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Hi Emily, Let me use an example to explain. Let's say we do this: 14/3 = 4, r2 In other words, 14 divided by 3 is equal to 4, with a remainder of 2. What this is really saying is that if we take three 4s, and add 2, we get 14. In other words, 3 * 4 + 2 = 14 Now, if we start with our equation, and multiply both sides by 3, we will get: 3 * 4 + 2 = 14. So we are left with 14 = 14, which makes sense. If we were to multiply the remainder (2) by 3 as well, we wouldn't get the right answer. We would get: (4*3) + (2*3) = 18. So we'd have 14 = 18, which is not right. Keep in mind that this remainder formula doesn't really follow the standard math conventions. Usually, when we have a sum in an equation (q + r), and we multiply that side by c, we would have to multiply both q and r by c. But here, since r represents the remainder, it does not get multiplied. You might also want to take a look at this blog post, which clarifies further: https://magoosh.com/gmat/2012/gmat-quant-thoughts-on-remainders/ I hope this helps! This quotient and remainder calculator helps you divide any number by an integer and calculate the result in the form of integers. In this article, we will explain to you how to use this tool and what are its limitations. We will also provide you with an example that will better illustrate its purpose.
When you perform division, you can typically write down this operation in the following way: a/n = q + r/nwhere:
When performing division with our calculator with remainders, it is important to remember that all of these values must be integers. Otherwise, the result will be correct in the terms of formulas, but will not make mathematical sense. Make sure to check our modulo calculator for a practical application of the calculator with remainders. 🔎 If the remainder is zero, then we say that a is divisible by n. To learn more about this concept, check out Omni's divisibility test calculator.
It's useful to remember some remainder shortcuts to save you time in the future. First, if a number is being divided by 10, then the remainder is just the last digit of that number. Similarly, if a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder. Lastly, you can multiply the decimal of the quotient by the divisor to get the remainder.
Learning how to calculate the remainder has many real-world uses and is something that school teaches you that you will definitely use in your everyday life. Let’s say you bought 18 doughnuts for your friend, but only 15 of them showed up, you’d have 3 left. Or how much money did you have left after buying the doughnuts? If the maximum number of monkeys in a barrel is 150, and there are 183 monkeys in an area, how many monkeys will be in the smaller group?
The quotient is the number of times a division is completed fully, while the remainder is the amount left that doesn’t entirely go into the divisor. For example, 127 divided by 3 is 42 R 1, so 42 is the quotient, and 1 is the remainder.
Once you have found the remainder of a division, instead of writing R followed by the remainder after the quotient, simply write a fraction where the remainder is divided by the divisor of the original equation. It's that easy!
There are 3 ways of writing a remainder: with an R, as a fraction, and as a decimal. For example, 821 divided by 4 would be written as 205 R 1 in the first case, 205 1/4 in the second, and 205.25 in the third.
The remainder is 2. To work this out, find the largest multiple of 6 that is less than 26. In this case, it’s 24. Then subtract the 24 from 26 to get the remainder, which is 2.
The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.
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When the positive integer n is divided by 3, the remainder i [#permalink] When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n? Math ReviewQuestion: 15Page: 220 Difficulty: medium _________________
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Re: When the positive integer n is divided by 3, the remainder i [#permalink]
Carcass wrote: When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n? If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.GIVEN: When the positive integer n is divided by 3, the remainder is 2 The possible values of n are: 2, 5, 8, 11, 14, 17, 20,... GIVEN: When n is divided by 5, the remainder is 1 The possible values of n are: 1, 6, 11, 16, 21,... 11 is the smallest value that appears in both lists of possible n-values. Answer: 11Cheers, Brent _________________
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Re: When the positive integer n is divided by 3, the remainder i [#permalink] When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ? a)0 b)1 c)2 d)3 e)5
Intern Joined: 14 Mar 2020 Posts: 41
Re: When the positive integer n is divided by 3, the remainder i [#permalink]
sandeep1995 wrote: When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ? a)0 b)1 c)2 d)3 e)5 can anyone solve this problem with a short trick?
