Tổng hợp kiến thức và cách giải bài tập dấu hiệu chia hết cho 3

Identifying the signs of division by 3 will help them solve homework and calculate faster. So what is the divisible number by 3, how to identify and how to solve it? Let’s find out more in the following article.

Signs are divisible by 3

Signs of division by 3 are known as a rule to determine whether some are divisible by 3? Specifically:

Which number is divisible by 3?

To determine which number is divisible by 3, we will rely on the following signs:

• The sum of the digits is divisible by 3: A number is divisible by 3 is when the sum of those digits will also be divisible by 3.

• Signs of sum for large numbers: If a large sequence cannot calculate the sum of those digits, we can take that number to divide the balance by 3. If the result is with a balance of zero, the number will be divisible by 3 and vice versa.

Signs are divisible by both 3 and 9

For the numbers with the sum of the digits divisible by 9 will be divisible by both 3 and 9.

For example:

Number 189 has a total of 1 + 8 + 9 = 18) for 9, at this time 189 will also be divided by 3.

Signs are divisible by 3 consecutive natural numbers

With consecutive natural numbers, people can identify whether the number is divisible by 3 or not based on the nature of that sequence. Specifically:

• Consecutive 3 numbers divisible by 3: Case 3 consecutive natural numbers, even mutual each other can be divided by 3. For example: 8, 9, 10 are all divided by 3.

• Consecutive 2 numbers divisible by 3: In case 2 consecutive natural numbers have the sum of the digits divisible by 3, both of them are divisible by 3. For example: 6 and 9 (6 + 9 = 15) are divided by 3.

• Consecutive 4 numbers divisible by 3: In case 4 consecutive natural numbers have the sum of the digits divisible by 4, those numbers are all divided by 3. For example: 5, 6, 7, 8 (5 + 6 + 7 + 8 = 26) are all divided by 3.

Similarly with consecutive ranges 5, 6, 7 … Other natural numbers can also apply this rule to determine the signing sign of 3.

Conditions are divisible by 3 of some

The condition for some integers to divide by 3 is that when that number is divisible by 3 and no residues.

Give an integer a, if A is divided by 3, we have: a % 3 = 0

In particular, “%” is a mathematical symbol used to indicate the division of the balance. If the result of a division of A is 0 is 0, that is, there is no leftover, then A is divided by 3.

For example:

Number 9 is divisible by 3 because 9 % 3 = 0.

Number 16 is not divisible by 3 because 16 % 3 = 1 (with excess 1).

Number 27 is divisible by 3 because 27 % 3 = 0.

0 has all divided by 3?

In mathematics, 0 is a divisible number for all other numbers or all integers are divisible by 1 and each other integer can be divisible by itself. So, 0 can be divided by 3.

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Properties of the divisible sign by 3

If a number is divisible by 3 will include the following characteristics:

• If a number is divisible by 3, it may be odd or even numbers.

• The divisible number by 3 is not sure to divide by 6, 9, 12 … but some divisible by 6, 9, 12 … divisible by 3.

For example: Prove that the number 1890 is divisible by 3.

Solution: Call N is a set of elements of 1890.

N = {1; 8; 9; 0}

The sum of the elements in N is: 1 + 8 + 9 + 0 = 18. At this time we see 18 divided by 3 so the number 1890 is divisible by 3.

Common note and mistakes when using the divisible signs by 3

In the process of solving the exercises about the signs of division by 3, they need to note some of the following issues:

Some common errors when doing math exercises are divisible by 3

• False calculation error: This is a common error when performing the division or division. So, check the calculation steps to make sure your baby solves the calculation properly, because only a mistake or sign will also be wrong.

• Do not check carefully: When solving maths divisible by 3, many babies do not carefully check the results of the division of the balance, so it is easy to miss the case where the balance is 0, so it leads to the conclusion that the number is divisible by 3 or not is also wrong.

• False rounding: When solving maths to divide the balance, some babies often round the wrong results. So please round up the decimal number if necessary.

