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To understand dividend definition, we first have to learn about multiplication and division. Multiplication means adding similar things together, but all the things must be of equal quantity. Division means dividing something into equal parts.
The division is the opposite of multiplication. Multiplication is also known as repeated addition, whereas; division is also known as repeated subtraction.
Multiplication:
When there are two different things in a scenario, one is a group, and the other is the number of items in that group; then, we can find the total number of items using multiplication.
For example, there are 5 baskets. In each basket, there are 3 apples.
Here, the basket is a group, and apples are items. Items are the things inside a group.
To find the total number of apples, we can add all the apples in all the baskets. 3 3 3 3 3 = 15. So, there are 15 apples in total. Here we are adding 3, 5 times.
Instead, we can directly calculate 5 times 3, written as 5 x 3 = 15.
We multiply two numbers to get a product. The numbers multiplied by each other are called ‘Multiplicand’ and ‘Multiplier’.
Multiplicand x Multiplier = Product
The multiplicand and multiplier could either be a whole number or a decimal number.
Rules related to multiplication:
If the multiplicand and multiplier both are whole numbers, the product will be a whole number only.
Example: 2 x 5 = 10
If a multiplicand is a decimal number and a multiplier is a whole number, the product could either be a decimal number or a whole number.
Example 1: 4.2 x 3 = 12.6 (product is a decimal number)
Example 2: 4.5 x 2 = 9 (product is a whole number)
If a multiplicand is a whole number and a multiplier is a decimal number, the product could be a whole number or a decimal number.
Example 1: 4 x 2.3 = 9.2 (product is a decimal number)
Example 2: 4 x 2.5 = 10 (product is a whole number)
If the multiplicand and multiplier are decimal numbers, the product could be a whole number or a decimal number.
Example 1: 4.4 x 2.5 = 11 (product is a whole number)
Example 2: 4.2 x 2.5 = 10.5 (product is a decimal number)
Division:
We know that division is the reverse of multiplication. So, let’s now reverse the question and understand it. While reversing, we can observe that there could be two different scenarios here. Let us discuss both.
Scenario 1:
There are 15 apples in total. There are 5 baskets. How many apples can be put into each basket?
Let us do it in a primitive way.
Let us start putting 1 apple in each basket.
Now, we have 15 – 5 =10.
We still have 10 apples left. Let us again put 1 apple in each basket.
Now, we have 10 – 5 = 5 apples. Now, 5 apples are left.
So, let us one more time put 1 apple in each basket. Now, we have 5 – 5 = 0.
Here we subtracted 5, 3 times, and so our answer is 3. This was solved using repetitive subtraction by doing 15-5-5-5 = 0.
Hence, 5 are subtracted 3 times. Instead of this, we could directly calculate 15/5 = 3.
Scenario 2:
There are 15 apples in total. 3 apples could be placed in each basket. How many baskets would be required?
Using repeated subtraction, we could write, 15-3-3-3-3-3=0 which means 3 is subtracted 5 times.
Hence, 5 baskets would be required.
We could otherwise calculate it as 15/3 = 5.
We saw two scenarios here. In both cases, 15 were divided by a number. So, here 15 is called the ‘Dividend’. And the number which divides 15 is called the ‘Divisor’. The result which we get after dividing is called the ‘Quotient’.
So the formula could be written as:
Formula 1
Dividend / Divisor = Quotient
If 15/3 = 5, then here,
15 is the dividend,
3 is the divisor and
5 is the quotient.
Formula 2
Dividend = Divisor x Quotient
If 15 = 3 x 5, then here,
15 is the dividend,
3 is divisor and
5 is the quotient,
In some cases, the dividend is not exactly divisible by the divisor, and so it leaves a remainder.
For example, 20 apples are divided among 3 children. We can write this mathematically as 20/3.
Here each child will get 6 apples, but still, 2 apples will be left.
Here,
20 is the Dividend,
3 is the Divisor,
6 is the Quotient and
2 is the Remainder
Formula 3
Dividend = (Divisor x Quotient) Remainder
So, 20 = (3 x 6) 2
Or, 20 = 18 2
Or, 20 = 20
Formula 4
Dividend – Remainder = Divisor x Quotient
So, 20 – 2 = 3 x 6
Or, 18 = 18
Rules related to division:
The dividend could either be a whole number or a decimal number. If it is a whole number, we can carry out division simply. It may or may not leave a remainder depending upon the divisor.
If it is a decimal number, we will still carry out the division in the same way by imagining that there is no decimal. Then after we get the quotient, we will place the decimal in the quotient by counting the number of places after the decimal.
For example, 315.3 / 3
Step 1: remove decimal from dividend and divide. So, 3153 / 3 = 1051
Step2: place the decimal in the quotient. So the answer is 105.1 (there was 1 place after the decimal in dividend, and so there should be 1 place after the decimal in quotient as well)
The divisor could either be a whole number or a decimal number. If it is a whole number, we can carry out the division in a regular way. But if it is a decimal number, then we should first remove the decimal and then divide.
For example, 3153 / 0.3
Step 1: remove decimal. So 3153 / 0.3 = 31530 / 3 (multiply 10 to both numerator and denominator)
Step 2: divide. 31530 / 3 = 10510
The dividend and divisor both could be decimal numbers. In such cases, we should first remove the decimal from the divisor or the denominator and then carry out the division.
For example: 20.55 / 0.5. First, remove the decimal from the denominator(divisor). We will get 205.5 / 5. Now divide it normally, and we will get 411. Now place the decimal. So the answer is 41.1
The dividend and divisor both could be a whole number still; we can get decimal numbers in the quotient or a whole number as well.
For example, 20/3 = 6.66666 (Here, in the quotient 6 is repeated continuously. Such decimal numbers are called repeating numbers. They are also not ending, so we call them non-terminating. Hence, 6.6666 is a repeating and non-terminating decimal)
For example, 18/3 = 6 (Here, the quotient is a whole number)
The dividend and divisor could be a decimal number still; the quotient could either be a whole number or a decimal number.
For example, 20.5 / 0.5 = 41 (The quotient is a whole number)
For example, 20.5 / 5 = 4.1 (The quotient is a decimal number)
The remainder will always be a whole number.
Conclusion
All the mathematical terms have been discussed in detail above, including their meanings, examples, formulas, and rules. Try to make your examples and solve more sums. This will help you to understand things in detail. All the best.
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