We’ll look at the link between the dividend, divisor, quotient, and remainder in division. The dividend is the number that we divide. The divisor is the number by which we divide. The obtained result is known as the quotient. The remainder is the amount that is left over.
How do you find the dividend divisor quotient?
If we know the dividend, remainder, or divisor, we can use the dividend divisor quotient remainder formula. The formula can be used as needed. Dividend = Divisor Quotient + Remainder is the formula for calculating dividends. Dividend/Divisor = Quotient + Remainder/Divisor is the formula for divisor.
What is divisor formula?
Formula for Divisors Let’s look at the divisor formula when the remainder is 0 and when it’s a non-zero number. Divisor = Dividend Quotient if the remainder is 0. Divisor = (Dividend – Remainder)/ Quotient if the remainder is not 0.
Which is the quotient?
The quotient is the result of multiplying two numbers together. For example, if we divide 6 by 3, the result is 2, which is known as the quotient. It’s the result of the division procedure. An integer or a decimal number can be used as the quotient. We have an integer as a quotient for accurate divisions like 10 5 = 2, and a decimal as a quotient for divisions like 12 5 = 2.4. The remainder of the division in a division procedure with a decimal quotient as the answer is the decimal part of the quotient.
In general, knowing the quotient aids in determining the dividend’s magnitude in relation to the divisor. Divide the divisor by the dividend to get the quotient. A quotient that is greater than the divisor but less than the dividend is called a quotient. Let’s take a closer look at the quotient and the ways for calculating it.
What is the quotient calculator?
When a number is split by another number, a Quotient Calculator is a free online tool that calculates and shows the quotient. Cuemath’s online calculator speeds up calculations and provides results in a matter of seconds.
What is called divisor?
A divisor is an integer that entirely divides another number or leaves a remnant. Dividend Divisor = Quotient is how a divisor is represented in a division equation. We get 5 when we divide 20 by 4. The divisor is the number that divides 20 evenly into five pieces, which is 4.
What is difference between divisor and dividend?
We divide a number by any other number to produce a new number as a result of division. As a result, the dividend is the number that is divided here. The divisor is the integer that divides a given number. The quotient is the number that we get as a result of this. A divisor that does not entirely divide a number produces a number known as the remainder.
Is there any relation between dividend divisor quotient and remainder?
Let’s take a closer look at each of these division-related scenarios to make sure you’re ready for all forms of quotient/remainder questions on the GMAT. A simple example can demonstrate the importance of division terminology: 7/4 = 1 + 3/4 = 7/4 = 1 + 3/4 = 7/4 = 1 + 3/4 = 7/4 = 1 + 3/4 = 7/4 = 1 + 3/4 = 7/4 = 1 + 3/4 = 7/4 = 1 + 3/4 = 7/4 =
The dividend is the phrase that we’re dividing by something else. The divisor is the number four, which divides. The quotient is 1, the whole number component of the mixed fraction. And then there’s number three. Even if you need to be reminded of the language, this is likely to feel familiar.
The basic remainder formula is Dividend/Divisor = Quotient + Remainder/Divisor in the abstract. We may get another useful variant of the remaining formula by multiplying through by the Divisor: Quotient*Divisor + Remainder = Dividend.
To answer the following official GMAT question, all you need is a basic understanding of this vocabulary and the remaining equation:
The quotient of N divided by T is S, while the remainder is V. N is equal to which of the following expressions?
The dividend in this division problem is N, which is being divided by something else, the divisor is T, the quotient is S, and the remainder is V. We get N = ST + V by plugging the variables into our remaining equation of Dividend = Quotient*Divisor + Remainder… and we’re done! C is the correct answer.
(Note that if you forget the remainder formula, you can solve this problem with simple numbers.) Let’s say N is 7 and T is 3. 2 + 1/3 = 7/3 V = 1 since the Quotient is 2 and the remainder is 1. We’ll need a N of 7 if we punch in 3 for T, 2 for S, and 1 for V. Choice C will give us a N of 7, because 2*3 + 1 = 7, which is true.)
When we need to construct a list of possible values to evaluate in a data sufficiency question, a statement will frequently provide us with information about the dividend in terms of the divisor and the remainder.
Consider the following example: when x is divided by 5, the residual equals 4. Here, x is the dividend, 5 is the divisor, and 4 is the remainder. We’ll just call it q because we don’t know what the quotient is. It will be written as x = 5q + 4 in equation form. We can now construct x values by selecting q values, keeping in mind that the quotient must be a non-negative integer.
x Equals 4 if q = 0. x Equals 9 if q = 1. x Equals 14 if q=2. Take note of the pattern that emerges when we look at our x values: x = 4, 9, 14, or 19… In essence, the remainder is the first permissible value of x. After that, we just keep adding the divisor, 5, over and over again. You could keep going indefinitely without doing any math: 4, 9, 14, 19, 24, 29, etc. This is a useful shortcut to utilize when dealing with complex data sufficiency issues, such as the following:
1) If you divide x – y by 5, the residue is one.
