Key Division Terms Every Student Should Know
Division vocabulary includes words which we often use while solving all division related problems. Division vocabulary words include division, division symbol, dividend, divisor, quotient, and remainder. Here, we will learn the division vocabulary with interactive examples that will help you to understand and solve division problems easily.
What Is Division?
The term “division” means to split into equal parts or groups. The division is an outcome of “fair sharing” because it splits everything equally.
Division Symbol
The division symbol indicates to divide into equal groups or parts.
We often use the symbol obelus () , or sometimes slash (/) to mean divide:
15 5 = 3
15 / 5 = 3
This is read as “fifteen divided by five equals three”.
Division Example
Let us understand division with an example below:
Example:
There are 12 chocolates in total. Divide these 12 chocolates evenly among 3 of your friends. How will you divide the chocolates?
Solution: To evenly divide a total of 12 chocolates among 3 friends, we will divide 12 by 3.
Image: 12 divided by 3
Image: 12 Chocolates
12 3 = 4
This is read as twelve divided by three equals four.
Hence, each friend will get 4 chocolates.
Example 2:
Look at the fish given below:
Image: 9 fish in 3 groups
Here, 9 fish are swimming into a group of three.
This can be written as: Total 9 fish divided into groups of 3 makes three groups of each.
This will be calculated as: 9 3 = 3
What Is a Dividend?
In division, the dividend is the number to be divided. In other words, a dividend is the whole that is to be splitted or divided into equal parts.
Example:
There are 12 candies that are to be equally divided among 3 children. Here 12 is the dividend.
Image: 12 candies divided equally among 3 children
12 candies 3 children = 4 candies to each child.
12 is the dividend, and 12 3 = 4
What Is a Divisor?
The divisor is the number we divide the dividend by. In other words, a divisor is a number by which another number is divided.
Example:
In 12 3 = 4, 3 is the divisor.
↓
Divisor
Divisor Representation in Division
In division, divisor is represented as:
Dividend Divisor = Quotient
Example:
On dividing 12 by 3, we get 4. Here 3 is the number that is dividing 20 (dividend) completely into 4 parts and is known as the divisor.
Dividend Divisor Quotient
12 3 = 4
What Is a Quotient?
A quotient is the result that we get after dividing one number by another number. In other words, quotient is the number that we get after dividing dividend by divisor.
Example:
Let us divide 12 by 3.
Image: 12 cupcakes divided equally in small groups of 3
Here, the larger group of 12 cupcakes is known as the dividend. The small equal groups of 3 are known as divisors. The number of cupcakes in each group is termed a quotient. Here, there are 4 cupcakes in each smaller group, which is the quotient.
What Is a Remainder?
The remainder is the number that is left over or remaining when dividing one number by another. In other words, when we are not able to make an equal group or equally share all the objects, we are left with a number known as the remainder.
Remember: The remainder value is always less than the divisor.
Example:
1. We have 9 pencils to share with 2 children.
Solution: But 9 cannot be split into 2 equal groups.
So each child gets 4 pencils and one is left over.
Image: 9 pencils divided equally among 2 children with one pencil left.
9 2 = 4 R1
This is read as 9 divided by 2 equals 4 with a remainder of 1. And we write it as: 9 2 = 4 R1
Do You Know?
The dividend is the whole number that is divided by another number.
The divisor is a number that divides the other number (dividend) either completely or with a remainder.
The quotient is the result obtained after division of two numbers.
The remainder value is always less than the divisor value.
If the remainder value is greater than the divisor, it means division is incomplete.
The remainder value can either be greater, lesser, or equal to the quotient value.
Conclusion
In short, division is a process of dividing a group of things into equal parts, and division vocabulary such as dividend, division symbol, divisor, quotient, and remainder are the terms used in the division process.
FAQs on Division Vocabulary Explained for Students
1. What are the five main vocabulary words used in division?
The five main vocabulary words, or terms, essential for understanding division are:
- Dividend: The total number that is to be divided.
- Divisor: The number that the dividend is being divided by.
- Quotient: The result or the answer obtained from the division.
- Remainder: The value left over after the division is complete.
- Division Symbol: The sign (÷ or /) that indicates a division operation.
2. How can the concept of division be explained in simple words?
In simple terms, division is the mathematical process of splitting a whole number or a set of items into smaller, equal groups. For example, if you have 12 chocolates (the dividend) and want to share them equally among 4 friends (the divisor), division helps you determine that each friend will receive 3 chocolates (the quotient).
3. What is the formula that connects the dividend, divisor, quotient, and remainder?
The relationship between the four main terms of division is defined by the division algorithm, which can be expressed with the formula: Dividend = (Divisor × Quotient) + Remainder. This equation is very useful for verifying the accuracy of a division calculation. For instance, in the problem 13 ÷ 4, the quotient is 3 and the remainder is 1. Using the formula, we can check this: 13 = (4 × 3) + 1.
4. What does a remainder of zero mean in a division problem?
A remainder of zero signifies that the division is exact. It means the divisor divides the dividend perfectly, with no amount left over. This indicates that the dividend is a multiple of the divisor. For example, when 20 is divided by 5, the quotient is 4 and the remainder is 0, showing that 20 can be perfectly split into 5 equal groups of 4.
5. Why must the remainder always be less than the divisor?
The remainder must always be smaller than the divisor because if it were equal to or larger than the divisor, it would imply that another equal group could have been formed. The purpose of division is to make as many equal groups as possible. For example, if you are dividing by 5, and your remainder is 5 or more, it means you could have made at least one more group of 5, so the division was incomplete.
6. How are division and multiplication related to each other?
Division and multiplication are inverse operations, which means they are opposites and can undo each other. Every division fact has a corresponding multiplication fact. For example, if you know that 24 ÷ 6 = 4, you also inherently know that 6 × 4 = 24. This relationship is a fundamental concept in arithmetic and is extremely helpful for checking answers.
7. How does knowing division vocabulary help solve real-life word problems?
Understanding division vocabulary is crucial for translating real-life scenarios into mathematical problems. Words like “share equally,” “distribute,” “split into groups,” or “average” are signals to use division. By identifying the total amount to be shared as the dividend and the number of groups as the divisor, you can correctly set up the problem. This clarity helps in accurately finding the quotient, whether it's the number of items per person or the size of each group.
