3 Must-Know Algebraic Manipulation Skills

3 Must-Know Algebraic Manipulation Skills

Algebra is the language of using letters to represent numbers. Do you know how to manipulate Algebraic expressions correctly? 

You will also be using Algebra often in Secondary school and later years. So primary 6 is a good chance to build up your understanding of Algebra.

Here are 3 must-know Algebraic Manipulation Skills. Also, remember to check out the 3 Common Algebra Mistakes.

 

Algebraic Manipulation Skill 1: Simplification

Algebraic simplification is the first must-know math concept.

When you are given numbers in the question, you can solve the question for a final numerical answer.

For instance, “John has 3 sweets. He buys 2 more sweets. How many sweets does John have?” 

The answer is “3 + 2 = 5”

But in Algebra, you are given letters to represent unknown numbers. So you can’t solve the question for a final numerical answer.

But you can simplify and give a final algebraic answer.

For example, “John has m sweets. He buys 2 more sweets. How many sweets does John have?”

The answer is “m + 2”. And that is the final answer. 

Do note that you cannot add m to 2 to become 3m as they are considered “unlike” terms. This is a very common mistake. 

 

Algebraic Manipulation Skill 2: Substitution

After you have known how to simplify algebraic expressions, the next math concept will be substitution.

As I mentioned earlier, Algebra is the language of using letters to represent unknown numbers. Sometimes, the question will give you the value of the letter and require you to give a numerical answer.

In this case, you need to substitute (or replace) the letter with the number given and work out the final answer.

When you do a substitution, keep in mind the order of operations. 

Example: If a = 2, find the value of a + 2 x 3?

The order of operations states that multiplication comes before addition. So you do “2 x 3” first which is 6. Then you substitute the letter a with 2 and add 2 to 6. The final answer is 8.

 

Now, take a look at another example.

If a = 2, what is the value of (a + 2) x 3?

The order of operations states that bracket comes before multiplication. So you replace the letter a with 2 and do the addition in the bracket first. Then you multiply the answer by 3.

So the answer is “4 x  3 = 12”.

Notice that the final answer is different from the previous one. 

 

Algebraic Manipulation Skill 3: Solving Equations

To solve equations correctly using Algebra, you must first understand the question clearly, followed by learning how to express the question in algebraic form.

For instance, “Subtract p from 20” can be expressed as “20 – p”. 

Next, you must understand how to solve Algebraic equations by the balancing method.

In simple terms, when you bring a positive term from one side of an equation to the other side, you must change the sign to a negative.

Likewise, if you bring a negative term from one side of an equation to the other side, you must change the sign to a positive.

Examples of Algebraic Equations

x + 1 = 3

x = 3 − 1 

x = 2 (Ans)

y − 2 = 3

y = 3 + 2

y = 5 (Ans)

Lastly, keep in mind when to put brackets and always put units at the end.

For example, “John has $p. He receives $20. The final answer is $(p + 20). Don’t forget the $ and bracket!

 

After you are clear with these Algebraic Manipulation skills, you can extend the same skill to using Simultaneous Equations which is another powerful skill to solve challenging problem sums.

You can also enrol in my online course, “8 Must Know Methods of Solving Math Problem Sums“. You will learn how to use “units and parts” as well as 7 other important methods to solve many problem sums. 

 

Free Download: 80 Useful Tricks to Solve Math Problems Easily

We hope that this article has helped your child to better understand the must-know Algebraic Manipulation skills. 

Before you go, download this eBook for free to learn 80 useful tricks to solve Math problems easily.

The 80 tricks taught in this eBook will be very useful in helping your child ace his or her Math exams!

80 Tricks to Solve Math Problems

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