2) If you divide x + y by 5, the result is 2.
(A) While assertion (1) is sufficient on its own, statement (2) is not.
(B) While statement (2) is sufficient on its own, statement (1) is not.
(C) Both statements are sufficient when read together, but neither statement is sufficient when read separately.
Statement 1 in this problem offers us alternative values for x – y. Remember the pattern from earlier: x – y must be a multiple of 5 plus 1. We know that x – y = 1 or 6 or 11, etc., if we start with the remainder (1) and keep adding the divisor (5). We can assert that x = 1 and y = 0 if x – y = 1. In this situation, x2 + y2 = 1 + 0 = 1, and when 1 is divided by 5, the residual is 1. We can claim that x = 7 and y = 1 if x – y = 6. Now x2 + y2 = 49 + 1 = 50, and when 50 is divided by 5, the remainder is 0. Statement 1 is insufficient by itself because the remainder varies depending on the scenario.
Statement 2 provides us x + y’s possible values. Let’s employ that pattern once more: x + y must be a multiple of 5 by at least 2. We know that x + y = 2 or 7 or 12, etc., if we start with the remainder (2) and keep adding the divisor (5). We can assert that x = 1 and y = 1 if x + y = 2. In this situation, x2 + y2 = 1 + 1 = 2, and when 2 is divided by 5, the residual is 2. We might assert that x = 7 and y = 0 if x + y = 7. Now x2 + y2 = 49 + 0 = 49, and when 49 is divided by 5, the remainder is 4. Statement 2 is also insufficient on its own because the remainder varies depending on the scenario.
Now that we’ve arrived at the typical C or E scenario, let’s put them to the test: choose one scenario from Statement 1 and one from Statement 2 and watch what occurs. Let’s pretend that x – y = 1 and x + y = 7. When these equations are added together, we get 2x = 8, or x = 4. If x equals 4, y equals 3. Now x2 + y2 = 16 + 9 = 25, and when 25 is divided by 5, the result is 0.
Remember this: in order to choose a non-E Data Sufficiency answer, we must know that the value will remain the same in each situation permitted by the question and statements. Let’s attempt a different scenario just to be safe. Let’s pretend that x – y = 6 and x + y = 12. When we add the equations together, we obtain 2x = 18, or x = 9. If x = 9, y = 3, and x2 + y2 = 81 + 9 = 90, then x2 + y2 = 81 + 9 = 90. When 90 is divided by 5, the remaining is 0 once more. This will be the case regardless of the values we choose – we can establish without a doubt that the remainder is 0. Because the statements are sufficient when taken together, the correct answer is C.
Let’s review some key points about GMAT quotient/remainder questions and the all-important remainder formula now. You’ll almost certainly see remaining questions on the GMAT, so make sure you understand the concept. First, double-check that you understand the remainder formula: Dividend = Divisor*Quotient + Remainder Dividend = Divisor*Quotient + Remainder Dividend = Remainder Dividend = Second, if you need to choose values, simply start with the remainder and keep adding the divisor. If you can comprehend these two concepts, the rest of the questions will be much easier to answer.
Remember that division is something you were previously fairly strong at as a primary school student, so don’t be intimidated by the terms as an adult!
In these issues, the GMAT thrives on abstraction, so if you are sidetracked by language or abstraction, just use little numbers to remind yourself how the operation works.
Dividend = Divisor*Quotient + Remainder is a crucial remainder equation, but it may be reconstructed if you forget it.
Try 7 divided by 4 like we did at the start.
The outcome is 1, with a remainder of 3.
And the quotient is 1 because 4 is multiplied by 7 once, leaving 3 unaccounted for.
So, to go back to 7, increase the divisor (4) by the number of times it passed into 7, and then add the remaining 3: 7 = 4(1) + 3.
Once the abstraction in quotient/remainder problems is removed, the remainder is a concept you’ve been familiar with your entire life!
Do you want to brush up on GMAT division questions and the remainder equation?
Try your hand at some practice questions from the Veritas Prep GMAT Question Bank or practice tests, or read some of our other articles on this frequently-tested GMAT topic.
Does quotient include remainder?
The Remainder And The Quotient The quotient is the outcome of division. The remainder is the amount that is left over. The rest is a portion of the end result.
