Laying the Foundation: How to Obtain the Quotient?
The Significance of Thương Số
In the process of division, one number is divided by another number to obtain a different number as the output. Here, the number being divided is called the dividend, and the whole number dividing a certain number is called the divisor. If the divisor does not completely divide a number, it will yield a remainder. The division operation is denoted by the symbols ‘÷’ or ‘/’. Therefore, we can represent the division method as follows:
Cổ tức (Dividend) = Thương số (Quotient) x Số chia (Divisor) + Phần còn lại (Remainder)
When the remainder is zero:
Cổ tức (Dividend) = Thương số (Quotient) x Số chia (Divisor)
Therefore,
Thương số (Quotient) = Cổ tức (Dividend) ÷ Số chia (Divisor)
The Parts of a Division Problem
We can represent the division operation as:
Cổ tức ÷ Số chia (Divisor) = Quotient and Remainder
When a dividend is divided by a divisor, we obtain a result. Therefore, essentially, division is the inverse process of multiplication, such that when we multiply the quotient and divisor, we will obtain the dividend. Thus, we can also define the dividend, divisor, and remainder here:
- Cổ tức (Dividend): The number that needs to be divided.
- Số chia (Divisor): The number by which the dividend is divided.
- Phần còn lại (Remainder): The value that remains after the division process. When a number is evenly divisible, the remainder is zero, but when dividing a number, the remainder is not equal to zero.
Understanding Thương Số Representation
Thương số (Quotient) is widely used throughout the field of Mathematics and is often referred to as a fraction or a ratio. Let’s take a look at its representation to better understand it.
In the above representation, we can see that the numerator is the dividend and the denominator is the divisor. When the numerator is divided by the denominator, the result is the quotient. Now let’s see the long division representation in the image below.
How to Determine the Quotient of a Number?
When working with division problems, we first need to identify which number is the dividend and which number is the divisor. To find the quotient of a number, the dividend is divided by the divisor. It means the problem is in the form:
Số bị chia (Dividend) ÷ Số chia (Divisor) = Quotient
If a dividend is completely divisible by the divisor, we do not get a remainder (Remainder must be zero). If the dividend is not completely divisible by the divisor, we get a remainder.
For example: 12 ÷ 2 = 6
In this case, the dividend 12 is perfectly divisible by 2. Therefore, we obtain the quotient value of 6 and the remainder is 0.
Now, let’s consider another example, 15 ÷ 2. In this case, 15 does not divide evenly by 2, so we get the quotient value of 7 and the remainder is 1.
Examples of Quotients
Q.1: Divide 24 by 4.
Solution: 24 ÷ 4 = 6
Therefore, 6 is the answer.
Q.2: Find the quotient of 105 ÷ 5.
Solution: 105 ÷ 5 = 21
Therefore, 21 is the quotient.
Q.3: Divide 60.5 ÷ 5.
Solution: 60.5 ÷ 5 = 60.5 / 5 = 12.1
Therefore, 12.1 is the answer.
Q.4: Solve 108/12.
Solution: 108/12 = 9
Therefore, the quotient is 9.
Q.5: Write the quotient and remainder for the following values:
Solution:
Dividend Quotient Remainder
114 ÷ 12 9
632 ÷ 65 2
125 ÷ 91 34
Practice Questions
- Divide 177 by 3.
- Divide 800/4.
- Find the value of 45/12.
- Find 63 ÷ 9.
Frequently Asked Questions about Thương Số
What does Thương Số mean?
In Mathematics, the quotient is a result when one number is divided by another number. In other words, a dividend divided by a divisor gives us the quotient as the result.
What are the different parts of a division problem?
The different parts of a division problem are as follows:
- Dividend
- Divisor
- Quotient
- Remainder
Is the quotient the answer to a division problem?
Yes, the quotient is the solution to any division problem. If a number 5 is divided by 5, we get the quotient as 1, which is the answer to the division problem.
What is the quotient of 17 divided by 3?
If 17 is divided by 3, we get the quotient as 5 and the remainder as 2. In other words, 17 (Dividend) ÷ 3 (Divisor) = 5 (Quotient) + 2 (Remainder).
What is the formula for the quotient?
The formula for the quotient is given as:
Dividend ÷ Divisor = Quotient (if the remainder is 0)
The general formula for any division problem is:
Dividend ÷ Divisor = Quotient + Remainder
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