Solving simple equations

Simple equations are equations those have just one variable and which can be solved by using very algebraic operations. At times, you can even solve them mentally. These are also called one step equations because in one step. Since they involve variables and need to perform algebraic operations for solutions, they are also referred as algebra simple equations.

In many cases the one step equations are based on word problems and those are framed as per the statement of the word problem. Let us illustrate a few examples to understand how to solve simple equations.

Let x + 1 = 5. The solution is to find the value of x. We see on the left side a 1 is added to the variable. So to isolate that, we need to undo that addition by the inverse algebraic operation, which is subtraction. Since 1 is added to the variable, in the undoing process we need to subtract 1 on the left side. But since this is an equation doing any operation only on one side is prohibited since the balance of the equation is disturbed. Hence to maintain the balance a 1 must also be subtracted on the right side.

So the method of solution is (x + 1) – 1 = 5 – 1, or, x = 4, which is the solution. The solution can be checked by plugging that value in the original equation. That is, if x = 4, then the left side becomes as, x + 1 = 4 +1 = 5 = right side. Hence the solution is correct.

Let x – 3 = 4. Here the undoing operation is ‘add 3’ on both sides. So, (x – 3) +3 = 4 + 3, or, x = 7 which is the solution.
Next let us the equation 3x = 9. In this case, the variable is multiplied by 3 on the left side. In this case, the undoing operation is ‘divide by 3’ on both sides. So, (3x/3) = (9/3) or, x = 3, which is the solution. Similarly the undoing operation for a division is ‘multiply by the same number’ on both sides. For example, if, (x/2) = 4, then, (x/2)*2 = 4*2 or, x = 8.

Let us see how one step equations are formed from word problems.
‘Ben is 5 years older than Joan and Joan is 3 year old. How old is Ben?’ Let ‘x’ be the age of Ben. Since he is 5 years older that Joan, the equation is x – 5 = 3 and the solution is x – 5 + 5 = 3 + 5 or x = 8. Hence Ben is 8 years old.

Templates for the Diagrams Representing Set Operations

The Venn diagram template can be associated with set theory in mathematics. Sets represent collection of objects which are similar in nature. So, the all real numbers together form a set. Even the integers together can form a set. These are similar numbers which is necessary to form a set. The triple Venn diagram template is used when three sets intersect.

There is a common area when the sets intersect. There are various operations that are to be learnt in the set theory. The operations like union or intersection can be used to solve various problems. The set theory is used to solve the problems in a simpler manner.

They give a clear understanding of the problems. The 3 circle Venn diagram template is used when three sets are intersecting. These templates can be very useful and helpful. They must be chosen carefully.

The Venn diagram templates are used to make these better understandable so that the problems can be better understood and can be solved easily. Even Free Venn diagram templates are available online and can be chosen at will to solve the problems. They can be really helpful. A wide variety of them are available and the right choice must be made. For this to happen one must be thorough with the concepts in set theory and these diagrams.

These diagrams are pictorial representations of the problems in the set theory. Once they are drawn one is able to understand the problem better and can solve it more easily and in a smaller amount of time. So, one must learn how to draw these diagrams.

The intersection of two sets in these diagrams denotes common area between the two sets. It contains the common elements which are present in both the sets. So, the common area in these diagrams is the intersection and denotes the elements which are present in both the sets.

The same can be true if there more than two sets. In case of three sets also this is the case. The common area denotes the elements which are present in all the three sets. The union of sets denotes all the elements present in the sets of which the union is found. There is also the concept of empty set. If there is no common area in the diagram, then it denotes an empty set. It basically means there are no common elements between the sets.

Basics of Simple Interest

The term interest refers to the cost of borrowing money. The interest calculation varies from plan to plan and is also based on the lenders and the time period of lending/depositing the amount. This interest is calculated in different ways such as interest only on principal, interest on principal and interest so far earned/incurred, monthly interest, cumulative interest etc.  The amount for which the interest is calculated can be a loan (amount borrowed for need) or a deposit (amount deposited as savings).

Definition
The interest which is calculated only on the principal amount borrowed or deposited is termed to be Simple Interest that is denoted as SI in short.  This type of interest does not include the interest so far incurred or earned on the principal amount.

When an amount is borrowed, the amount borrowed is called the Principal. The duration which the borrower takes to return the Principal is termed as the time period and is calculated in number of days/months/year.  The next and most important part is the rate of interest which states the interest percentage for the given principal amount.  All the three put together explains what is Simple Interest. The interest percentage is directly proportional to the lender and the time duration to repay the amount.   Also it depends upon whether it is a loan or a deposit.

Formula for SI Calculation
Formula 1: “R as number”
The Simple Interest Formula is given by S.I = (P*N*R)/100.

Formula 2: “R as percentage”
The Simple-Interest Formula is given by S.I = P*N*R.

This shows how to calculate Simple Interest using the interest for the given principal amount P, with rate of interest R/period of a given period of time P.

Example of SI Calculation
If a principal amount of Rupees 1000 is borrowed/deposited by a person for a period of 2 years with 3% rate of interest, then the simple-interest is given by

By applying the values of P, N and R given, we get

Formula 1: R as number

We know that the rate of interest is 3%. We take R = 3

S. I.  = (P * N* R)/100
S. I.  = (1000 * 2 * 3)/100 = 6000/100 = 60

Formula 2: R as percentage

We know that R = 3% = 3/100 = .03

S.I. = P * N* R
S.I. = 1000*2*.03 = 60.00 = 60

Applications of SI
In post offices, schemes such as MIS pay simple interest for the amount deposited for five years as recurring deposit.

Credit cards charging simple-interest for the amount to be paid is more beneficial.