• Not considering the negative numbers: Most children check the number that is divisible by 3 not only the positive number. But many exercises also have negative numbers, so if some sounds are divisible by 3, the corresponding number is also divisible by 3.

Note about the negative number and zero in the divisible sign by 3

• The negative number is divisible by 3: If some sounds are divisible by 3, the corresponding positive number is also divisible by 3. For example, – 9 divided by 3 because 9 is divided by 3.
• The number 0 is divisible by 3: The number 0 is a divisible number by 3 because it does not have enough when divided by any positive integer.

For example:

Number -9 divisible by 3 because -9 % 3 = 0.

The number 0 is divided by 3 because 0 % 3 = 0.

Number -15 is divisible by 3 because -15 % 3 = 0.

Number 12 is divisible by 3 because 12 % 3 = 0.

Exercise Signs divisible by 3

In order to help them better understand the knowledge of some of the signs divisible by 3, here are some exercises that Mầm non Cát Linh summarizes for your baby to refer and practice.

Exercise in textbooks + Answers

Grade 4 Mathematics page 98 Lesson 1

In the following numbers, which number is divisible by 3?

231; 109; 1872; 8225; 92 313.

Answer:

+) Number 231 has a total of 2 + 3 + 1 = 6.

But 6 divided by 3 so the number 231 is divided by 3.

+) Number 109 has a total of 1 + 0 + 9 = 10.

But 10 is not divisible by 3 so the number 109 is not divisible by 3.

+) Number 1872 has a total of 1 + 8 + 7 + 2 = 18.

But 18 divided by 3 so the number 1872 is divisible by 3.

+) Number 8225 has a total of 8 + 2 + 2 + 5 = 17.

But 17 is not divided by 3 so the number 8225 is not divided by 3.

+) Number 92 313 has a total of 9 + 2 + 3 + 1 + 3 = 18.

But 18 divided by 3 so the number 92 313 is divisible by 3.

So in the given numbers, the numbers are divisible by 3 are:

231; 1872; 92 313.

Grade 4 Mathematics page 98 Lesson 2

In the following numbers, which number is not divisible by 3?

96; 502; 6823; 55 553; 641 311.

Answer:

+) Number 96 has a total of 9 + 6 = 15.

Which 15 is divisible by 3 so the number 96 is divided by 3.

+) Number 502 has a total of 5 + 0 + 2 = 7.

But 7 is not divisible by 3 so the number 502 is not divisible by 3.

+) Number 6823 has a total of 6 + 8 + 2 + 3 = 19.

But 19 is not divided by 3 so the number 6823 is not divided by 3.

+) Number 55 553 has a total of 5 + 5 + 5 + 5 + 3 = 23.

But 23 is not divided by 3 so the number 55 553 is not divided by 3.

+) Number 641 311 has a sum of 6 + 4 + 1 + 3 + 1 + 1 = 16.

But 16 is not divided by 3 so the number 641 311 is not divided by 3.

So in the given numbers, the numbers are not divisible by 3:

502; 6823; 55553; 641311

Grade 4 Mathematics page 98 Lesson 3

Write three numbers with three digits and divisible by 3.

Answer:

They can write numbers such as: 351; 648; 891.

Grade 4 math problems page 98 Lesson 4

Find the appropriate digit in the blank box to get all divisible by 3 but not divisible by 9: 56 …; 79 …; 2 … 35.

Solution:

+) Leave 56 … divisible by 3 then 5 + 6 + … = 11 + … divided by 3.

The number to fill in the dot is: 1 or 4

We get the numbers: 561 or 564 or 567 (type 567 because 567 is divisible by 9)

So the numbers are divisible by 3 without divisible by 9 561 or 564.

+) Leave 79 … divisible by 3 then 7 + 9 + … = 16 + … divided by 3.

The number to fill in the dot is: 2 or 5 or 8

We get the numbers: 792 or 795 or 798 (type 792 because 792 is divisible by 9)

So the numbers are divisible by 3 but not divisible by 9 795 or 798.

