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Remainder is the part remaining after the fulfillment of the division process. For example, if there are a total of 4 balls and we divide the balls among 3 three students then we are left with 1 ball. In mathematical terms, the remaining 1 ball is the remainder. The remainder can also be defined as something remaining after the calculations are completed. Many times, remainders are rounded to obtain an answer in the whole number. Here, we will be learning more about the remainder and discussing some important questions.
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Key Takeaways: Remainder, Division, Quotient, Dividend, Divisor
Also read: Surface Area of a Cylinder Formula
What is Remainder in Division?
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As the name suggests, the remainder is something that remains or is left after a task is completed. In mathematics, some numbers cannot be divided completely and remainders are left. For example - the number 11 can be divided by the number 2. After completion of division, number 1 is left which is the remainder.
Another example of the remainder in the division is supposed there are 15 chocolates which are needed to be divided between Siya, Riya, Priya, and Ziya. Each of them will get 3 chocolates. Out of 15 chocolates, 12 will be distributed among four of them. The 3 remaining chocolate is the remainder.
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What is the Definition of Remainder?
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Remainder the leftover number which we get after division. When the division is incomplete even after numerous steps we get a remainder. One thing that needs to be kept in mind is that the remainder is always less than the divisor. In the above-given example of 15 chocolates, the divisor is 4 and the remainder is 3.
Remainder in Mathematics
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There are a total of four parts of in division:
- Dividend - It is the number that is divided.
- Divisor - It is the number or value that divides the numbers.
- Quotient - When one number is divided by another number, the number we get is the quotient.
- Remainder - It is the number left when a dividend is not completely divided by the divisor.
The relation between dividend, divisor, and the quotient is:
Dividend = Divisor x Quotient
As already mentioned, the remainder is the number that is left when the dividend is not completely divisible by the divisor. Therefore, we can say:
Dividend = Divisor x Quotient + Remainder
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What is the Remainder Formula?
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In mathematics, the remainder formula is:
Dividend = Divisor x Quotient + Remainder
Remainder = Dividend – (Divisor x Quotient)
How to Find the Remainder?
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In Mathematics, finding the remainder is an easy process. One just needs to divide a number by another number with its multiples and what is left is the remainder. Let's understand this with an example.
35= 6 x 5 + 5, here 5 is the remainder
114 = 7 x 16 + 2, 2 is the remainder
Remainder using Long Division Method
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One of the simplest ways to find the remainder is using the long division method. We can take the chocolate example mentioned below and try to solve it through a long division method.
Thus, the remainder is 3. On a number of occasions, the remainder can be 0. If we divide 10 by 2 or 15 by 3 then the remainder will be 0. Here are a few of the examples of remainders.
| Division | Remainder |
|---|---|
| 17/4 | 1 |
| 56/12 | 8 |
| 13/5 | 3 |
Properties of a Remainder
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- The remainder is always less than the divisor. A division is incorrect if the divisor is equal to or greater than the remainder.
- If the divisor (4) divides the dividend (12) perfectly then the remainder will be zero.
- Another property of remainder is it can be equal, greater or lesser to the quotient.
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How to Represent Remainder?
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There are two ways to represent remainder which are as follows:
- The first is writing the quotient and the remainder with an "R" in between them. The number 14 divided by 4 can be written as 14/2 = Q=3 and R=2. Here Q=3 is a quotient and R=2 is a remainder.
- The second way to represent the remainder is by writing it as a mixed fraction.
- Another way to represent the remainder is by showing it as a part of a mixed fraction. The number 14 divided by 4 can be written as 14/4 = 3 2/4.
Things to Remember
- The remainder is referred to as something that remains or is left after a task is completed. In mathematics, some numbers cannot be divided completely and remainders are left.
- The relation between dividend, divisor, and the quotient is: Dividend = Divisor x Quotient
- The remainder is the number that is left when the dividend is not completely divisible by the divisor. Therefore, we can say: Dividend = Divisor x Quotient + Remainder
- The remainder is always less than the divisor. A division is incorrect if the divisor is equal to or greater than the remainder.
Also read: Isosceles Triangle Theorems
Sample Questions
Ques. What is the definition of the remainder? (1 mark)
Ans. The remainder is the last number left after the completion of the division. If we divide 15 by 4 then the remainder will be 3.
Ques. Can the remainder be zero? (1 mark)
Ans. Yes, when the divisor divides the dividend completely then the remainder will be o. For example - 5 divided by 2 leaves the remainder 0.
Ques. Can remainder be equal to quotient? (1 mark)
Ans. Yes, the remainder can be equal quotient. As per the mathematics rule, the remainder can be equal, lesser, or even greater than the quotient.
Ques. Is Remainder less than the divisor? (1 mark)
Ans. Yes, the remainder is always less than the divisor. The division will be invalid if the remainder is more than the divisor.
Ques. What is the remainder if 25 is divided by 4? (1 mark)
Ans. When 25 is divided by 4 the remainder will be 1.
Ques. What is the quotient in Mathematics? (2 marks)
Ans. The quotient is the number of times the divisor is divided by the dividend. This could be better understood with an example. Suppose, 36 is divided by 5. In this equation, the quotient is 7 because 36 =7*5 +1. Thus, 7 is the quotient and 1 is the remainder.
Ques. Choose the correct remainder when 64 is divided by 8? (1 mark)
(A) 2
(B) 5
(C) 0
(D) 1
Ans. The correct answer is 0, since 64 is perfectly divided by 8.
Ques. What is the remainder if 24 is divided by 7? (2 marks)
Ans. If 24 is divided by 7 then the remainder will be 3. How, let’s explain.
24= 7x 3= 21 + 3, thus 3 is the remainder
Ques. What is the formula of the remainder? (2 marks)
Ans. The remainder formula is Dividend = Divisor x Quotient + Remainder
If we need to find the remainder then we can mold this formula into this:
Remainder = Dividend – (Divisor x Quotient)
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