Remember when you first learned math, and it was pretty straightforward? Back then, math problems were just numbers obeying the same rules. Even word problems were still limited to known quantities. But then along came algebra, with letters instead of numbers, and that’s where plenty of students start to get confused.
Although algebra is a key building block for many higher mathematical concepts, including linear equations, it’s easy to get frustrated and confused. Solving algebra problems while trying to remember solutions and steps to finding the value of various pronumerals can be a little daunting, particularly once you start moving on from basic algebra to quadratic equations. That’s not to mention negative numbers!
Fortunately, we’ve put together a handy guide to mastering any level of algebra for you. It’s easier than you think. Getting to grips with algebraic expressions and equations is simply a matter of learning the rules that govern the numbers and pronumerals.
One advantage of algebra – and math in general – is that the rules remain constant. No matter how difficult a problem appears to be, if you understand the rules for solving it, you can figure out the solution. Understanding basic algebra will help you as you move into trigonometry, calculus, and other higher math concepts. Practice really does make perfect, so try some of these tricks out and see how well they work for you.
Know Your Basic Arithmetic
You probably learned addition, subtraction, multiplication, and division back in elementary or primary school. All mathematics is built around these fundamental, basic operations. Even the most complicated algebraic expressions use these basic concepts.
In this case, basic doesn’t necessarily mean what’s easiest. Anyone who has tried long division can tell you that!
Learning the basics here actually means understanding what’s most important. Having a good, solid understanding of how to add numbers together, subtract them, multiply and divide is key to improving your algebra skills.
Because a lot of our numerical system is built around groupings of ten, be sure to remember which numbers can be added or subtracted together to make ten.
Memorise your times tables so multiplication and division become easier. You’ll probably have access to a calculator, but if you don’t, this is an invaluable skill.
There is a strict, sequential order that all mathematical operations have to follow. If you do these out of order, you’ll end up with the incorrect answer.
To master algebra, you’ll need to know the order of operations by heart. This is:
- Parentheses (or brackets)
- Multiplication & Division
- Addition & Subtraction
In other words, when looking to solve equations, start with anything contained in the parentheses. Next, do the exponents (that’s squared or cubed numbers, and so on). Multiplication and division are next, and you do these in the order of left to right, even if that means the division must come first.
Addition and subtraction are the last part of the equation to solve, and once more you must do these from left to right, even if the subtraction appears before an addition.
Know How To Use Negative and Positive Numbers in Algebraic Equations
Negative numbers can be a little imposing because they’re hard to translate into daily life scenarios. Nothing was ever minus three centimetres long, and you can’t have negative twelve eggs in your fridge.
However, for the purposes of algebra, knowing the rules for negative numbers is extremely important. Basically, if you have a number line, the negative version of a number is the same distance from zero as the positive, just in another direction.
- Adding two negative numbers makes the result more negative.
- Subtracting a negative is the same thing as adding a positive number.
- Multiplying or dividing two negatives will give you a positive number.
- Multiplying or dividing a negative by a positive number will give you a negative number.
Organise Long Problems Like Quadratic Equations
Somebody has to mark your paper – so you might need to go over your working out to show your thinking and your steps in finding the solution. Be kind to yourself, and to the teacher marking your math exam, and keep your long problems nice and organized.
- Start a new line for each step toward solving the equation.
- Keep your equals sign in the same place for every line.
- Keep the numbers in the same place if they haven’t changed from one line to the next.
For example, to solve a = (12/3) – 4 + 8 × 2, we would lay it out as below. Note that we are following the order of operations.
a = (12/3) – 4 + 8 × 2
a = 4 – 4 + 8 x 2
a = 4 – 4 + 16
a = 0 +16
a = 16
This might feel like overkill for elementary algebra, but this layout is really helpful for more complex formulas, like if you’re working on a quadratic equation.
In elementary algebra all the way up to the most complex stuff, you’ll often encounter letters in place of numbers. These are called variables. Simply put, each variable represents a number of unknown values. Unknown values are the bread and butter of any algebra problem. Understanding variables will help you understand algebra, and help you find solutions to the scariest equations.
The number’s value in the equation may be unknown, but because it is still a number, it will obey all the rules we’ve outlined above. Common variables, to give a few examples, are x, y, z, a, b, and c, although you will occasionally see other letters.
- Not all symbols are variables. Pi, which has a fixed value of 3.14, is often represented by the symbol π.
- Recurring variables have equal value. If the variable x appears multiple times in one equation, they are of the same value. For example, x – x must equal zero.
Cancelling Equations To Solve Equations
You can simplify algebra significantly by isolating variables and employing the “cancelling” strategy. This makes solving equations much simpler.
- You can cancel addition with subtraction and vice versa.
- You can cancel multiplication with division and vice versa.
- You can cancel exponents with the root and vice versa. For example, cancel a square number by finding the square root.
For example, consider how to solve the equation b + 5 = 6 x 9.
You can move the 5 over to the other side of the equals sign by subtracting five from both sides.
b + 5 – 5 = 6 x 9 – 5
b + 0 = 6 x 9 – 5
b = 6 x 9 – 5
From there, you can employ your order of operations to solve for b.
b = 6 x 9 – 5
b = 54 – 5
b = 49
This is a great way to make complex equations and more difficult mathematical expressions more palatable. Equations like this are more easily solved when you can cancel out certain elements.
Review After Every Lesson
Make sure you understand how you solved your problems, and be sure to take note of any issues you had. This way, next time you’re in class, you can ask questions about anything you missed and improve your understanding that way.
Prep Studies & Test Prep
One of the great things about mathematics is how much practice improves your ability. When you’re preparing for a test, be sure to do practice exams.
Do plenty of exercises to test your problem-solving ability, preferably under exam conditions. That means you’ll eliminate distractions and set aside a block of time in which you’re only doing algebra to the exclusion of all else.
Practice tests are one of the best ways to quickly solidify your knowledge in any given area.
We hope this guide to algebra is helpful and you feel more confident solving those pesky equations. Algebra is really just an extension of the mathematics and concepts you’ve already learned in elementary or primary school. Although it can seem daunting to have to deal with variables, ultimately all numbers obey the same rules when you apply the correct approach to solving the problem.
Remembering your order of operations, basic arithmetic, and throwing in a few tricks like cancelling and so on are great ways to quickly improve your algebra powers. If you can consistently apply these skills by engaging in practice tests and revision, you’ll be a master of algebra in no time!
You can always use helpful online study resources like Zookal Study to help manage your time and improve your study habits, optimise your work/life balance, and get the most out of your study time.