12 Helpful Rules of Division (With Examples)

Rules Students Should Know for Division
  • Divisibility by 2. If the last digit in a number is 0 or an even number, it’s divisible by 2. …
  • Divisibility by 4. If the last two digits of a number are divisible by 4, the whole number is. …
  • Divisibility by 6. Numbers divisible by 6 can also be divided by both 3 and 2.

It is essential to have a strong understanding of the rules of division in order to succeed in mathematics. Division is an important skill that is used by students, professionals, and everyday people alike. By having a firm understanding of the rules of division, you will be able to accurately and efficiently divide numbers and solve complex problems. This post will provide a comprehensive overview of the rules of division and how they apply to mathematics. It will cover topics such as how to divide numbers, basic rules of division, and the importance of understanding the rules of division. By the end of this blog post, you will have the necessary knowledge to confidently and accurately divide numbers.

Math Antics – Basic Division

What are the rules of division?

The rules of division include basic memorization techniques that make division calculations easier by creating patterns you can use to deconstruct both simple and complex problems. The guidelines establish requirements that a number must meet in order to neatly divide into another number. While some division rules can be applied with small, one-step formulas, others need two or three steps to assess a number’s divisibility. Although some of these formulas are large, division rules can speed up the process of dividing by large numbers.

What is division?

A mathematical operation called division divides a larger number into equal groups. When you divide a multiplication product into a certain number of groups, you get a result. This is how division works. This outcome, known as the quotient, shows how many groups your initial value can be divided into or how many individuals make up each group. In a division problem, there are several elements:

Rules of division for solving mathematical problems

To help you with both simple and complex mathematical calculations, use the following division rules:

Rules you can use when dividing by one

Any integer (a number that is not a fraction) is always divisible by one; this is the only rule that pertains to one. For example:

100 / 1 = 100

25 / 1 = 25

32 / 1 = 32

Divisibility rule for dividing by two

You can determine if a number can be divided by two if the last digit is even (e.g., 2, 4, 6, 8, and so on). For example:

136 / 2 = 68

42 / 2 = 21

82 / 2 = 42

Due to the fact that they are all even numbers, these examples are all divisible by two.

Rules for dividing by three

If you can divide the sum of the digits in a number by three, you can test your ability to divide a number by three. Consider testing the number 111 to see if it is divisible by three. Add all the digits together and evaluate the result. Your number is if the outcome is also divisible by three. Since three is divisible by three and 111’s digits add up to three, the number is also divisible by three. As an additional illustration, add the digits of the number 123 together:

1 + 2 + 3 = 6

Since the number six can be divided by three, the number 123 can as well.

Rules to apply for dividing by four

When determining whether a number is divisible by four, look at the last two digits to see if they are. Consider the situation where you are attempting to determine whether 345 is divisible by four. Knowing the last digit can help you find the solution quickly. The entire number is also divisible by four if the last digit is a four. Take a look at the following examples:

12 can be divided by four, so 112 can as well.

112 / 4 = 28

16 can be divided by four, so 416 is also divisible by four.

416 / 4 = 104

Helpful rules for dividing by five

If the last digit of a number is a zero or a five, you can check if you can divide it by five.

Due to the last digit being a zero, the number 30 can be divided by five.

30 / 5 = 6

Due to the fact that the last digit is a 5, 175 can be divided by 5.

175 / 5 = 35

Divisibility rules to use for six

If a number meets the criteria for both division by two and division by three, you can test whether it can be divided by six. A six-digit number must also be even and divisible by three. For example:

Since 66 is even and divisible by three, it can be divided into six equal parts.

66 / 6 = 11

228 is divisible by six because it is even and divisible by three.

228 / 6 = 38

Rules you can use for dividing by seven

You can check if you can divide a number by seven by subtracting the double of the last digit from the first two digits.

(First two digits) – (2 x last digit)

For instance, use the following formula to determine whether 182 is divisible by seven:

(18) – (2 x 2) is 14, and since 14 is divisible by 7, 182 is also divisible by 7.

182 / 7 = 26

Rules to utilize for dividing by eight

If you divide a number by two, three, and the outcome is still a whole number, you can determine if you can divide it by eight. Any number that is not a decimal or a fraction is referred to as a whole number.

(Initial number ÷ 2) ÷ (2) ÷ (2)

For example:

300 / 2 = 150, 150 / 2 = 75, 75 / 2 = 37. 5.

300 is not divisible by eight.

816 / 2 = 408, 408 / 2 = 204, 204 / 2 = 102.

816 is divisible by eight.

Rules for dividing by nine

If you can divide the sum of the digits in a number by nine, you can test your ability to divide a number by nine.

First digit plus second digit plus third digit plus fourth digit equals

For instance, you can add up the digits in a number and see if the result is also divisible by nine to see if 1,500 is divisible by nine. In this instance, the number 1 + 5 + 0 + 0 = 6, which cannot be divided by 9. Therefore, 1,500 is not divisible by nine.

Nine is a multiple of 27 since 9 + 6 + 5 + 7 = 27. Therefore 9,657 is divisible by nine.

Divisibility rules for dividing by 10

If a number’s decimal point is zero, you can check if you can divide it by ten. For example:

Because it doesn’t end in a zero, the number 234 cannot be divided by 10. 300 is because it ends in a zero.

300 / 10 = 30

Rules to use when dividing by 11

If a number can be divided by 11 after digit addition and subtraction, you can test if you can divide it by 11.

First digit minus second digit plus third digit minus fourth digit equals

For example:

Given that 2 – 3 + 4 = 3 and that three cannot be divided by 11, neither can 234

11 is divisible by 11, and 5 – 3 + 9 equals 11. Therefore, 539 is divisible by 11.

Rules to use when dividing by 12

If the number you’re dividing complies with the rules for division by three and four, you can test if you can divide it by twelve. Consider that you want to determine, for instance, whether 453 is divisible by 12. The result of multiplying four, five, and three is twelve. Check your number’s last two digits to see if they can be divided by four next. Since 453 violates both the rules for four and three, it cannot be divided by twelve.

(First digit) + (second digit) + (third digit) =

The resultant number is divisible by 12 if its final two digits can be divided by 4.

For example:

5 + 2 + 4 = 11

Since 24 can be divided by 4, 524 can be divided by 12.


What are the 3 rules of division?

A number is fully divisible by three if the sum of its digits is also divisible by three, according to the rule of threes on divisibility. Consider a number, 308. Take the sum of the digits (i) to determine whether or not 308 is divisible by 3. e. 3+0+8= 11). Check to see if the sum can be divided by 3 now.

What are the 5 steps of division?

Similar to long division, it divides, multiplies, divides, subtracts, brings down, and repeats or finds the remainder.

What is the first rule of division?

First Principles of Division: Two numbers are taken into consideration, each of which represents a measurement or count. One of the sums is divided into several parts according to the second. The amount of one part is the result.

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