## AdditionIn arithmetic, ## AdditionThe addition is a term used to describe to add two or more numbers together. In other words, it ## NotationA By using the plus symbol, we can perform addition between different numbers such as For example, in the first basket, there are five apples, and in the second basket, there are 4 apples. If we count the apples of both the basket, we get 9 apples. In arithmetic, we can represent it in the mathematical expression as:
## Addition Facts- In addition, the order of addition does not matter. It always gives the same answer.
**2+4+6+8=20 or 8+6+4+2=20 or 6+2+8+4=20** - Adding 0 to any number or vice-versa gives the same number as a result.
**7+0=7 or 0+7=7** - If we add any number to itself two-times, it is the same as multiplying a number by 2.
**8+8=16** It is same as:**8×2=16** - The repeated addition of 1 is the same as counting.
1+1=2,1+1+1=3
## Addition TableThe following table helps the children to memorize the sum of two numbers. You can find the sum of two numbers, between 0 to 10. Before moving to the addition, we must be aware of the term In arithmetic, a carry is a digit that is transferred from the right column to the left column and added to the transferred column. ## Addition of one-digit NumbersWe can find the addition of one-digit numbers with the help of the above table. Suppose we want to add 2 and 3 together. Search Similarly, we can find the sum of any single-digit number. ## Addition of Two-digit Numbers- Arrange the given numbers in the column for easy understanding.
- Add the
**ones place**digits together, transfer the**carry**, if any. It gives the unit place of the answer. - Add the
**tens place**digits and carry them from the previous step (if any). - Write the answer.
Let's implement the above steps in an example.
## Addition of Three-digit Numbers- Arrange the given numbers in the column for easy understanding.
- Add the
**ones place**digits together, transfer the carry, if any. It gives the unit place of the answer. - Add the
**tens place**digits, and carry from the previous step (if any), transfer the carry, if any. It gives the tens place of the answer. - Add the
**hundreds of place**digits, and carry from the previous step (if any). It gives the hundreds or thousands or both (depend on the sum) place of the answer. - Write the answer.
Let's implement the above steps in an example.
Similarly, we can add four-digit numbers, also. ## Addition of IntegersAn integer includes all positive and negative numbers, including 0. A number may have a positive or negative sign. The addition of integers with the sign follows the rules. Generally, we do not represent a positive number with + sign. In the following table, we have summarized the additional rule of positive and negative numbers. We have taken two numbers
## Examples10+20=30 ## Addition of Decimal NumbersTo add two or more decimal numbers, follow the rules given below: - Write the number in the column form but remember that decimal point must be lined up.
- Make the number of equal lengths, if unequal.
- Add the columns together and put a decimal point in the answer.
## Addition of Rational NumberThe rational numbers are the numbers that are in the fraction form . Let's see how to add the rational number.
- Add the numerators and put the resultant in the answer.
- Simplify the fraction if required.
In general, we can say that if are two fractions, the addition of fractions will be:
On simplifying the fraction , we get 2.
- Find the LCM of the denominators because we need to make denominators the same.
- Divide the LCM by the denominators.
- Multiply the resultant in the numerators, respectively, and simplify.
- Add numerators, and get the answer.
In general, we can say that if are two fractions, the addition of fractions will be:
Let's solve the question according to the above steps.
## Addition of Complex NumbersComplex numbers are added by adding real and imaginary parts separately. In general, we can say that if (a+bi)+(c+di)=(a+c)+(b+d)i
In the above example, 6 and 5 are real parts, and 4i and 3i are imaginary parts. So, we will add real parts together and imaginary parts together. (6+4i)+(5+3i)=(6+5)+(4i+3i)
(12+10i)+(7-9i)=(12+7)+(10i-9i)
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