Mental Math & Manual Calculation (Part 2: Strategic Implications)

In the following article, we’re going to delve into mental math and manual calculation best practices for the GMAT exam. You can either read this article or watch the corresponding video on YouTube. To make things easier to digest, we’ve broken the contents of the video up into 3 parts. If you haven’t read part 1 yet, we recommend you go back and do that before venturing further. In this segment, we will specifically discuss the strategic implications of the GMAT’s mathematical components. In segment 3, we’ll outline the manual calculation drills on mathaids.com.

Calculation Strategies

In order to achieve a competitive quantitative GMAT score, it is imperative that you sharpen your ability to perform manual calculations as efficiently as possible. A few tips include: 

• Practice the personalized drills provided on mathaids.com to improve speed and accuracy. 

• Utilize factors of 2, 5, 10, 100, and ½ to facilitate streamlined mental calculations. The reason these numbers are useful is that they reflect the counting mechanisms inherent in the human body: two hands, 5 fingers, and ten toes are the basis of decimals. 

• Learn to double and half numbers quickly. 
  • If each digit is ≤ 4, double each digit:
    • 24 X 2 = 48 | 204 X 2 = 408

• • If each digit is > 4, doubly the left-most digit first and work to units:
    • 596 X 2 = (5-00 X 2) + (90 X 2) + (6 X 2) = 1,000 + 180 + 12 = 1,192

• If your units digit is even, divide the leftmost digit by 2 first and work to units:
• 476 ÷ 2 = (400 ÷ 2) + (70 ÷ 2) + (6÷2) = 200 + 35 + 3 = 238

• Proportionally manipulate by factors of 10.
  • When multiplying by 10, shift the decimal one place to the right:
    • 2.3 X 10 = 23 | 23 X 10 = 230

• • When multiplying by 10ⁿ, shift the decimal n places to the right:
    • 2.3 X 100 = 230 | 2.3 X 1,000,000 = 2,300,000

• When dividing 10ⁿ, shift the decimal n places to the left.
• 590 ÷ 10 = 59 | 590 ÷ 100 = 5.9 | 590 ÷ 1,000 = 0.059

• Expedite addition and subtraction by seeking factors of 10.
  • 484 + 72 | Shift 2 to 484 from 72 to reimagine as 486 + 70
    • Units digit will remain 6 since we’re adding to 70
    • Sum hundred and tens digits | 46 + 7  = 55 → 486 + 70 = 556

• • 973 - 81 | Subtract 1 from each number to reimagine as 972 - 80
    • Units digit will remain 2 because we’re subtracting 80
    • Subtract hundred and tens digits | 97 - 8  = 89 → 973 + 81 = 892

• Expedite multiplication by seeking factors of 10.
  • 48 X 72 | Recognize that the closest and easiest multiple of 10 here is 50
    • 72 X 100 = 7200 | Half of this value is 72 X 50
    • 7,200 ÷ 2 = 3,600 = 72 X 50
    • Subtract 72 X 2 = 144 from 3,600 for 72 X 48
    • 72 X 50 - 72 X 2 = 72 (50 -2) = 72 X 48
    • 3,600 - 100 - 44 = 3,456 = 48 X72

• Finally, manipulate manually for long division. The fact is that it doesn’t really take that long, just make sure you remember how to do it. 

Conclusion

We hope these strategies have empowered you to tackle GMAT calculations with newfound confidence and ease! Remember to read part 3 of this mental math and manual calculation article, where we will discuss the manual calculation drills available on mathaids.com.

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