Mathematics Tips: অংকের সমাধানের কিছু সহজ পদ্ধতি

Mathematics Tips: অংকের সমাধানের কিছু সহজ পদ্ধতি

How to Find HCF:

To find the HCF (Highest Common Factor) of two or more numbers, follow these steps:

1. List out the factors of the numbers. 

2. Identify the common factors in the list. 

3. Determine the highest common factor among the common factors.

For example:

Let's say we need to find the HCF of 12 and 20. 

Factors of 12 are 1, 2, 3, 4, 6, and 12. 

Factors of 20 are 1, 2, 4, 5, 10, and 20. 

The common factors between 12 and 20 are 1, 2, and 4.

To find LCM (Least Common Multiple) of two or more numbers, follow these steps:

1. List out the multiples of the numbers. 

2. Identify the common multiples in the list. 

3. Determine the Least common multiple among the common multiples.

For example, 

Let's say we need to find the LCM of 3 and 5. 

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... 

Multiples of 5 are 5, 10, 15, 20, 25, 30... 

The common multiples between 3 and 5 are 15 and 30.

To find the Cube Root of a number, follow these steps:

1. Identify the number whose Cube Root is to be found.

2. Divide the number by some potential cube roots until we get a quotient that is not a perfect cube. 

3. Then, we find the cube root of the quotient and multiply it by the value of the potential cube root.

For example,

Let's say we need to find the cube root of 125. 

1. We can identify that 125 is the number whose cube root is to be found.

2. We start by dividing it by some potential cube roots. For example, let's divide it by 5. 

   125 ÷ 5 = 25

   25 ÷ 5 = 5

   Here, the quotient 5 is not a perfect cube, and we cannot divide it further.

3. The cube root of 5 is approximately 1.71.

   Therefore, the cube root of 125 is:

   1.71 x 5 = 8.55 (approximately)

To find your Zodiac sign, follow these steps:

1. Identify your date of birth.

2. Determine the Zodiac Sign based on your birth date following the table below:

    Aries: March 21 - April 19

    Taurus: April 20 - May 20

    Gemini: May 21 - June 20

    Cancer: June 21 - July 22

    Leo: July 23 - August 22

    Virgo: August 23 - September 22

    Libra: September 23 - October 22

    Scorpio: October 23 - November 21

    Sagittarius: November 22 - December 21

    Capricorn: December 22 - January 19

    Aquarius: January 20 - February 18

    Pisces: February 19 - March 20

For example, if your date of birth is on 10th August, your Zodiac sign is Leo.

The oxidation state or oxidation number can be determined by the following steps:

1. Determine the total number of valence electrons of the atom or molecule.

2. Write the chemical formula for the molecule or ion.

3. Identify the electronegativity of each atom in the compound.

4. Assign the shared electrons between the atoms based on their electronegativity difference.

5. Determine whether the atom has lost or gained electrons and identify the overall charge of the molecule or ion.

6. Calculate the oxidation state by adding up the charges on each individual atom.

For example, let's find the oxidation state (or number) of sulfur (S) in sulfuric acid (H2SO4).

1. The total number of valence electrons of sulfur (S) is 6.

2. The chemical formula for sulfuric acid is H2SO4.

3. The electronegativity of sulfur (S) in the compound is 2.58.

4. The electronegativity of hydrogen (H) and oxygen (O) are 2.2 and 3.44, respectively.

5. Oxygen (O) is more electronegative than sulfur (S), so it will pull the shared electrons towards itself, resulting in a negative charge on oxygen (O) and positive charge on sulfur (S).

6. Since there are two hydrogen atoms (H) in the compound, they have a total charge of +1. Also, each oxygen atom (O) has a charge of -2. Therefore, applying the rule that the sum of all the oxidation states in a compound is equal to the charge on the molecule, we get:

  H2SO4: 2(+1) + S + 4(-2) = -2

  Solving the equation, we find that the oxidation number of sulfur (S) in H2SO4 is +6.

 Therefore, the oxidation state of sulfur (S) in sulfuric acid (H2SO4) is +6.