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Intern
Joined: 14 Jun 2011
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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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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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Manager
Status: 700 (q47,v40); AWA 6.0
Joined: 16 Mar 2011
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GMAT 1: 700 Q47 V40
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Kudos [?]: 56 [0], given: 3

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.
Regards
Rahul
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Regards
Rahul

CEO
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Kudos [?]: 2169 [2] , given: 359

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Expert's post
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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Manager
Status: Trying to survive
Joined: 29 Jun 2011
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GMAt Status: Quant section
Concentration: Finance, Real Estate
Schools: WBS (D)
GMAT Date: 12-30-2011
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Kudos [?]: 94 [0], given: 94

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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Senior Manager
Joined: 08 Jun 2010
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Kudos [?]: 66 [0], given: 13

Most important concept was to remember that when you round up numerator and denominator you should remember by how much you are rounding up.
Manager
Joined: 14 Apr 2011
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Kudos [?]: 20 [0], given: 19

Thanks for these tips!
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