3 Common Algebra Mistakes

3 Common Algebra Mistakes

Algebra is a new topic which students learn in primary school. Here are 3 common Algebra mistakes. Make sure you avoid them.


Common Algebra Mistake 1: Adding Unlike Terms Together

This is the most common mistake in algebra. Letters and numbers are ‘unlike’ terms. When students see “5a + 10”, they simply add 5 to 10 and write the answer as “15a”. This is wrong. You cannot add the “10” to “5a” because they are considered unlike terms. 

You can only add ‘like’ terms together. For instance, “5a” and “2a” are ‘like’ terms because they both carry the letter “a”. So “5a + 2a = 7a”. 

But “5a + 10” cannot be simplified anymore and you can only leave it in this form.

Question: How do we simplify “5a + 2 + 2a + 3”?

In this case, you group the like terms together.

So, you rearrange and group the “a” together, followed by the numbers together. 

You will get “5a + 2a + 2 + 3”.

And this can be simplified further to “7a + 5”. And this will be the final answer.


Common Algebra Mistake 2: Failure to Put a Bracket

The next very common mistake in algebra is the failure to put brackets in the correct place. Take a look at these 2 expressions: “a + 2 x 3” vs “(a + 2) x 3”.

What is the difference?

For the first one, you do the multiplication first due to the order of operations which states that multiply comes before plus.

For the second one, you do the bracket first because the bracket comes before multiplying. 

So, when you read the question, you must be very careful about when to use brackets.

For example, “Mary has 2a oranges. She brought 3 more oranges. Jane has twice as many oranges as her. How many oranges does Jane have?”

In this example, you take 2a + 3 first. Then Jane’s oranges will be “(2a + 3) x 2” which can be simplified to “4a + 6”. This will be the final answer. The bracket in the working is essential.


Common Algebra Mistake 3: Failure to Put as a Fraction

Example: “The first number is b. The second number is 3. What is the average of these 2 numbers?”

Many students write “b + 3 ÷ 2” or “(b + 3) ÷ 2” as the final answer. 

Both are wrong.

The final answer should be “(b + 3)/ 2”. You cannot leave your answer in ÷. You need to change it to a fraction.


Make sure you don’t commit these algebra mistakes and you will save a lot of precious marks in your exams. 

Also, remember to check out the 3 Must-Know Algebraic Manipulation Skills



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