<p>I'm not dumb, I'm taking AP Calculus next year and I've been getting 700~'s on the math section of the SAT. There's just one concept I get stuck on, the remainder. It just sounds so weird to me, is it like the answer of a fraction or like what's left over</p>
<p>so if 15/3, is the remainder 5 or 0? Because it's a perfect fraction but then it has an answer of 5. Please give me a detailed explanation.</p>
<p>With 15/3 there is no remainder, because a fraction is actually just a division problem. (Did you ever notice that the “grade school” division symbol - the line with a dot on top and bottom - is just an abstract depiction of a fraction?)</p>
<p>If you had 16/3, though, the remainder is 1. So 16/3 = 5 r 1 or 5 1/3.</p>
<p>So when you do 16/3 you get a funny looking answer and when you get decimal answer do you round to the higher digit or to the lower digit. So for example would you round 4.7 to a 4 or a 5? (Also I didn’t notice that until you told me)</p>
<p>The general rule for rounding the nearest whole number is if its => .5 round up,
<.5 round down. So 4.7 would be rounded to 5. On the SAT, there is plenty of space to write atleast 1 decimal place. For example, if the answer to a grid in is 2.9. If you wrote 3, thats incorrect. And if the question asks something about rounding to nearest integer or tenths place etc, just follow that rule. And if the answer is 16/3 ~~ 5.333, you couldnt just write 5, again you would have to write 5.333</p>
<p>I have written 3 blog posts on this exact topic. I will post an edited version of the first one below. Unfortunately I can’t put images in here, so I hope it can be followed without them. If you want me to post the second one, let me know.</p>
<p>Can We Solve Remainder Problems Without Using Long Division?? Part 1</p>
<p>For the next few weeks I would like to help you get your head around SAT math problems involving remainders. This will be the first of three such messages.</p>
<p>SAT math problems with remainders seem to give students a difficult time and limit SAT scores. This is mostly because a fundamental step in solving the problem is missed – performing long division.</p>
<p>You cannot solve a remainder problem by simply dividing in your calculator. There are, however, calculator algorithms that can give you the answer very quickly. We will talk about these a bit later in this post.</p>
<p>A common error that students make is to perform a division calculation on their TI-84 calculator or similar device, and simply take the first number after the decimal point and use this digit as the answer to the problem.</p>
<p>Let’s try an example:</p>
<p>Suppose we are asked “Find the remainder when 14 is divided by 4.”</p>
<p>In your calculator, 14/4 = 3.5.</p>
<p>Penciling ’5′ as your answer would be incorrect. Seriously incorrect. This ’5′ is actually part of the answer to the question “What is 14 divided by 4?” It has nothing to do with the remainder.</p>
<p>Students that are currently scoring in the mid-range in PSAT/SAT math seem to have the biggest problem with remainder questions. Many cannot perform long division correctly, and some do not even realize that long division is needed. This keeps many students from getting their SAT scores to the next level.</p>
<p>Let’s take a look at how we can solve the problem of finding the remainder when 14 is divided by 4 in three different ways. This problem may seem very basic for some of you, but let’s go over it anyway to make sure we have a strong foundation before solving more difficult remainder problems.</p>
<p>Method 1 – Long Division: So 4 goes into 14 three times with 2 left over. In other words, 14 = 4(3) + 2. So we see that the remainder when we divide 14 by 4 is 2.</p>
<p>Let’s break this down step by step (I had to delete this part since it is dependent on images).</p>
<p>Below is a visual representation of 14 divided by 4. In the figure below we are grouping 14 objects 4 at a time. Note that we wind up with 3 groups (the quotient) and 2 extra objects (the remainder). (again, image can’t be shown - sorry).</p>
<p>Method 2 – First Calculator Algorithm:</p>
<p>Step 1: Perform the division in your calculator: 14/4 = 3.5</p>
<p>Step 2: Multiply the integer part of this answer by the divisor: 4*3 = 12</p>
<p>Step 3: Subtract this result from the dividend to get the remainder: 14 – 12 = 2.</p>
<p>Method 3 - Second Calculator Algorithm:</p>
<p>Step 1: Perform the division in your calculator: 14/4 = 3.5</p>
<p>Step 2: Subtract off the integer part of this result: ANS – 3 = .5</p>
<p>Step 3: Multiply this result by the divisor: 4*ANS = 2.</p>
<p>Note that these calculator algorithms work exactly the same no matter how large the numbers are that you are dividing. So now you try to find the remainder when 15,216 is divided by 73 by using one of these calculator algorithms. Figure out which of the two algorithms you prefer. Solutions will be provided in the next blog post.</p>
<p>Next week, we will use what we have learned today to solve actual SAT problems involving remainders.</p>
<p>Looking at this again, are you asking how to put answers in the free response section of math on the SAT?<br>
Then 16/3 should go in just like that OR 5.333 (if it is a repeating decimal answer, you are supposed to use ALL the boxes)</p>
<p>I believe 17/3 should go in as 17/3 OR 5.666 OR 5.667 All three of those answers would be accepted. </p>
<p>You cannot put in mixed numbers, such as 1 1/2 - it would have to be 3/2 or 1.5</p>
<p>You also should not truncate or round to any place less than the amount of boxes provided. So 17/3 would be 5.666 or 5.667 (they accept both rounded and truncated, I believe) but it would be wrong to put 5.7 or 5.67</p>
<p>@Maryjay60</p>
<p>17/3, 5.66, or 5.67 are all acceptable; there aren’t enough boxes to grid in 5.666 or 5.667</p>
<p>Sorry. Couldn’t remember how many boxes are there. Idea is the same, though.</p>
<p>Ohh ok I get the concept now, you fit as many of the multiples as you can until the next multiple is more than denominator. Thanks all for help and according to the Bluebook, fractional answers for remainders are okay too.</p>