Long Division of Small NumbersDate: 03/26/2014 at 23:23:35 From: Jay Subject: 200/3500 I recently started learning and using long division again. I'm studying for the Armed Services Vocational Aptitude Battery and I would need to do long division on most of my problems, like 200/3500 I tried to find out what would go into 200 to get me close to 3500. I got 200 x 17 = 3400. From the looks of the answer that the book gave me (0.057), I assumed I was already wrong. I'm lost on how they got that. Just where do you start? Like I said, it's been a while since I worked with long division problems like this. I'm lost on how to solve the answer. Date: 03/27/2014 at 08:13:11 From: Doctor Ian Subject: Re: 200/3500 Hi Jay, Note that a fraction is a division, and a division is a fraction. So one thing you can do is simplify the fraction before doing the division: 200 2 ------ = ---- 3500 35 You can just divide 35 into 2, and you'll get the same answer. You can also scale the numerator, so long as you scale the result in a compensating way. That is, 2 2 * 1000 ---- = ---------- * 1/1000 35 35 This lets you divide 35 into 2000, then multiply the result by 1/1000. So let's try that: 7 help 50 _____ 35 ) 2000 1750 ---- 250 235 --- 15 We get approximately 57. Multiply that by 1/1000, and we get 57/1000, or 0.057. Note that if you're in a multiple choice situation, or one where you just need an estimate, you could take one more step beyond reducing to 2/35. You could multiply that by 3/3, to get 6/105, which is close to 6/100, or 0.06. The basic idea is always the same: Try to change the problem you have into one that's easier to deal with, but has (whether exactly or approximately) the same answer. Make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 03/27/2014 at 13:11:12 From: Jay Subject: 200/3500 Why is the 7 placed above the 50? And where does it come from? Date: 03/27/2014 at 16:26:55 From: Doctor Ian Subject: Re: 200/3500 Hi Jay, Let's first look at what it means to do a division. It's really just a way of writing a multiplication. For example, look at this division: 18 ___ 4 ) 72 This means the same thing as 72 = 4 * 18 More generally, these are two ways of expressing exactly the same fact: quotient _________ AND dividend = divisor * quotient divisor ) dividend So far, so good? Now, note that we could write those as 8 10 ___ 4 ) 72 AND 72 = 4 * (10 + 8) That is, we're just using the distributive property to break these up. Still with me? Okay, so how do we do this division a bit at a time? We bite off little pieces, starting from here: ___ 4 ) 72 We can note that 40 is smaller than 72, while 80 is larger. So we can subtract 40 as a first step, keeping track of the fact that 40 is 4*10: 10 ___ 4 ) 72 72 = 4 * (10 + ?) 40 -- 32 Now we might note that 20 is less than 32, and subtract 20 as a next step: 5 10 ___ 4 ) 72 72 = 4 * (10 + 5 + ?) 40 -- 32 20 -- 12 Now we might note that 12 is just 4*3, so we can finish up: 3 5 10 ___ 4 ) 72 72 = 4 * (10 + 5 + 3) 40 -- 32 20 -- 12 12 -- 0 And what this division is telling us is that 3 5 10 ___ 4 ) 72 40 <- 4*10 -- 32 20 <- 4*5 -- 12 12 <- 4*3 -- ----------------------------------------------- 0 4*10 + 4*5 + 4*3 = 4*(10 + 5 + 3) = 4*18 = 72 That is, you're looking for some numbers such that 72 = 4*(? + ? + ? + ... ?) The 'long division' algorithm is designed to be very efficient, in terms of doing the least amount of writing. But you don't need to be efficient! You can bite off pieces of any size that you like: 4 4 2 5 3 ___ 4 ) 72 12 <- 4 * 3 -- 60 20 <- 4 * 5 -- 40 8 <- 4 * 2 -- 32 16 <- 4 * 4 -- 16 16 <- 4 * 4 -- 0 All together, 72 = 4 * (3 + 5 + 2 + 4 + 4) = 4 * 18 Can you answer your own question now? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 03/28/2014 at 00:30:29 From: Jay Subject: Thank you (200/3500) I got it! Thank you so much! I figured that is where it came from! Just wanted to ask and make sure! This is very helpful. I will continue to use this site. I'm so happy I stumbled upon it! This will help me with my ASVAB substantially, allowing me to score higher. I really appreciate your service! |
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