Algebra formulas

19 Sep

Algebra formulas in math can be used for various purposes like factorization, finding percentages, profit – loss, simple interest, HCF & LCM etc. Some of the formulas we use are:

1. For factorization:

(H + K) 2 = H2 + K2 + 2 HK

(H – K) 2 = H2 + K2 – 2 HK

(H + K) 3 = H3 + K3 + 3 HK (H + K)

(H – K) 3 = H3 – K3 – 3 HK (H – K)

H3 + K 3 = (H + K) (H2 + K2 – HK)

H3 – K 3 = (H – K) (H2 + K2 + HK)

H4 + H2 K2 +K 4 = (H2 + K2 – HK) (H2 + K2 + HK)

H3 + K3 + Z3 – 3 HKZ = (H + K + Z) (H2 + K2 + Z2 – HK – KZ – HZ)

If H + K + Z = 0, we can write:

H3 + K3 + Z3 = 3 HKZ

(H + K + Z) 2 = H2 + K2 + Z2 + 2 HK + 2 KZ + 2 HZ

2.       For finding percentages:

If we need to find percentage decrease then:

p = (100 / (100 + r)) * 100

If we need to find percentage decrease then:

p = (100 / (100 – r)) * 100

In case of finding percentages in population problems:

a.       For population increase

p = P (1 + r) /100) * 100

p = P / (1 + r) /100) * 100

b.       For population decrease

p = P (1 – r) /100) * 100

p = P / (1 – r) /100) * 100

Similarly, we can have many other formulas for solving algebraic problems.

Next we discuss the law of definite proportions, according to which every pure matter at all times will comprise of same elements that are present in the same proportions by atomic weight.

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how many hours in a year

6 Aug

A year is a period of the Earth moving around the Sun. The Julian year has the 365.25 days, A Julian year is a unit of time defined as exactly 365.25 days. There are 24 hours in a day and every day has same amount of hours. Now we will discuss How Many Hours In A Year ?Answer is, a Julian year has 24 x 365.25 hours means 8766 hours but a sidereal day not exact 24 hours, it is currently 23 hours 56 min and 4.1 sec, so a Julian has 8765.81 hours.

A year that is not a Julian year but run according to calendar, is called calendar year. A calendar year has 365 or 366 days. Accordingly calendar a calendar-year run 1st January to 31st December. Which means calendar year has 366 days called leap years. A year has 365 days called a common year. A leap year usually occurs every 4 years. February 29 is a date that added to the leap year.

A common year has 365 x 24 = 8760 hours, and

A leap year has 366 x 24 = 8784 hours.

Year type

Days in a year

Hours in a year

Julian years

365.25 days

8766 or 8765.81 hours

Calendar years (common year )

365 days

8760 hours

Calendar years (leap years)

366 days

8784 hours

 

The amount of heat per unit mass required raising the temperature by one degree, called Specific Heat. The Specific Heat Formula manly used to calculate Enthalpy, Enthalpy shows amount of heat needed to change the temperature.

Specific Heat Formula:

Q = cmΔt

Where     Q = amount of heat needed.

                    c = specific heat capacity.

                   m = mass of the heated substance.

                   Δt = difference in the temperature before and after applied the heat.

In Icse Syllabus 2013include Specific Heat formula. Icse is the Indian Certification of Secondary Education is self-financing education institutions. 

(know more about hours, here)

Complex Fraction Calculator

1 Aug

Fraction is a mathematical concept which is able for expressing any numerical value in the form of any number of equal parts. In the simple we can say that fraction is a way to represent any number in a parts with various different sizes when we add all these parts then it make a whole number. Suppose there is a cake and no. of members are 5 then how to distribute to everyone that get a equal piece of cake. At that time the concept of fraction is used that solves the problem by equalizing a cake into one – fifth parts.

We first talking about complex fraction calculator. Complex fraction calculator is a different category of fraction calculator that helps in resolving complex fraction problem either in form of word form or in algebra equation form. To deal with complex fraction we first need to understand this question that how a complex fraction works.

Complex fraction can be considered as a fraction which contains a numerical value into their upper and below portion. There is a not a typical concept, it is simple to understand. To solve complex fraction we need to find common value which must be lowest that helps in solving complex fraction problem. To successfully deal with this problem in an easier manner, complex fraction calculator helps us that follow some rules that are given below:


A) Here first we required to convert the sign between the fraction value. It means convert divide operation into multiplication operation.

B) After that reverse the below fraction into the right of above fraction.

C) At last check if there is any possibility to simplify them into their lowest term still there is no scope to simplify them.

The Third Law of Thermodynamics was invented by the great chemist Walther nernst in the year between 1906 to 1912. In current session of borad exam, the icse syllabus 2013 guide the students to make their study plan.

subtracting improper fractions

21 Jul

Any number written in the form of numerator by denominator (u / v) is known as fraction. As we know that the upper part of a fraction value is numerator and the lower part of a fraction is denominator of fraction. First it is necessary to discuss about the improper fraction. Any fraction that has numerator value larger than the denominator value is known as improper fractions. Examples: 16/2, 29/12.

Now we will discuss the steps of subtracting improper fractions. It is very easy to subtract the fractions which have denominator smaller than numerator because we have to multiply both the denominator value to find the LCM. The step to subtract the improper fraction is mention below:

Step 1: To subtract the improper fraction first we have to take two improper fractions.

