In this blog, I will outline the five most common numerical mistakes I’ve seen made by students of all levels – be it primary school students in their SATS or secondary school students in their non-calculator GCSEs. I will explain why people get it wrong so often, how you avoid this and what the correct solution is. If you’re studying for your GCSEs, you can read two similar blogs I wrote last year – 5 common mistakes in foundation GCSE maths and 5 common mistakes in higher GCSE maths.
1. Multiplying integers by fractions
Question:
Incorrect solution:
I have seen this one a lot, and it’s a strange one because you would think people would know that you can’t multiply a number by 3 and it not change, which is what has happened here. Often this error happens as part of a larger question, so students don’t pay as much attention to it as they should.
The mistake that has been made here is we have multiplied both the top and the bottom of the fraction by 3. So basically, you are multiplying it by 1 (because 3 ÷ 3 = 1). You should only multiply the numerator by 3, not the denominator as well. 3 is basically 3 ÷ 1, so many students like to write it in that way to help them to avoid making the above mistake. Like so…
Correct solution:
There are a few questions like this in our fractions worksheet, so you can work through those for some more practice of this type of question.
2. Adding decimals
Question:
Work out 0.24 + 0.3
Incorrect solution
0.24
+ 0. 3
0.27
0.24 + 0.3 = 0.27
This is very common and it comes from not lining up the column addition correctly (or often I have noticed students will just look at it and write 0.27 without doing any working). 0.3 is 0.30, not 0.03. So we should line up our column addition like this…
Correct solution
0.24
+ 0.30
0.54
0.24 + 0.3 = 0.54
3. Dividing an integer by a fraction
Question:
Incorrect solution:
This is quite similar to number 1. I’ve noticed this mostly happens when students don’t do any workings and just do it in their heads. 4 ÷ 2 = 2, so I think people are on auto-pilot and just do the same here. We’re going to take a very similar approach to number 1.
Correct solution:
When you divide by a half, that is actually the same as multiplying by 2. This is the same with any other number, so if you divide by a fifth that is the same as multiplying by 5.
Again, our fractions worksheet would be a good place to practice this, as it also includes lots of practice of dividing fractions which is needed for this type of question.
4. Remainders and decimals
Question:
Work out 21 ÷ 4, giving your answer as a decimal.
Incorrect solution:
21 ÷ 4 = 5 remainder 1
So 21 ÷ 4 = 5.1
The 5 is correct here, as 21 goes in to 4 five times. However the issue is with the remainder. The remainder is 1, but students often assume that means the remainder is 0.1. But it is not, it is ¼ because we are dividing by 4. And ¼ is 0.25. However the best way to avoid making this mistake is to use the bus stop method with decimal numbers. Like so…
Correct solution:
Using the bus stop method, which is definitely the best method:
21 ÷ 4 = 5.25
5. Long multiplication with two decimals
Question:
Work out 1.12 × 2.4
Incorrect solution:
Incorrect solution:
1.12
× 2.40
0.00
44.80
+ 224.00
268.80
First of all, it should be fairly obvious that this is incorrect. What I always recommend with these questions is to estimate the answer first, so you know what your answer should be close to.
We were asked to find 1.12 × 2.4
1.12 is close to 1 and 2.4 is close to 2. 1 × 2 = 2, so I would expect our answer to be close in value to 2. Getting an answer of 268.80 is nowhere near this, so we know something is wrong.
Correct solution:
In the long multiplication I did above, I actually got all the numbers right and in the right order. The issue came with the position of the decimal place. I kept the decimal place in the same position throughout, like we would do if we were using the column method for addition or subtraction. This was a mistake – what actually should happen is the decimal place should move two places to the left again. I recommend that when you are multiplying two decimals together, you ignore the decimals in your multiplication and only put the decimal in right at the end. Like this:
112
× 24
448
+ 2240
2688
So we have the numbers 2688. Now we just need to determine where to put the decimal place. This is where our estimate comes in handy. We know that the answer should be close to 2, so the answer must be 2.688, as this is the position of the decimal that gives us the closest number to 2.
So the answer is 2.688
I hope you have found this blog useful. To practice techniques such as these and other numeracy skills, I’d recommend working through Year 6 SATS papers. You can find these here.
If you are in Bristol and need some additional in-person support, book a free taster session.
Click here to read testimonials from some of our clients (and here for Google reviews).
Click here to access our free worksheets.
