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Remainders and decimals (GRE and GMAT)

In order to understand the relationship between a decimal and remainder, reviewing the lesson video about remainders (GRE version, GMAT version, ACT version) might be helpful. Basically, when we're using remainders, we don't bring in any decimals—a remainder provides a way of looking at division with only integers.

Let's look at a simple example to show the relationship between decimals and remainders. If I divide 7 by 2, I can calculate in two ways:

  • Decimal Answer: 7/2 = 3.5 
  • Remainder Answer: 7/2 = 3 R1

That is, 2 goes into 7 a total of 3.5 times or 2 goes into 7 a total of 3 whole times (2*3=6, and 6 is the multiple of 2 that's closest to 7) and leaves a remainder of 1 (since 7-6 = 1).

Now, you can also notice what that .5 from the 3.5 represents. That's how many more 2s could go into 7 after we've already accounted for three 2s (i.e. 6). That is, how many 2s go into the remaining 1? We simply solve for 1/2 = .5, where this is the decimal representation of the same thing. A decimal in a quotient represents how big the remainder is in respect to the divisor. There's a half of a 2 left after dividing out three 2s from 7. 

Let's go over another example: we'll divide 14 by 5, and we'll find the remainder. First we can do the division using decimals: 14/5 = 2.8. So the result is almost 3 - but not quite. To find the remainder, we need to make the result of the division (the "quotient") a whole number. So 2.8 becomes 2. (Notice that that 3 wouldn't work, since 5*3 = 15, which is bigger than 14). So the result of the division must be 2, so we have two 5s. That's 2*5=10. We can subtract this from 14, to get 14-10=4. This is the remainder: 

14/5 = 2 R4 

Here are some blog posts that have some more information on remainders:

GMAT Quant: Thoughts on Remainders

GRE Division, Mixed Numerals, and Negatives

If you're studying for the SAT or the ACT, you don't need to worry about these blog posts - the info here is more advanced than what you'll see on the test! Your best bet is to watch the SAT / ACT lesson videos :) 

 

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