Manager Joined: 09 Mar 2020 Posts: 164
Re: When the positive integer n is divided by 3, the remainder i [#permalink]
asmasattar00 wrote: sandeep1995 wrote: When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ? a)0 b)1 c)2 d)3 e)5 can anyone solve this problem with a short trick? You can use trail and error method. The remainder is 1 when divided by 5, thus the number should be greater than multiple of 5 by 1. 5*1 = 5 + 1 = 6. On dividing with 5 gives remainder 1, but is perfectly divisible by 2. This does not satisfy the condition. 5*2 = 10 + 1 = 11. And then divide the number by 3 to see if you get the remainder as 2. This satisfies the condition.When the numbers are bigger, this method might be time consuming.
Intern Joined: 14 Mar 2020 Posts: 41
Re: When the positive integer n is divided by 3, the remainder i [#permalink]
sandeep1995 wrote: When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ? a)0 b)1 c)2 d)3 e)5 is option A(0) is the right answer?
Manager Joined: 09 Mar 2020 Posts: 164
Re: When the positive integer n is divided by 3, the remainder i [#permalink]
asmasattar00 wrote: sandeep1995 wrote: When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ? a)0 b)1 c)2 d)3 e)5 is option A(0) is the right answer? Let's try to solve n first. It is given that when n is divided by 3, we get 2 as remainder and also that n-2 must be divisible by 5. Start looking at the table of 3, we can see that n can be 17, since 3*5 = 15 and when remainder is added, we get 17, plus n-2 = 15 is divisible by 5. For t, start with the table of 3, and we can see that when t=18, this is divisible by 3 and when it is divided be 5, you get a remainder of 3. Hence, n=17 and t=18. Thus, nt = 17*18 = 306. On dividing it with 15, you should get 6 as remainder. Please check if the options you've typed are correct.Posted from my mobile device
Intern Joined: 14 Mar 2020 Posts: 41
Re: When the positive integer n is divided by 3, the remainder i [#permalink]
sukrut96 wrote: asmasattar00 wrote: sandeep1995 wrote: When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ? a)0 b)1 c)2 d)3 e)5 is option A(0) is the right answer? Let's try to solve n first. It is given that when n is divided by 3, we get 2 as remainder and also that n-2 must be divisible by 5. Start looking at the table of 3, we can see that n can be 17, since 3*5 = 15 and when remainder is added, we get 17, plus n-2 = 15 is divisible by 5. For t, start with the table of 3, and we can see that when t=18, this is divisible by 3 and when it is divided be 5, you get a remainder of 3. Hence, n=17 and t=18. Thus, nt = 17*18 = 306. On dividing it with 15, you should get 6 as remainder. Please check if the options you've typed are correct.Posted from my mobile device once again thanks for your productive response
Senior Manager Joined: 10 Feb 2020 Posts: 496
Re: When the positive integer n is divided by 3, the remainder i [#permalink]
GreenlightTestPrep wrote: Carcass wrote: When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n? If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.GIVEN: When the positive integer n is divided by 3, the remainder is 2 The possible values of n are: 2, 5, 8, 11, 14, 17, 20,... GIVEN: When n is divided by 5, the remainder is 1 The possible values of n are: 1, 6, 11, 16, 21,... 11 is the smallest value that appears in both lists of possible n-values. Answer: 11Cheers,Brent its easy to understand this rule, just one question, when we should apply this? because questions are really different every time, so how to recognize where this rule will be applicable? _________________
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When the positive integer n is divided by 3, the remainder i [#permalink] Given that when n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. And we need to find the least possible value of n Theory: Dividend = Divisor*Quotient + Remainder n is divided by 3, the remainder is 2 n -> Dividend3 -> Divisora -> Quotient (Assume)2 -> Remainders=> n = 3*a + 2 = 3a + 2n is divided by 5, the remainder is 1 => n = 5b + 1 (Assume b is the quotient)So, that value of n is possible which will satisfy both the conditions=> n = 5b + 1 = 3a + 2=> 5b = 3a + 2 - 1 = 3a + 1=> b = \(\frac{3a+1}{5}\)So, for b to be integer 3a + 1 should be a multiple of 5a = 1, 3a + 1 = 3*1 + 1 = 4a = 2, 3a + 1 = 3*2 + 1 = 7a = 3, 3a + 1 = 3*3 + 1 = 10 => POSSIBLE=> n = 3a + 2 = 3*3 + 2 = 11So, Answer will be 11 Hope it helps!Watch the following video to learn the Basics of Remainders _________________
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When N is divided by 8 it leaves a remainder 3 and quotient R when n is Divid the value of N?
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