Arithmetic and Linear Equations

1. What is Arithmetic?

Arithmetic is a branch of mathematics that deals with basic numerical operations, such as addition, subtraction, multiplication, division, and sometimes exponentiation.

2. What are the Basic Arithmetic Operations?

The basic arithmetic operations are:

• Addition: Combining two or more numbers to find their sum.
• Subtraction: Finding the difference between two numbers.
• Multiplication: Combining equal groups of numbers to find the total.
• Division: Splitting a number into equal groups or finding how many times one number is contained in another.

Read more about Arithmetic Operations.

3. What is a Linear Equation?

A linear equation is a mathematical equation that represents a straight line on a coordinate plane. It is an equation of the form ax + b = 0, where ‘x’ is the variable, ‘a’ is the coefficient of ‘x’, and ‘b’ is the constant term.

Read more about Linear Equations.

4. How do we solve a Linear Equation with One Variable?

To solve a linear equation with one variable, follow these steps:

• Step 1: Simplify both sides of the equation if necessary.
• Step 2: Isolate the variable term on one side of the equation by performing inverse operations (addition, subtraction, multiplication, or division) on both sides.
• Step 3: Solve for the variable to find its value.

Read more about Linear Equation in One Variable.

5. How do I solve a system of Linear Equations?

A system of linear equations consists of two or more linear equations with the same variables can be solved using the following methods:

• Substitution Method
• Elimination Method
• Cross-Multiplication Method

Learn more about the methods of solving Pair of Linear Equation in Two Variable.

Representation of quantities can be done with the help of numbers and figures. But for the calculation and interrelation purpose, we need different mathematical operators. For example, we can represent two baskets filled with mangoes and there are 5 mangos in the first basket and 6 mangos in the second basket. If someone asked, How many mangos are there in total? Then we can count them all and tell the answer but to make the whole process easy we introduce addition operators. We can easily add them and tell the final answer. So to reduce the complication and make the process simple we introduce mathematical operators.

Following are different types of mathematical operators.

• Addition: It is represented by ‘+’ sign and used for the addition of two or different objects.
• Subtraction: It is represented by ‘-‘ sign and used to subtract two or different objects.
• Multiplication: It is represented by ‘×’ sign and used to multiply two or different objects.
• Division: It is represented by ‘÷’ sign and it is used for the division of two objects.

What is Summation?

Summation is the process of the addition of two or more numbers to get the result. For example, when 2 and 5 are added then we will get the result as 7. The addition is the primary mathematical operator. The number which we add is called as addend and the answer which we got after addition is called ‘sum’.

What is Subtraction?

Subtraction is the process in which we find the difference between two numbers. For example, when 2 is subtracted from 5 then we got the answer 3. It means that 5 is three more than 2. The number which we subtract is called as ‘subtrahend’ and the number from which it is subtracted is called as ‘minuend’ and the answer which we got is called as ‘difference’.