Addition

Addition

Edited By Team Careers360 | Updated on Jan 29, 2024 10:41 AM IST

The word “Addition” means the grouping of two or more things together. When coming to numbers, we have the first operation as counting. Counting two or more groups of things together is nothing but the “addition operation”. Thus, addition is an arithmetic operation. If we consider the different groups as different numbers, to make them together, we need to do the sum of those numbers. Here the word “sum” represents the addition operation. So, we can say the meaning of addition is “the sum of two or more numbers together”. The addition operation is represented by a plus (+) sign. The words, sum, plus, making together are synonyms of the word “addition”. This is the basic operation in mathematics, which is essential in every topic. For example, the addition of 4 and 5 is represented by “4+5” and it is read as “four plus five”. The result of this addition is 9. I.e., after 4 we need to count 5 more numbers. So, we get the resulting number as 9. There are different methods for dealing with additions in mathematics and different concepts based on the process of addition.

This Story also Contains
  1. Meaning of addition
  2. Process Of Addition On The Number Line
  3. Horizontal Addition
  4. Vertical Addition
  5. Addition Without Carry
  6. Addition With Carry
  7. Different Properties Based On Addition
  8. Applications Of Additions

Meaning of addition

The meaning of addition is “making together”. Consider three boxes filled with three different colours of balls. First, we need to count the total number of balls according to their colour. Then, counting all together gives the total count of the balls irrespective of their colour. So, to know the “total”, we use the operation called “addition” or “sum”. The addition operation is denoted by the plus (+) symbol. The same procedure is applied to the numeral too. So, the digits or the numbers before and after the “plus” symbol is known as “addend” and the result is represented after an equal (=) symbol. That result is said to be the “sum”.

I.e., addend (1) + addend (2) = Sum

Process Of Addition On The Number Line

Here the addition operation is explained by the number line. A number line is the pictorial representation of numbers on a line. The addition of two numbers is calculated by different methods. One of the easiest methods for class 1, class 2, and the other primary classes is to perform addition operations between two numbers or more than two numbers.

1706456231856Here,

  • The addition of four and five is explained by the number line

  • The number line has numbers from zero to 15. Even we can increase more as per the requirement.

  • The number 4 is represented by pointing a dot at its place.

  • Now, we need to add 5 to the 4. So, after 4 we need to count 5 more places to the right.

  • Thus, we get the number 9. That means the sum of 4 and 5 is 9.

  • In such a way, the addition is calculated between any two numbers or more than two numbers.

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Horizontal Addition

  • This is also one of the methods of addition operation.

  • For understanding the basic concepts for class 1, 2, 3, and 4 students, this is the best way of teaching addition operations for smaller numbers (with a smaller number of digits).

  • Here the Horizontal addition means, the appends are written Horizontally i.e., writing them one after the other by a plus sign separating them and an equal sign after them with the result in a single line.

  • This is the general representation of the addition operation.

  • Example: 1706456231607 \[4+5=9\]

Vertical Addition

  • This is the contrast method of horizontal addition.

  • This is also used for the students in pre-primary and primary classes to make them understand the addition process for bigger numbers (with a greater number of digits).

  • Here, in the vertical addition operation, the appends are written one below the other and are framed in a structural format. So, that one can add the appends easily by counting.

  • This is also mostly used representation and this method provides a way for the concepts like “addition with carry and without carry”.

  • Example: 1706456231680

\begin{array}{r}

4 \\

+\quad 5 \\

\hline 9

\end{array}


Addition Without Carry

The appends when added, if the result is less than or equal to 9, then they do not produce any carry which is to be forwarded to its predecessor append. Here the vertical addition method clearly explains this concept. Here the carry is nothing but the digit in the tens place of the sum obtained by two appends.

Example: 1706456231749

\begin{array}{r}

42 \\

+\quad 53 \\

\hline 95

\end{array}

Addition With Carry

The appends when added, if the result is more than 9, i.e., tens (10, 11, 12, …), then they produce a carry which is to be forwarded to its predecessor append. Here also the vertical addition method clearly explains this concept. This will happen mostly for the bigger numbers.

Example: 1706456231384

Different Properties Based On Addition

  • There are different properties established by the basic addition operation

  • Such as commutative, associative, additive identity, etc.

  • The commutative property is shown as 1706456231478 \[4+5=5+4=9\].

  • The associative property is shown as 1706456230437 \[4+\left( 2+3 \right)=\left( 4+2 \right)+3=9\].

  • The additive identity property is shown as 1706456230640 \[0+9=9+0=9\].