+) Leave 2 … 35 divisible by 3 then 2 + … + 3 + 5 = 10 + … divided by 3.

The number to fill in the dot is: 2 or 5 or 8

We get the numbers: 2235; 2535; 2835 (type 2835 because 2835 is divisible by 9)

So the numbers are divisible by 3 but not divisible by 9 is 2235 and 2535.

CONTENT EXERCISE

Question 1: Give 5 numbers; 1; 3; 6; 7. How many natural numbers have three digits and divisible by 3 made from the above numbers that the digits do not repeat.

Question 2: Prove that the product of 3 consecutive natural numbers is always divisible by 3.

Question 3: From 4 digits 3; 4; 5; 0. Mix into natural 3 -digit numbers satisfying:

a) Divided by 3.

b) Divided by 3 but not divided by 9.

Question 4: Give 3*46. Replace * with the digit to get the number divided by 3.

Question 5: Of the number 156; 2018; 2505; 11 200; 781:

a) Which number is divisible by 3?

b) Which number is not divisible by 3?

Question 6: Find x, know: X is divided by 3 and 360 <x <370;

Question 7: No calculation, consider whether the sum and difference below are divided by 3?

240 + 123 240 – 123

2454 + 374 + 135 2454 – 374 – 135

Question 8: Class 4A has more than 30 students but the number of students is not more than 40 but queuing in a pair, the two rows are equal and divided into 3 groups, there are equal number of students.

Question 9: Give the numbers: 3564; 4352; 6531; 6570; 1248.

a) Write a set of numbers a divisible by 3 of the above numbers.

b) Write a set of b numbers divisible by 9 of the above numbers.

c) Use symbol ⊂ to show the relationship between two sets A and B.

Question 10: Find the Y digit to the number 58Y91 divisible by 3 and the sum of the digits of 58Y91 is smaller than 25.

Question 11: Find natural numbers x know 921 <x <925 and x divided by 3.

Question 12: Number 853471 divided by 3 excess?

Question 13: The largest number of 2 digits divided by 2, for 3 and 5 are excess 1?

Question 14: Write in the dot:

Of the numbers 96; 502; 6823; 55 553; 641 311, the number is not divisible by 3 is: …………………………………………………………………………….

……………………

3. A) Write two numbers with four digits and divisible by 3:

b) Write three individuals with three digits and divisible by 9: …………………………………………………………………………….

Question 15: Correctly recorded, wrong s:

Find the right digit in the blank so that: 9 …….. 24 is divided by 3 but not divided by 9

The appropriate number is:

a) 9 ……..

b) 6 ……..

c) 3 ……..

d) 0 ……..

The secret to learning knowledge of signs divisible by 3 efficiency

To help children learn to understand the knowledge of divisible to 3, parents and children can apply some of the following tips:

• Understanding the concept of divisible signs by 3: To understand the exercise, we must first understand the concept. So let your baby understand that a natural number is divided by 3 means that when dividing that number by 3, there is no balance (the balance is 0).

• Identify the divisible numbers by 3: Based on the rules and properties that identify the divisible signs by 3 to quickly identify the numbers to be searched correctly.

• Familiarize yourself with the division of the balance: Make sure your children master the knowledge of dividing the balance to see if the calculation is leftover, thereby easily determine whether that number is divisible by 3.

• Applying in problems: Apply signs of divisible numbers for 3 of related problems such as finding numbers of special properties, arranging numbers, division calculations … such as finding all numbers divisible by 3 from 1 to 50, finding the sum of the divisible numbers by 3 in the sequence of numbers, …

• Regular training: Theoretical learning is not enough, so parents encourage and ask the baby to practice exercising regularly to improve the ability to calculate for the baby.

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Conclude

Above is the basic knowledge sharing information about the signing signs for 3. This is a rather important math topic, because the applicability in learning and practical is very high. So parents should equip this baby carefully to help children achieve the best academic achievement offline.

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