Verbal Reasoning – Complete the Calculation (Type I)

The Complete the Calculation question type will require you to fill in the missing number on either side of the equation. To put it simply an equation is when two sides of an equals sign (=) calculate to be the same. This could be:

Version 1) 7 = 7

and also:

Version 2) 3 + 4 = 1 + 6

The key word here is calculate, now the Complete the Calculation question type will most likely appear in the style of Version 2. The only difference that you will notice is that one of the numbers on either side will be missing. You will be expected to figure out the missing number to complete the calculation.

This means you need to calculate correctly the side of the equation that has all the numbers, this will then allow you to answer the side of the equation that has the missing number because you will know what it should all equal to.

Now the answer must:

• Be a number
• Balance the equation meaning that either side of the equals side should calculate to the same final number

These type of questions start off relatively easy but then begin to get harder by either:

• Having more complex BIDMAS / BODMAS
• Working with bigger numbers
• Working with longer calculations
• All of the above whilst under time pressure

Remember, all this is about is doing things in order. The Complete the Calculation question type focuses in on the following skills:

• Strong mathematical skills e.g. multiplication, division, addition and subtraction and the practice of working things out quickly
• Knowledge of the Order of Operations. You need to apply the right method in the right order at the right time
• Working quickly and efficiently
• Having strong mental Maths
• Having a process / method to work out incomplete information from a different set of complete information
• Being able to breakdown a calculation into its individual parts to then get to the final calculation

As mentioned already, this is all about doing things in order, so the best thing you can do is give yourself the time and chance to think things through. The skills that are being tested here aren’t just your Maths skills, but your ability to adapt, shift and change them to the requirements of the question.

It is about knowing BIDMAS / BODMAS, but also understanding that when it comes to actual application, equations change so you must be able to block the noise and apply the standard regardless of where things appear. It expects you to be precise and analytical, which means you can take the question and break it up into its small parts to get to your answer.

This, however, won’t work if you do not have a strong mathematical foundation, which as seen above includes you being confident in most of your times tables and also different methods in adding, subtracting and dividing numbers. The best way of getting there is just through constant practice, which will help you work things out quicker in your head.

What does Complete the Calculation Question Type Look Like?

As you can see from the example below the Complete the Calculation question type is in the following format:

• General example with instructions
• 1 equation per question
• 1 missing number per equation in brackets
• 1 mark per question
• Multiple choice options on the answer sheet

How do I answer this question

Before starting a question like this you must have some confidence in your mathematics skills – this doesn’t have to just be mental maths, it also includes working out on paper. You must also be familiar with breaking down equations and comfortable with taking numbers over the equals sign and how state changes e.g. a minus number changes to a plus, a plus changes to a minus etc.

On top of this, you need to also have an idea around BODMAS.

BODMAS is an acronym, which is a word made up of the first letter of other words. For mathematics BODMAS is a way of calculating questions in order. So your maths skills will help you calculate the answer and the BODMAS method will help you get to it in the right order.

To avoid confusion lets just stick to BODMAS for now (it means the same as BIDMAS!). Now BODMAS (in priority) stands for:

1. Brackets – Anything in brackets must be done first
2. Order – Do anything to do with Orders of Magnitude, these include: Square root, indices
3. Division and Multiply – Do this from left to right in the order that they appear
4. Addition and Subtraction – Finally do this from left to right in the order they appear

That is generally the approach you need to follow and can be applied to any Complete the Calculation question that comes up. So the aim here is to be consistent, systematic and apply the formula. But this is only half the job, lets break down the process.

Process for answering the Complete the Calculation Question Type

Now you know your general mathematics and you also have an idea around BODMAS (which is the order in which things should be calculated), so how will you apply this to a question, lets look at an example:

Question 1:

19 – 6 + 2 = 28 + [___] – 15

So looking at Question 1 above, we want to apply the following step by step process:

1. Identify which side of the equation is complete
2. Identify which side of the question is missing a number
3. Check BODMAS to remember the order in which you should calculate things
4. Calculate the side that has ALL the numbers so you then know how much the other side should equal to
5. REMEMBER: Both sides of an equation equal the same final value – each side just needs working out
6. Now you know the final value of one side, you know how much the other side must equal, this will help when trying to figure out the missing number
7. Work through the side that is missing a number, make the calculation easier to work out by taking numbers across the equals sign and use BODMAS where needed

Now the above is the general process, lets apply it to Question 1:

1. The left side is complete, so I need to work that out first
2. The right side has the missing number so I need to work that out second

Lets start with the left side of the equation 19 – 6 + 2:

1. There are no brackets (this is a bracket) – so there are no calculations to do in brackets
2. There are no Order of Magnitudes to work out second
3. There are no Division or Multiplications to work out
4. There is addition and subtraction so lets work on that from left to right only working out the first 2 values each time, then with the result of that working out the next values
5. 19 – 6 = 13 then we take that and add it to 2 so 13 + 2 = 15, so the final value is 15

Now we know the left side equals 15, we can be sure the right side must equal 15 because an equation equals the same on both sides, so lets find that missing number!

Lets have a look at the right side 28 + [__] – 15:

1. Lets put our final value from the first section in : 28 + [__] – 15 = 15
2. Now lets apply BODMAS
3. No numbers brackets
4. No Orders of Magnitude
5. No Division or Multiplication
6. There is Addition and Subtraction – so we know 28 plus something minus 15 gives us 15

What we want to do here is make the equation easier to handle, we do this by reducing the numbers on the side with the missing number on, this will help us focus on the missing number.

To reduce the numbers we can simply take one of the numbers over the equals sign to the other side, but keep in mind the state of the number changes e.g. it goes from a minus to a plus! You can take any number over from the left of the equals sign to the right side of the equals sign, but generally adding numbers is easier than taking away so lets try that:

28 + [__] = 15 + 15

So what I did here was take the – 15 from the left side and move it over the equals sign to the right! By doing this the minus 15 changes to a plus 15 and means I need to add those numbers so:

28 + [__] = 30

Now all we have to do is work out 28 add what makes 30! Just by counting up we can count that it is 2, so the missing number is 2!