Many students find it hard to go from simple sums to more complicated equations. Pre algebra in maths is very important when you go from "2 + 3" to "x + 3 = 5."You will feel more confident taking on more difficult reasoning and problem-solving tasks once you have mastered this.
What is Pre Algebra?
Before you start working with complicated formulas, you need to know what they mean. In short, it is the study of math symbols and how to use them. While primary school maths focuses on calculations with fixed numbers, this subject introduces the idea of "variables"—letters that stand in for numbers we don't know yet.
Learning basic algebra acts as a foundational step. It ensures that you are comfortable with integers, fractions, and decimals before you start dealing with the intense graphing and quadratic equations found in later years. It makes simple maths a useful tool for tackling problems in the real world.
Important Topics
To excel in this subject, you need to familiarise yourself with specific topics. These are the most important parts of your maths journey.
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Integers and Operations: Moving beyond positive numbers to include negative numbers. You will learn how to add, subtract, multiply, and divide integers with a sign.
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Fractions, Decimals, and Percentages: Learning how these three all mean the same thing; parts of a whole, and how to transition between them.
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Factors and Multiples: Understanding Prime Factorisation, Highest Common Factor (HCF), and Lowest Common Multiple (LCM).
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Ratios and Proportions: Ways to compare amounts and see how they vary in relation to each other.
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Basic Equations: This is where you first encounter variables like $x$ and $y$ and learn how to balance an equation to find their value.
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Exponents and Radicals: Dealing with squared numbers, square roots, and powers.
Pre Algebra Formula
A good formula sheet can make your schoolwork a lot easier. Below is a table of the most common formulas and properties you will use daily in your studies.
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Category
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Property/Formula
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Explanation
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Commutative Property
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a + b = b + a
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The order of numbers doesn't change the sum.
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Associative Property
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(a + b) + c = a + (b + c)
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Grouping numbers differently doesn't change the result.
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Distributive Property
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a(b + c) = ab + ac
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Multiplying a sum by a number is the same as multiplying each addend.
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Identity Property (Add)
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a + 0 = a
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Adding zero keeps the number the same.
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Identity Property (Mult)
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a * 1 = a
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Multiplying by one keeps the number the same.
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Inverse Property (Add)
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a + (-a) = 0
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A number plus its opposite equals zero.
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Area of Rectangle
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Length x Width
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Used to calculate the space inside a 2D shape.
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Perimeter of Square
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4 x Side
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The total distance around the outside of a square.
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Read More - Algebra 1 - Topics, Formula, Examples
How to Solve Basic Pre Algebra Equations
Solving equations is about keeping things balanced. Imagine a seesaw; whatever you do to one side, you must do to the other.
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Identify the Variable: Look for the letter (like $x$).
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Isolate the Variable: Your goal is to get the letter all by itself on one side of the equals sign.
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Use Inverse Operations: If the equation shows addition, use subtraction to "undo" it. If it shows multiplication, use division.
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Check Your Work: Plug your answer back into the original equation to see if it makes sense.
For example, in the equation $x + 10 = 15$, you would subtract 10 from both sides to find that $x = 5$.
Pre Algebra Worksheet for Practice
The best way to get better is through consistent practice. Use this worksheet to test your current knowledge.
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Simplify: -15 + (-8) = ?
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Solve for x: x - 12 = 25
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Simplify: 4(3 + 5) using the distributive property.
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Find the value: If y = 4, what is 3y + 10?
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Calculate: What is 25% of 80?
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Solve for m: 5m = 45
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Identify: What is the HCF of 12 and 18?
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Simplify: (-6) x (-4) = ?
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Fraction to Decimal: Convert 3/5 into a decimal.
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Order of Operations: Solve 10 + 2 x 5 - 4.
(Answers: 1: -23, 2: 37, 3: 12 + 20 = 32, 4: 22, 5: 20, 6: 9, 7: 6, 8: 24, 9: 0.6, 10: 16)
Read More - Algebra vs Calculus – What’s The Difference?
Pre Algebra for Beginners
You don't have to be a "maths person" to do well in basic algebra. It's all about pursuing a logical path.
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Draw Diagrams: Sometimes, drawing a number line will help you understand negative numbers better than merely looking at the symbols.
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Show Every Step: Don't try to do everything in your head. Writing down each step prevents small mistakes from ruining your final answer.
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Know "Why": Instead than just memorising a formula, try to figure out why it works. For example, the distributive property is essentially a means to make multiplication easier by dividing it up into smaller parts.
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Terms Flashcards: Use flashcards to remember words like "coefficient", "constant", and "expression" so you don't get confused by the wording of a question.
Common Mistakes to Avoid in Pre Algebra Topics
Many students struggle because of a few recurring errors.
One major pitfall is the "sign error". Forgetting that a negative times a negative equals a positive is a very common slip-up. Another issue is the "order of operations". Always remember the BODMAS/PEMDAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction). If you skip the brackets and go straight to addition, your answer will likely be incorrect.
Lastly, many students forget to perform the same operation on both sides of an equation. If you subtract 5 from the left, you must subtract 5 from the right to maintain equality.
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