Applications Of Additions

The addition operation is not only permitted for numerals or numbers. But also applied to all the other numbers such as decimals, fractions, and algebraic expressions. The addition operation is also framed in words that are called word problems. One must and should learn addition operations to understand the entire mathematics.

Frequently Asked Questions (FAQs)

1. How do an addition between two numbers?

The two numbers are added in such a way that the first number is counted for the second number of times forward. So, the resulting number is the sum of the required numbers.

2. What are appends?

The appends are nothing but the numbers which are to be added. Here the word “appends” means to mix up or add together.

3. How is an addition operation represented?

An addition operation is represented by a symbol called plus (+). This plus symbol is written in between the appends or the numbers to be added.

4. Is horizontal and vertical addition providing different sum?

No, both methods are the same and produce the same result. The only difference is the structure or the format of the addition.

5. What is the addition of the numbers 234 and 102?

The addition of 234 and 102 is calculated by  \[234+102=336\].

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Questions related to

Get answers from students and experts

Correct Answer: clues


Solution : The most appropriate option is the third option.

Explanation:
Clues refer to hints, evidence, or information that helps in understanding or solving something. In the context of the passage, moons, asteroids, and comets provide crucial information or hints about the formation and evolution of the solar system. They offer valuable insights that aid in understanding how the solar system came into existence and how it has changed over time.

The meanings of the other options are as follows:

  • Sets refer to a group of related objects or things.
  • Derivations refer to the process of obtaining something from a source or origin.
  • Biases refer to prejudices or inclinations that affect judgement or decision-making based on partiality or preference.

Correct Answer: 73


Solution : Given:
35 B 2 A 5 B (40 C 37) A (8 B 4) D 16 C 14 = ?

On replacing the letters with the mathematical signs as per the instructions given in the question, we get –
= 35 × 2 + 5 × (40 – 37) + (8 × 4) ÷ 16 – 14
= 35 × 2 + 5 × 3 + 32 ÷ 16 – 14
= 35 × 2 + 5 × 3 + 2 – 14
= 70 + 15 + 2 – 14
= 87 – 14 = 73

So, 73 is the required answer. Hence, the third option is correct.

Correct Answer: 207


Solution : Given:
A denotes addition, B denotes multiplication, C denotes subtraction, and D denotes division
27 B 3 C (11 A 3) A 14 B (100 D 10) = ?

After replacing the letters with the mathematical signs, we get:
= 27 × 3 – (11 + 3) + 14 × (100 ÷ 10)
= 27 × 3 – 14 + 14 × 10
= 81 – 14 + 140
= 207

So, 207 is the answer to the given equation. Hence, the first option is correct.

Correct Answer: 13


Solution : Given: 
A denotes addition, B denotes multiplication, C denotes subtraction, and D denotes division.
14 C (18 D 3) A 5 = ?

On replacing the alphabet, with mathematical signs we get –
= 14 – (18 ÷ 3) + 5
= 14 – 6 + 5
= 19 – 6
= 13

So, 13 is the answer to the given equation. Hence, the second option is correct. 

Question : Comprehension:

Read the following passage and answer the questions.

All foodstuffs change. Green fruits become ripe and eggs go bad or rotten. It is the enzymes naturally present in each food which bring about the complex chemical changes that lead first to ripening and then to rotting.

How does one control the activity of enzymes, bacteria, yeasts and moulds in food? All of them require air, moisture and a certain temperature, usually somewhere near the body temperature, to be active. Depriving them of one or more of these will suppress them. All microorganisms can be killed by heat sterilisation. This simply means heating the food to high enough temperatures by boiling, deep or shallow frying, roasting, baking and, for milk particularly, pasteurisation. After such sterilisation, if the food is sealed in airtight containers, it can be kept for a long time. A certain water content in food is necessary for microorganisms to be active. Drying in the sun is a simple way of bringing down the moisture level so low that the enzymes and microorganisms cannot flourish.

Some chemicals can suppress undesirable activity. The addition of salt, vinegar, spices and oil or sugar syrup are other ways of preventing foods from going bad. If heating kills, freezing inactivates the enzymes and microorganisms. This is what happens in a refrigerator, in which fruits, vegetables and milk can be kept for fairly long periods. For meat and fish, even colder temperatures, below freezing point, are necessary for preservation. All foods which are kept cold in this way, once taken out and returned to room temperature, are again subject to spoilage and change.

Question:
What action does freezing have on the enzymes?

Option 1: It activates them

Option 2: It kills them

Option 3: It preserves them

Option 4: It inactivates them

Correct Answer: It inactivates them


Solution : The fourth option is the correct choice.

The passage in the third paragraph mentions that freezing inactivates the enzymes and microorganisms. This helps to preserve food.

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