How to Learn Algebra

Algebra can seem intimidating, but once you get used to it, it’s not that difficult! You just have to follow the sequence to complete the sides of the equation and arrange the math carefully to avoid errors!

Table of Contents

Learn basic algebra principles

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Review basic calculations. To start learning algebra, you need to know basic math skills like addition, subtraction, multiplication, and division. These elementary math skills are essential for you to start learning algebra. It will be difficult for you to understand more complex concepts in algebra without learning those operations. If you need a refresher, you can read our article on basic math skills.

You don’t have to be very good at mental arithmetic to be able to solve algebra problems. Many algebra classes allow you to use a calculator to save time with simple calculations. However, you should at least know how to do basic math without using a calculator just in case you don’t have permission to use it.

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Know the order in which calculations are performed. For beginners, they often don’t know where to start when solving algebraic equations. There is a specific sequence for solving these problems: first all the operations in brackets, then exponentiation, multiplication, division, addition, and finally subtraction. You can find on the internet how to apply the sequence of calculations. In short, the order in which the calculations are performed is:

Parentheses
Index number
Multiplication
Division
Summation
Subtraction
In algebra, the sequence of calculations is important, because performing operations in the wrong order can sometimes lead to incorrect results. For example, if we have the problem 8 + 2 × 5, if we add 2 by 8 first we get 10 × 5 = 50 , but if we multiply 2 by 5 first we get 8 + 10 = 18 . Only the second result is correct.

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Know how to use negative numbers. In algebra, people often use negative numbers, so you should review how to add, subtract, multiply, and divide negative numbers before you start learning algebra. Here are some negative number basics — for more information, you should check out our articles on adding, subtracting, multiplying, and dividing negative numbers.

On the number line, a negative value of a number is the same distance as its positive value from zero, but in the opposite direction.
Adding two negative numbers will give a larger negative number (in other words, the number will be larger, but since it’s negative, it’s more negative).
The two minus signs cancel each other out — subtracting a negative number is the same as adding a positive number
Multiplying or dividing two negative numbers results in a positive number.
Multiplying or dividing a positive number by a negative number will result in a negative number.

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Know how to present long problems. Solving simple algebra problems can be very quick, but for complex problems, you have to take many steps. To avoid making mistakes, you should present the problem on a new line every time you start a solution step. If you’re solving an equation with two sides, try to write all the equals (“=”) signs in line with each other. So if there is a mistake somewhere, it will be easier for you to detect.

For example, to solve the equation 9/3 – 5 + 3 × 4, we present the problem as follows:

9/3 – 5 + 3 × 4

9/3 – 5 + 12

3 – 5 + 12

3 + 7

ten

Understanding variables

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Find symbols that are not numbers. In algebra, problems aren’t just numbers, you’ll see letters and symbols appear in them. These are called variables. Variables aren’t as complicated as you might think – it’s just a way of representing numbers with unknown values. Here are some common examples of variables in algebra:

Characters like x, y, z, a, b and c
Greek characters like theta (θ)
Note that not all symbols are unknown variables. For example, the number pi (π) is always about 3.14159.

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Treat variables as “unknown” numbers. With that said, a variable is basically just a number of unknown value. In other words, there are a number of numbers that can be substituted for the variable so that the equation holds. Often the goal of an algebra problem is to find the value of a variable — think of it as the “secret number” you need to figure out.

For example, in the equation 2x + 3 = 11, x is the variable. That is, there is a value that can be substituted for x to make the left side of the equation equal to 11. Since 2 × 4 + 3 = 11, in this case x = 4 .
One way to understand a variable is to replace it with a question mark. For example, we rewrite the equation 2 + 3 + x = 9 into 2 + 3 + ? = 9. This makes it easier to understand what needs to be done — we just need to figure out what number adds 2 + 3 = 5 to get 9. Of course the answer is 4 .

Learn how to “cancel” to solve equations

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Try to transform both sides of the equation so that one side of the equal sign contains only the variable. Solving an algebraic equation means figuring out the value of the variable. Algebraic equations usually include numbers and/or variables on both sides, and have the following form: x + 2 = 9 × 4. To find the variable, you must switch sides so that one side of the equation has only the variable. The rest on the other side of the equal sign is the answer.

In the example (x + 2 = 9 × 4), so that the left side of the equation has only the variable x, you need to remove the “+2”. You just need to subtract 2 from that side to get x = 9 × 4. However, to make both sides of the equation equal, you must also subtract 2 from the other side. So we have x = 9 × 4 – 2. According to the calculation sequence, we will multiply before subtracting, the result will be x = 36 – 2 = 34 .

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Suppress addition by subtraction (and vice versa). As seen above, if we want one side of the equation to have only the variable x, we have to remove the numbers next to it. For this to work, you must perform the “opposite” operation on both sides of the equation. For example, in the equation x + 3 = 0, since we have “+ 3” next to x, we will add “- 3” to both sides. “+ 3” and “- 3” cancel each other out so one side of the equation is left with only x, and the other side will have “-3”: x = -3.

In general, addition and subtraction are “opposite” operations — perform one operation to eliminate the other. See the example below:

For addition, you would subtract. For example: x + 9 = 3 → x = 3 – 9

For subtraction, you would add. Example: x – 4 = 20 → x = 20 + 4

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Suppress multiplication by division (and vice versa). Multiplication and division are slightly more difficult than addition and subtraction, but they also have an “opposite” relationship. If you see “×3” on one side, cancel it by dividing both sides by 3.

