Algebra, along with its sister branches like trigonometry and arithmetic, has a wide variety of applications in various real-life situations and professions like architecture, engineering, construction, and medical science. This makes algebra an exciting subject to learn. However, many students make some general mistakes in this section, just like any other subject. Many of these mistakes are usually a result of laziness or hurry by not paying attention to the concepts in depth. These mistakes can be easily avoided at all levels. So, we will try to list down some of these most common mistakes in algebra that we generally come across.
Most Common Mistakes:
- Division by zero:
Even the person who has taken only a few math classes in his entire life, definitely knows that 0/1 =0, but the problem is that many people make a mistake by saying that 1/ 0 = 0 or 1/ 0 = 1. Always remember that division by zero is undefined. That means you cannot divide any number by zero. You should always look out for such kind of mistakes.
- Parenthesis error
This is probably the error that is the most frustrating one. There are a couple of errors that people usually do while dealing with parenthesis. The first mistake is that some people think that parenthesis isn’t needed at certain steps. So, they often tend to forget about the parenthesis in the very next step. Let’s understand this with a few examples:
Correct: (4x) 2 = (4)2 (x) 2 = 16×2 Incorrect: (4x) 2 = 4×2
Note that there is a very vast difference between these two. When dealing with exponents, students only remember that the quantity immediately to the left of the exponent gets the exponent. So, in the incorrect case, x is the quantity immediately to the left of the exponent. So, people make a mistake by squaring only the x while leaving the four without a square. In the real scenario, the parenthesis is to the immediate left of the exponent. So, this signifies that everything inside the parenthesis should be squared. Parenthesis are required in this case to make sure that we square the whole thing, not just the x.
Correct: (-3)2 = (-3) (-3) = 9 Incorrect: (-3)2 = – (3) (3) = – 9
People usually remember the rule that the quantity to the left of the exponent gets the exponent. So, in the incorrect case, only three is to the left of the exponent, and so only the three should get squared. But, actually, in such a case, the entire number inside the parenthesis, along with its sign, will get the exponent. So, the correct answer will be 9 and not -9.
- Cancelling Errors
Let’s look at these kind of errors with the help of an example.
Correct: (8-3)/2 = 5/2 = 2.5
Incorrect: 8-3/2 = 4-3= 1
These two aren’t the same. So, if we first cancel the two in the denominator with the eight in the numerator, it is incorrect. Instead, in such a case, the denominator gets evenly distributed with all the numbers present in the numerator.
- Applying the Zero-Product Rule to Everything
The zero product rule allows you to solve an equation like (x+2) (x-3) = 0.
By realizing that the only way two things can multiply to give us zero is if one or both are zero, we solve this equation by taking (x+2)= 0, and saying one of the solutions is x= -2. And then, when we take, (x-3) = 0, the other solution is x=3. But, equating it to zero is the correct approach only when there is a zero on the right-hand side.
If instead, we had (x+2) (x-3) = 1. Then, we cannot use this approach. To solve this particular equation, you have to multiply both the terms on the left-hand side and then bring the right-hand side term and perform the required mathematical operation, to get a final solution.
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By slowing down and paying attention to what you’re doing, you can avoid the majority of these mistakes in algebra. However, if you need proper guidance along with technical support, we would recommend you to get enrolled with best tutoring services and start your preparation journey. Moreover, start practicing questions of algebra modeled according to the latest exam patterns.
We believe that you must have got some useful insights regarding some of the common mistakes that should always be avoided.