Mental Math and Manual Calculations: Best Practices for GMAT

Most GMAT test takers are often thrown off a little bit by the fact that no calculators are provided or allowed for the quantitative section in the GMAT exam. However, GMAC(the body that puts forth the exam) does not value Manual calculation as a premium skill. You will need to work on these skills but only as a basic foundation for this test because you are still expected to be able to operate all four basic manual functions. You should also be able to work with fractions, decimals, percentages, exponents, etc., as a baseline for the exam.

Your calculations should produce clean results or be able to be approximated. If you use some of the techniques discussed in this article, you should be able to avoid extensive long-hand manipulation. Usually, there are opportunities for approximation which should provide you opportunities to save some time.

For the integrated reasoning(IR) section, an interface calculator is provided. Most people usually forget that this calculator is available. You should remember to use it. Again, GMAC does not value long manual manipulation as a primary skill. Actually, you shouldn’t be doing any of that in IR. The IR calculator will come in handy as a resource to solve some calculations, such as 248,340 × 24.6, often found in the IR section. This kind of calculation is not always easy to solve mentally, its manual solution is not a skill value by GMAC. The calculator may also save you some valuable time during your exams.

What’s the best way to prepare for GMAT calculations?

There is just no way to pass the GMAT exams without doing calculations. If you want to meet your target score in the GMAT exam, especially if you have high-end GMAT goals, then this is one of the first abilities you will need to develop. If, for instance, you are unable to manipulate calculations in all of the non-integer formats of math, or you’re struggling with basic times tables, you have to find a way to improve that skill quickly to achieve your GMAT goals.  The best way to do that is by practicing as much as you can using Free math-aids.com Drills. Make this a personalized experience to improve, first and foremost, your areas of weakness.

How to Improve Your Mental Math Using Easy Factors & Multiples

1. Seek Factors of 2, 5, 10, and ½

Seek factors of 2, 5, 10, and ½ to facilitate easy mental calculation. (2 hands, 5 fingers, and 10 toes).

How to double and half numbers quickly 

If each digit \(\leq4\), double each digit. e.g., \(204\times2, 2\times2=4\)

$$0\times2=0$$

$$4\times2=8$$

$$204\times2=408$$

If any digit \(>\), then double the leftmost digit first and work towards the unit digit.

For example: \(596 × 2 = (500 × 2) + (90 × 2) + (6 × 2) = 1000 + 180 +12 = 1,192\)

OR:

Round up 596 to 600,

But \(596 = (600 – 4)\)

\((600 × 2) – (4 × 2) = 1,192\)

If the unit digit is even and you want to half the number, divide the left-most digit by 2 first, and work towards the units.

Example: \(476 ÷ 2 = (400 ÷ 2) + (70 ÷ 2) + (6 ÷ 2) = 200 + 35 + 3 = 238\)

2. Manipulation by factors of 10

When multiplying by 10, shift your decimal one place to the right.

• Example: \(2.3 × 10 = 23/23 × 10 = 230/230 × 10 = 2300\)

Note: there is always an implied decimal at the end of any integer.

When multiplying by 10ⁿ, shift the decimal n places right.

Example:
$$2.3 × 10 = 2.3 × 10^1 = 23 / 2.3 × 100 = 2.3 × 10^2 = 230 /2.3 × 1,000,000 = 2.3 × 10^6= 2,300,000$$

When dividing by 10ⁿ, shift the decimal n places to the left.

Example:

\(590 ÷ 10 = 590 ÷ 10^1\), shit the decimal 1 place to the left, \(590 ÷ 10 = 59\)

\(590 ÷ 100 = 590 ÷ 10^{2}\), shit the decimal 2 place to the left, \(590 ÷ 100 = 5.9\)

\(590 ÷ 10,000 = 590 ÷ 10^4\) shit the decimal 4 place to the left,\(590 ÷ 10,000 = 0.059\)

3. Expedite Addition and subtraction by seeking factors of 10

Example:

\(484 + 72\), shift the 2 from 72 to 484, reimagine it as \(486 + 70\)

 The units digit will remain a 6, (\(6 + 0\))

Sum the hundreds and the tens, \(48 + 7 = 55\)

Put the six back in, 556. This implies that  \(486 + 70 = 484 + 72 = 556\)

\(973 – 81\), subtract 1 from each number and think of it as \(972 – 80\) (if you do the same thing to each side of the minus sign, you will arrive at the same result).

             The units digit will remain 2, (\(2 – 0\)) 

             Subtract hundreds and tens digits \(97 – 8 = 89\)

             Bring the 2 back in as the units digit, 892. Therefore \(973 – 81 = 892\)

4. Expedite Multiplication by seeking factors of 10

This is a more realistic kind of manipulation to be found in the GMAT. 

