Ahmad has $p$ pencils. His teacher gives him 3 more pencils. Write an expression for the total number of pencils.

Ahmad starts with $p$ pencils

He gets 3 more: $p + 3$

Answer: $p + 3$

Subtraction Expressions

⚠️ Order Matters in Subtraction!

" $p - 5$ " means “start with $p$ and take away 5”. This is different from " $5 - p$ "!

Example: Subtraction

Problem:

Mary had 20 apples at first. She gave away $j$ apples. How many apples does Mary have left?

Mary started with 20 apples (a known number)

She gave away $j$ apples: $20 - j$

Answer: $(20 - j)$ apples

Tricky Phrases to Watch Out For

Phrase	Correct Expression
”15 less than $d$ ”	$d - 15$ (NOT $15 - d$ )
“Subtract $c$ from 25”	$25 - c$ (NOT $c - 25$ )
” $r$ years ago, he was…”	Current age $- r$

Multiplication Expressions

In algebra, we write multiplication without the × sign:

$4 \times m$ is written as $4m$
The number always goes before the letter

Example: Multiplication

Problem:

Leila has $q$ stickers. Siti has 5 times as many stickers as Leila. How many stickers does Siti have?

“5 times as many” means multiply by 5

Siti has: $5 \times q = 5q$

Answer: $5q$ stickers

Division Expressions

Division is written as a fraction:

$y \div 6$ is written as $\frac{y}{6}$

Example: Division

Problem:

$p is shared equally among 3 children. How much does each child get?

Sharing equally means division

Each child gets: $p \div 3 = \frac{p}{3}$

Answer: $\frac{p}{3}$ each

Simplifying Expressions: Like Terms

What Are Like Terms?

Like terms have the same variable. Unlike terms have different variables.

Like Terms (Can Combine)

$3y$ and $5y$ - both have $y$

$2m$ and $9m$ - both have $m$

Unlike Terms (Cannot Combine)

$4x$ and $7y$ - different variables

$6a$ and $6b$ - different variables

❌ Common Mistake

$3x + 2y \neq 5xy$ . Unlike terms cannot be combined! The answer stays as $3x + 2y$ .

Adding Like Terms

To add like terms, add the coefficients (numbers in front) and keep the variable:

$6y + 2y = 8y$ (because $6 + 2 = 8$ )

💡 Remember

A variable by itself means coefficient of 1. So $a = 1a$ , and $4a + a = 4a + 1a = 5a$

Subtracting Like Terms

Same principle - subtract the coefficients:

$10x - 3x = 7x$ (because $10 - 3 = 7$ )

Example: Simplifying Mixed Expressions

Simplify:

$6y + 2 + 2y + 5$

Step 1: Group like terms

Variable terms: $6y + 2y$

Constant terms: $2 + 5$

Step 2: Simplify each group

$6y + 2y = 8y$

$2 + 5 = 7$

Answer: $8y + 7$

Evaluating Expressions (Substitution)

Substitution means replacing a variable with a number and calculating the answer.

Example: Simple Substitution

If $x = 15$ , find the value of $4x + 9$ .

$4x + 9$

$= 4 \times 15 + 9$ (do multiplication first!)

$= 60 + 9$

$= 69$

⚠️ Order of Operations

Always do multiplication and division BEFORE addition and subtraction!

Solving Equations

An equation has an equals sign and tells us two things are equal. Solving an equation means finding what value makes it true.

The Balance Scale Concept

Think of an equation like a balance scale - both sides must be equal!

x + 3 = 10

Whatever we do to one side, we must do to the other to keep it balanced

Inverse Operations

To solve equations, use inverse operations (opposite operations):

To undo addition, use subtraction
To undo subtraction, use addition
To undo multiplication, use division
To undo division, use multiplication

Example: One-Step Equation (Addition)

Solve: $7 + j = 18$

To find j, subtract 7 from both sides

$7 + j = 18$

$j = 18 - 7$ (subtract 7 from both sides)

$j = 11$

Check: $7 + 11 = 18$ ✓

Example: One-Step Equation (Multiplication)

Solve: $9g = 72$

9 groups of g equals 72. Divide both sides by 9.

$9g = 72$

$g = 72 \div 9$ (divide both sides by 9)

$g = 8$

Check: $9 \times 8 = 72$ ✓

Multi-Step Equations

For two-step equations, follow this order:

First, deal with addition/subtraction (isolate the variable term)
Then, deal with multiplication/division (find 1 unit)

Example: Two-Step Equation

Solve: $2x + 14 = 70$

Step 1: Subtract 14 from both sides

$2x + 14 = 70$

$2x = 70 - 14$

$2x = 56$

Step 2: Divide both sides by 2

$x = 56 \div 2$

$x = 28$

Check: $2(28) + 14 = 56 + 14 = 70$ ✓

Word Problems with Algebra

The most challenging PSLE algebra questions are word problems. Here’s a systematic approach:

Define the variable: What does $x$ (or $n$ ) represent?
Write expressions: Translate the words into algebra
Set up the equation: What equals what?
Solve step by step
Answer in context: Include units and check!

PSLE-Style Word Problem

Problem:

There are 70 children playing table tennis or badminton in a sports hall. There are $x$ children playing table tennis. There are 14 more children playing badminton than table tennis. How many children are playing table tennis?

Step 1: Define variables

Table tennis = $x$ children

Badminton = $x + 14$ children (14 more)

Step 2: Write equation

Total: $x + (x + 14) = 70$

Step 3: Solve

$2x + 14 = 70$

$2x = 70 - 14 = 56$

$x = 56 \div 2 = 28$

Answer: 28 children are playing table tennis

Check: $28 + (28 + 14) = 28 + 42 = 70$ ✓

Common Mistakes to Avoid

❌ Mistake 1: Writing m × 8 Instead of 8m

In algebra, the number goes BEFORE the letter: write $8m$ , not $m8$ or $m \times 8$

❌ Mistake 2: Adding Unlike Terms

$3x + 2y$ cannot be simplified! They are unlike terms. It is NOT $5xy$ .

❌ Mistake 3: Wrong Order in Subtraction

“15 less than $d$ ” is $d - 15$ , NOT $15 - d$ . Read carefully!

❌ Mistake 4: Forgetting to Check

Always substitute your answer back into the original equation to verify!

Quick Reference

Operation	Algebraic Form	Example
Add	$n + 5$	”5 more than $n$ “
Subtract	$n - 5$	”5 less than $n$ “
Multiply	$5n$	”5 times $n$ “
Divide	$\frac{n}{5}$	” $n$ divided by 5”
Simplify	$3x + 2x = 5x$	Combine like terms
Solve	$x + 5 = 12 \Rightarrow x = 7$	Inverse operations

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PSLE Algebra: The Complete Guide for P6 Students

PSLE Algebra: The Complete Guide for P6 Students

Why Algebra Matters for PSLE

What Is a Variable?

Writing Algebraic Expressions

Addition Expressions

Subtraction Expressions

Tricky Phrases to Watch Out For

Multiplication Expressions

Division Expressions

Simplifying Expressions: Like Terms

What Are Like Terms?

Like Terms (Can Combine)

Unlike Terms (Cannot Combine)

Adding Like Terms

Subtracting Like Terms

Evaluating Expressions (Substitution)

Solving Equations

The Balance Scale Concept

Inverse Operations

Multi-Step Equations

Word Problems with Algebra

Common Mistakes to Avoid

Quick Reference

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