Step 2: Then calculate the LCM of both the fraction.

Step 3: Then multiplication of both the denominator value of a fraction is the LCM of both the fraction.

Step 4: At last subtract the numerator value to solve the improper fraction.

Let we have 17/3 and 13/10, then subtract one fraction by other fraction.

Here we need to follow the above given steps for the subtraction of improper fraction:

Step1: Firstly we have two numbers that is:

The given number is: 17/3 and 13/10;

Step2: Now find the LCM of both the fraction,

= 17 / 3 – 13 / 10,

The multiplication of both the denominator value is 30. So the LCM of both the improper fraction is 30. On further calculating the equation we get:

= (170 – 39)/30,

Step3: Now subtract the values of numerator:

On subtracting we get:

= 131/30.

At last we get the value is 131/30. Three States of Matter can be defined as the different forms in which the different phases of matter are taken. The three states of matter are solid, liquid and gas. The icse 2013 solved papers is very helpful for the examination point of view.

de moivre s theorem

13 Jul

De moivre’s theorem is used to find the roots of a complex for any power ‘n’, and the value of ‘n’ is integer. In mathematics, de moivre s theorem is obtained from Euler’s equation. It is also used to join the trigonometry equation to the complex number. The formula is also given for the demoivre s theorem:

⇒ (cos d + i sin d)n = cos (nd) + i sin (nd). The given formula is used to join the complex number and trigonometry. Here ‘i’ is an imaginary number. The value of iota square is given as ‘-1’ (i2 = -1). If we expand the left hand side, of the above formula then we compare real and imaginary parts and it is also possible to calculate the expression cos nd and sin nd in terms of sin d and cos d. (know more about de moivre s theorem, here)

Now, we will discuss how to find derivative of de moivre’s theorem? We know, de moivre’s theorem is obtained from Euler’s formula. So we can write it as:

⇒ ei d = cos d + i sin d, and the exponential law for integer powers is:

⇒ (ei d)n = ei nx;

Then the Euler’s formula is given as:

⇒ ei (nd) = cos (nd) + isin (nd);

In general we can say that, de Moivre’s theorem does not hold for non – integer powers. The above de moivre’s theorem does not involve the complex number to the power n.

Suppose z1 and z2 be two complex numbers, here the value of | z1| = r1, | z1| = r1, and | z2| = r2, and arg (z1) = ⊖1, arg (z2) = ⊖2.

Then, z1 = r1 (cos ⊖1 + i sin ⊖1);

And z2 = r2(cos ⊖2 + i sin ⊖2);

This is all about de moivre’s theorem. Average Speed can be defined as the total distance covered over the given time interval. Before attempt the board exam please go through the 10th cbse sample paper. It is very helpful for exam point of view.

 

how to do percentages

4 Jul

Percentage in mathematics can be described as a tool or a way to express any value in the form of fraction that has a denominator value equal to 100. In mathematics, the word percent derived from the Latin word “percentum” which means refers to the “per hundred”. Generally the concept of percent can be represented by using “%” symbol. Simply we can say that if we write 15% then it can also be written in fractional form as 15 / 100. Or in another sense we want to convert any number in the form of percent then we need to simply divide that number by 100 like we want to convert 15 as a percent then it can be performed as 15 / 100 = 15%.

 When we are discussing about the concept of percent then a question arises in our mind that how to do percentages. It means to say that how to solve different problems that are related to the concept of percentage. There are some of the ways are define that helps in solving various problem relate to percent.

Suppose there is problem that says how to calculate 10% of 500.

Then we can say that first we need to convert the percent value in the form of fraction that is 10 / 100. Now we need to perform the multiplication between these values that are given below

 (10 / 100 ) * 500 = 50

So, we can say that 10% of 500 is equal to 50.

In the same aspect we can also solve various other problem which is related to the concept of percent. When we discuss about the descriptive mathematics then generally a question arises How to Find Median when no. of data are even. students who are appear in the board exam then previous year question papers of cbse helps the students to make their plan of action to get a better score in board examination.

How to Find Percentage in Mathematics

2 Jul

Percentage is define as value that is calculated on per hundred. If we define 1% that means 1 out of 100. In this blog we understand how to find percentage. In mathematics there is need to define the values in form of percentage because sometime values are not understand in their actual form when any comparison is made so for this reason percentage is the best way. For calculation of percentage there is some steps that are as follows:

As we know percentage is a way of expressing a number in the form of fraction. So to calculate the percentage first identify the whole value means what is the total value on which we want to calculate the percentage.
The next step to find the percentage is decide the value from the whole value for which you want to calculate the percentage and after it define these values in the form of fraction means in the fraction at numerator put the value from the whole for which want to calculate the percentage and in the denominator side put the whole value means total value.
In the last step multiply this fraction value with the hundred and when you multiply it with the 100 it provide the equation in which one side is the expression contain the fraction multiplied with the 100 and on the other hand of the equation give the q / 100 or q %.
We can define it as if there is total 200 items and 50 of them are damaged than calculate the percentage of damaged items?
So As there is total items are 200 and 50 are damaged items that is expressed as 50 / 200 and for percentage 50 / 200 * 100 = 25 %.
You can also get to know How to Find the Area of a Square and other related math problems helps in understanding the way of solution. Cbse provide central board of secondary education sample papers helps student to identify the pattern of papers come into the exams.