What exactly is Algebra?
Algebra is a unifying thread across most mathematics which focuses on using letters and symbols to represent numbers and different formulae in an equation. It is understood that Algebra could have been used for as long as 4000 years. Many examples of Algebra can be found in the algebra equations worksheets on our site. Let’s take a look at one below:
This is just one of the ways to learn and teach how to express missing number problems algebraically.
The symbols and letters used in algebra equations worksheets are called ‘variables.’
The general rules that govern algebra and dictate how it is written down are called variables. Variables are symbols (typically letters like a, b, x, y) representing or substituting an unknown number. When we do not know the value of a number, we use a variable until we figure out what the number is as a kind of placeholder.
How to do Algebra:
As you’ll have discovered, algebra is one of the most difficult maths concepts for adults to teach and kids to understand. The best way to start is by explaining algebra in its simplest form – it’s a puzzle! For example, algebra questions often require pupils to figure out the value of a letter, often called x. So let’s work out an example to show you how to do algebra:
Example: x – 2 = 4
Introducing letters into maths equations can be daunting, but a question like this makes great sense once you know what to do. We want to find out what x is equal to, but we have – 2 on the left-hand side. To get rid of it, we’ll have to work out both sides to cancel it. In this case, we would add 2 to both sides. This leaves us with the following:
x = 4 + 2
x = 6
And there you go! If you’re ever unsure if the answer you’ve reached is right or not, work out the equation with x’s value. In this example, this would be:
X – 2 = 4
6 – 2 = 4
Since this equation works out correctly, we know we got the x value right! Remember always to keep the balance when working out an algebra equation – what we do to one side, we do to the other. An easy step-by-step guide on how to do algebra is as follows:
- Figure out what needs to be removed to get the value of x.
- Remove it by doing the opposite. If it’s x with addition, subtract the number(s). If it’s x with subtraction, add the number(s).
- Do that to both sides. Then, double-check your answer by replacing x with your found value.
Let’s work through another example so that we can strengthen our algebra skills:
Example: x + 5 = 12
Similarly to last time, we want to figure out the value of x but cannot because we have different numbers on the left-hand side. As our number is positive, we must subtract from both sides instead of adding. This leads to the following:
X + 5 = 12
X = 7
Again, if we want to double-check that our answer is correct, we can work out the equation with x’s known value:
X + 5 = 12
7 + 5 = 12
Since the equation makes sense, we know we’ve got it right. So keep on practicing; your class will be algebra geniuses before you know it!
Algebra for beginners:
Algebra can be tricky to get to grips with, but once you build up a strong basic knowledge of the “language” of algebra, it can be much easier! We’ve put together some tips and tricks to bear in mind when first learning algebra to make it easier to understand:
Read the problem instructions carefully. This sounds simple enough, but more often than not, confusion can arise because children try to “solve” a problem when they need to “simplify” it! Therefore, it’s important to encourage children to read the instructions carefully and keep a look out for keywords like “solve,” “simplify,” “factor,” or “reduce”:
- Solve. This requires reducing the problem to an actual numerical solution, e.g., x=4. Furthermore, it involves finding the value for the variable so that the problem is “true.”
- Simplify. Here, you need to manipulate the problem into a simpler form than before. However, it is worth noting you will probably not end up with a single numerical value for the variable.
- Factor. This is similar to “simplify” and is typically used with more complex equations. It would help if you could turn the problem into smaller terms and split an expression into a multiplication of simpler words.
- Reduce. Reducing involves a combination of factoring and then simplifying. To “reduce” a problem generally consists of a variety of factoring and then simplifying. First, you break the numerator and denominator into their factors, then look for common elements (top and bottom) and cancel them out. Whatever is left over is the “reduced” form of the equation.
Focus on isolating the variable. The key rule is that any operation you do to one side of the equation must also do to the opposite side. This keeps the equation balanced and equal.
Learn PEMDAS. In algebra, when working out an equation, you need to follow certain steps in the order called the “order of operations.” This is often simplified by the mnemonic “PEMDAS,” which stands for:
Parentheses. Perform operations inside parentheses first.
Exponents. Simplify any exponents next.
Multiplication. Multiply from right to left.
Division. Divide from right to left.
Addition. Add from right to left.
Subtraction. Subtract from right to left.
Can Algebra be used in daily life?
As a student, you may be forgiven for thinking that Algebra exists only to give you a hard time and that once you have passed your exams, it’ll be forgotten and be a huge waste of time. This couldn’t be further from the truth. You may not realize it, but your brain always uses algebraic calculations!
For example, when you work out how much money you need to take to the shop when you know the price of the items you want to buy, or when you are working out how much diesel or petrol you can buy with a specific amount of money in your pocket.
This image shows how to work out missing number problems like the real-world examples above.
An example of algebra used in real life is when you go to the shop. For example, say you go to a bookshop and want to buy a book that costs £5, but you only have £2. You’ll use algebra to find out how much more money you need!
We can write the problem as 2 + x = 5. We are therefore asking, “Two plus what number equals five?” Just as you can add the same value to each side of an equation without changing the meaning of the equation, you can also subtract the same value from each side of an equation. And, as we discussed earlier in “Algebra for beginners,” any operation we do to one side of the equation also needs to be done to the opposite side. So we can work out our problem by starting with the original equation 2 + x = 5 and subtracting two from both sides: 2 – 2 + x = 5 – 2. We can then simplify this to x = 3.
History of Algebra
Algebra dates back as far as Ancient Egypt and Babylon. While it’s hard to pin credit on one person, two names synonymous with algebra are Abu Jaafar Mohammad Ibn Mousa Al Khwarizmi and Diophantus often dubbed the “Fathers of Algebra.”
Al Khwarizmi developed methods for balancing and reducing algebraic equations and introduced algorithms which are mathematical operations or rules. Diophantus wrote 13 books titled “Arithmetica,” which contain problems and solutions that further fleshed out algebra.