Example:

\(48 × 72\) identify the easiest multiple of 10 closest to 48. It is 50

 \(72 × 100 = \frac{7,200}{\text{half of the product}}=72\times50\)

$$7,200 ÷ 2 = 3600 = 72 × 50$$

Then, subtract \(72 × 2 = 144\) from 3600 for \(48 × 72\)

By factoring, \(72 × 50 – 72 × 2 = 72(50 – 2) = 72 – 48\)

Finally,  \(3600 – 144 = 3600 – 100 – 40 – 4 = 3456\)

Where  \(48 × 72 = 3,456\).

With some practice, you can do this mentally in less than 30 seconds.

5. Long division

When dividing numbers, you may have to do it manually by long division.  Long division doesn’t take as long as the name makes it sound.

Example:        5,520 ÷ 24  

        24   5,520  230

              – 48

                   72

                   – 72

                             00

In long division, there aren’t many mental math tricks to do. You just go bit by bit, working easily towards the solution.

Manual Calculations Drills

The best way to improve these skills is through math-aids.com. math-aids.com is a free online resource with dynamically produced worksheets. The worksheets range in size from 10 to 100 questions and cover all GMAT calculation topics.

What is the best way to use math-aids.com?

The best way to get the most out of math-aids.com is by trying to rotate two to five worksheets daily for about five to twenty minutes worth of practice. This is not an activity to be conducted for hours at a time, it should be done in short sessions just to make sure that you are improving your speed and accuracy through repetition and execution. Practice areas of difficulty more frequently. This will be more rewarding in the end.

Remember also to practice both written manual calculations and mental math. Sometimes you will find the mental math not going fast enough, you should be able to do manual manipulation as well. Besides, you will have a scratchpad/board, so make use of it when you need to. Math-aids.com is an excellent resource for your practice.

Math-aids. com provides a great warmup before any “real” GMAT quantitative practice drills or exams. Most MBA students are already working or are in other programs,  and have daily responsibilities they have to take care of. Short rotating daily practices are a great way to step out of your routine and exercise mentally before doing GMAT practice or an exam.

Begin with top-6 math-aids.com topics. You can also use the search box to locate specific topics outside of these six that you may need to work on. Limit yourself, however, to topics that you have seen explicitly on the GMAT.

Top-Six Math-aids.com Topics

Multiplication

• Times tables advanced times drills. This allows you to select up to 15×15
•  Single or multiple digit multiplication worksheets

 You can tailor your practice accordingly depending on your needs, but this is a good place to start. Every second counts in the GMAT exam. Therefore, no matter how good you are at multiplication, continue rotating through this topic to keep a sharp edge. 

Division

• Long division worksheets.  
• Division times tables, timed drills worksheets. Do some practice here, just to be able to do the basics. For example, you don’t have to slow down just to divide 54 by 9. Have two-digit and low three-digit Multiplication/division times tables locked in.

Exponents and Radicals

• Work with exponents with multiplication and division that will help you remember how to manipulate exponents manually 
• Work also on simplifying radical worksheets- remembering how to pull out perfect square factors and simplifying. For example, determine the square root of \(72 = √36 × √2 = 6√2\). 

Memorize the times’ tables and exponents up to at least 15² and 10³. 

Fractions

Adding and subtracting three fraction worksheets. 

Multiplying fractions with cross canceling. The exam rewards efficiency, so it is beneficial to know when you can cancel out numerators and denominators.

Decimals

• Adding and subtracting worksheets with decimals.
• Multiplying by powers of 10 with decimals. The exam tends to focus on this as far as decimals are concerned. A more GMAT-relevant skill set is remembering how to manipulate decimals using scientific notation. 

Percent

• Percentage calculation worksheets 
• Word problem – percentage word problems. Percentages normally appear as word problems in the GMAT exam.

There is a lot of information and worksheets for math-aids.com that are relevant to the GMAT. Be willing to go and find other topics that you know you need to work on, it could be mental math or manual manipulation and do them with math aids.

Become math ambidextrous for these non-integer calculations so that when you encounter fractions on the GMAT, you can manipulate them without having to translate to percents or decimals and be able to do the same for decimals and percentages. 

Being able to do manual manipulation may not be highly rewarding, but it is a necessary skill that you will continue to use as you do your GMAT practice. Math-aids.com practice worksheets are never-ending. Use this resource as much as you can and use the skills for future GMAT problems. Moreover, remember to practice using real GMAT problems from one of our study resources available on this website. If you’re out to improve your scores, you’ve got no choice but to practice.