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06 Jul 2011, 17:07
I am looking for a strategy that will help me calculate 138/.82 fast. I am having the hardest time learning how to divide decimals fast. Thanks

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06 Jul 2011, 17:51
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legacydst wrote:
I am looking for a strategy that will help me calculate 138/.82 fast. I am having the hardest time learning how to divide decimals fast. Thanks

$$\frac{138}{.82}=\frac{138}{82*10^{-2}}=\frac{138}{82}*10^2=\frac{69}{41}*100$$

Multiply numerator & denominator by 5 as 40*5=200

$$\frac{69*5}{41*5}*100=\frac{69*5}{200}*100=\frac{69*5}{2}=35*5=175$$

Result should be less than 175.

If you have choices as 165, 167, 169, 170, 171, better use long division of 69/41 and multiply by 100 by shifting decimal 2 digits to the right.
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07 Jul 2011, 00:48
Generally I follow the common factor strategy. In this case, 46 seems to be a strategy.
Coming to decimals in the denominator, they are best handled by drawing up equivalent fractions. In your case, .82 is almost 4/5. So I would calc 138/.82 as 138*5/4 = 34.5*5 nearly 172.5. So any answer that is as close to this as possible would be my pick.
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07 Jul 2011, 08:05
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If you are looking for a fast estimation technique, here is how I would estimate the expression:

138/.82 ~ 140/.80 -->1400/8 --> 350/2 ~ 175

If you need more precise estimation, you can move backward to correct your answer. In my calculation I overestimate 138 (140 is about 1.5% larger) and underestimate 0.82 (0.8 is about 2.5% lower). so, the more precise estimation would be 175 - (1.5% + 2.5%)*175 ~ 175-7 ~ 168. It seems to be difficult but in fact it's not if you know how to estimate small percentages fast. For example, 1% of 175 is 1.75, so 4% of 175 is 2*2*1.75 = 7.
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12 Jul 2011, 10:37
TIP for multiplication and division always use fractions
and decimals for summation and subtraction

138/0.82= 138/(82/100)= 138*(100/82)=69*(100/41)=69*2.5=69*2 + 69*0.5 = 172.5 ( i rounded 100/41 to 100/40 )
you can round 69 to 70 then it become easier 70*2.5=175
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16 Jul 2011, 21:31
Most important concept was to remember that when you round up numerator and denominator you should remember by how much you are rounding up.

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16 Jul 2011, 23:57
Thanks for these tips!
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25 Jun 2015, 00:44
Hello from the GMAT Club BumpBot!

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25 Jun 2015, 18:03
Hi All,

While this is an old series of posts, there are tips to be had beyond the obvious 'mathematical advice' offered herein. While it might be tempting to get 'caught up' in the calculations (since the Quant section of the GMAT does require the use of THAT skill), the Quant section of the GMAT is NOT a 'math test', so you should be on the lookout to NOT do any unnecessary math.

In certain DS questions, simply 'setting up' the work is enough to determine sufficiency or insufficiency, so a big calculation is not required. In certain PS questions, the answer choices are 'spaced out' enough that rounding or estimation is the faster method to get to the correct answer (and sometimes the prompt itself will TELL YOU to estimate). In many cases, if you find yourself thinking "it will take forever to do all of this math", then there is probably another way to approach the question.

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26 Oct 2016, 02:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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