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Let’s say you have 12 donuts and want khổng lồ distribute them equally among your three friends. How bởi you decide fairly how much each gets?

You just divide the donuts equally among your friends! This method of distributing a group of things into equal parts is termed as division. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.

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What is Division in Math?

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.

The main goal of dividing is lớn see how many equal groups are formed or how many are in each group when sharing fairly.

In the above example, khổng lồ divide 12 donuts into 3 similar groups, you will have lớn put 4 donuts in each group. So, 12 divided by 3 will give the result 4.

Mathematical Notation for Division

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There are various signs that can be used lớn indicate division, such as

÷/
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For example:

27 ÷ 327/3
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Special Names for Numbers in Division Equation

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Each part involved in a division equation has a special name.

Dividend: The dividend is the number that is being divided in the division process.

Divisor: The number by which the dividend is being divided by is called the divisor.

Quotient: The quotient is a result obtained in the division process.

Remainder: Sometimes, we cannot divide things exactly. There may be a leftover number. That leftover number is called the remainder.

The relationship between these four parts can be expressed as follows:

Dividend = Divisor x Quotient + Remainder

This is also called the division formula to kiểm tra whether the answer is correct or not.

For example, let’s divide 16 by 3. The leftover will be 1.

Here, dividend = 16, divisor = 3, quotient = 5 and remainder = 1

So, 16 = 3 × 5 + 1

Properties of Division

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To understand division better, let’s look at a few general division rules & properties:

1. If we divide a whole number (except zero) by itself, the quotient or the answer is always 1.

For example:

· 7 ÷ 7 = 1

· 25 ÷ 25 = 1

2. If we divide a whole number by zero, the answer will be undefined.

For example:

6 ÷ 0 = undefined

325 ÷ 0 = undefined

3. Zero divided by any number will give the answer zero.

For example:

0 ÷ 5 = 0

0 ÷ 100 = 0

4. If we divide a whole number (other than zero) by 1, the answer will be the number itself.

For example:

4 ÷ 1 = 4

11 ÷ 1 = 11

5. If a whole number is divided by another whole number, the quotient may not necessarily be a whole number.

For example:

15 ÷ 2 = 7.5

20 ÷ 3 = 6.67

6. In the case of exact division (with no remainder), the divisor multiplied by the quotient is the dividend. This property holds true only if all three numbers are non-zero whole numbers.

For example:

If 30 ÷ 5 = 6 then 5 × 6 = 30

7. If there are three non-zero whole numbers a, b & c, and b × c = a, then,

a ÷ b = c and a ÷ c = b

For example:

5 × 10 = 50, then,

· 50 ÷ 5 = 10

· 50÷ 10 = 5

Long Division

In math, long division is the mathematical method for dividing large numbers into smaller groups or parts. It helps in breaking down a problem into simple and easy steps.

Long Division Steps

Every long division can be solved with the five steps given below.

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Here’s an example that will help you understand the division steps.

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Let’s do some division examples lớn practice the long division steps.

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Solved Examples

1. Divide 171 by 3.

Solution:

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So, Quotient = 57, Remainder = 0

(Note: The writer has created the images for all the long division calculations themselves)