With multiplication and division, you must perform the opposite operation for every term on the other side of the equation, even if there is more than one term. See the example below:

For multiplication, you would divide. Example: 6x = 14 + 2 → x = (14 + 2) /6

For division, you would multiply. Example: x/5 = 25 → x = 25 × 5

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Suppress exponentiation by taking root (and vice versa). Exponential is a fairly advanced algebra topic — if you don’t know exponentiation, see the article on exponentiation for more information. The “opposite” of an exponentiation is a root operation with the same degree of that power. For example, the opposite of the power of ² is the square root (√), the opposite of the power of ³ is the square root ( ³ √), and so on.

This is a bit confusing, but in the case of exponential equations, you have to root both sides of the equation. On the other hand, when solving problems with roots, you have to calculate powers of both sides of the equation. See the example below:

For exponents, you would take the root. For example: x ² = 49 → x = 49

For the root, you would calculate the exponentiation. Example: x = 12 → x = 12 ²

Enhance algebra skills

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Use pictures to illustrate the problem. If you can’t figure out an algebra problem, try using graphs or pictures to illustrate the equation. You can even use objects like coins if available.

For example, solve the equation x + 2 = 3 using boxes (☐)

x +2 = 3

+☐☐ =☐☐☐

We will subtract 2 from both sides by removing 2 boxes (☐☐) from both sides:

+☐☐-☐☐ =☐☐☐-☐☐

=☐, or x = 1
As another example, let’s solve the equation 2x = 4

=

We’ll divide both sides by 2 by separating the boxes on each side into two groups:

|☒ =☐☐|☐☐

= , or x = 2

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Use the “reasonability test” method (especially for word problems). When turning a word problem into an algebra problem, try to test the formula by substituting simple values for variables. Does the equation satisfy when x = 0? When x = 1? When x = -1? It’s easy to make small mistakes like writing p=6d while wanting to say p=d/6, but it’s easy to spot if you do a quick check before continuing to solve.

For example, the problem is for a football field whose length is 30 meters longer than its width. We use the equation l = w + 30 to represent this relationship. You can check the plausibility of the equation by simply substituting in values. For example, if the football field has a width w = 10m, then the length will be 10 + 30 = 40m. If it has a width of 30m, then the length is 30 + 30 = 60m, and so on. The equation makes sense — we’ll get a longer football field as the width gets wider.

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Remember that in algebra, the answer is not always an integer. In algebra and other advanced forms of mathematics, the answer may not be an integer. The answer is usually a decimal, fraction, or irrational number. Calculators can help you find complex answers, but keep in mind that your teacher may ask you to write down the exact answer instead of a long decimal.

For example, suppose we reduce an algebraic equation to x = 1250 ⁷ . If you enter 1250 ⁷ into the calculator, you will get a huge number of decimals (because the computer screen is not large enough, it will not be able to display the whole number). In this case, we should write the answer as 1250 ⁷ or simply the number by writing in mathematical notation.

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Once you’re confident with basic algebra skills, try factoring . One of the most difficult algebra skills is factoring — a shorthand for simplifying complex equations. Factoring is a semi-advanced algebra topic, so you should refer to the article linked above if you’re having trouble with it. Here are a few brief hints for factoring equations:

The equation of the form ax + three breaks down to a(x + b). Example: 2x + 4 = 2(x + 2)
The equation of the form ax ² + bx breaks down to cx((a/c)x + (b/c)), where c is a common factor of a and b. Example: 3y ² + 12y = 3y(y + 4)
The equation of the form x ² + bx + c decomposes into (x + y)(x + z) where y × z = c and yx + zx = bx. For example: x ² + 4x + 3 = (x + 3)(x + 1).

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Practice, practice and practice! To be good at algebra (and any form of math) you need a lot of practice. Don’t worry, you just need to focus during class, do all your homework and ask your teacher or classmates to help you, you will start to become proficient in algebra.

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Ask your teacher to explain difficult algebra problems. If you’re having trouble learning algebra, don’t worry because you’re not alone with it. Your teacher is the first person you should turn to when you have a question. After class, politely ask your teacher for help. Good teachers will often be happy to repeat the lesson at the end of class, and even give you extra homework.

If they can’t help you for some reason, ask about other tutoring options at the school. Many schools have after-school programs that can help you learn more and get more guidance to improve your algebra skills. Finding free and readily available support isn’t something to be ashamed of — it’s a sign that you’re smart enough to solve your problem!

Learn intermediate math topics

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Learn to graph x/y equations. A graph is a very useful tool in algebra because it allows you to display ideas in an easy-to-understand visual form, which you would normally have to use numbers. In elementary algebra, graphing problems are usually limited to equations with two variables (x and y) and are plotted on a simple 2-D graph with the x and y axes. With this type of equation, all you have to do is plug in one value for x and then solve for y (or vice versa) to get two values that correspond to a point on the graph.

For example, in the equation y = 3x, if you substitute 2 for x, you get y = 6. That means the point (2,6) (two units to the right of the y-axis and six above the x-axis) is part of the graph of this equation.
Equations of the form y = mx + b (where m and b are numbers) are especially common in basic algebra. These equations always have a slope m and intersect the y axis at y = b.

Advice

There are many algebra learning resources online. For example, just enter a simple search keyword like “algebra help” and the browser will list dozens of useful results. You should also look in wikiHow’s collection of math articles. You can find tons of algebra material, so start exploring today!
A very good site for those new to algebra is khanacademy.com. This free site offers a wide variety of well-organized lessons on a variety of topics, including algebra. There are video tutorials on everything from the very basics to college-level topics, so don’t hesitate to tap into the Khan Academy resources, and make use of all its supporting functions!
Don’t forget that the best resources for learning algebra may be the people you meet every day. Try talking to a friend or classmate if you want extra help with the lesson.

Steps