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Addition and Subtraction
Addition and subtraction are arithmetic operations in mathematics that are used to calculate the sum and difference between different operands such as whole numbers, integers, fractions, algebraic expressions, and so on. Let us learn about the different methods of addition and subtraction in this article.
|1.||What is Addition and Subtraction?|
|2.||Addition and Subtraction with Regrouping|
|3.||Addition and Subtraction on Number Line|
|4.||FAQs on Addition and Subtraction|
What is Addition and Subtraction?
Addition is done by summing up or putting things together. It is a way to combine numbers, operands, or objects. On the other hand, subtraction is done by taking away or removing things. It is a way to reduce numbers, operands, or objects.
The addition formula is stated as: Addend + Addend = Sum. Here, addends are the numbers that are being added, the symbol (+) indicates the addition operation and the sum indicates the result.
The subtraction formula is stated as Minuend - Subtrahend = Difference. Here, minuend is the number from which the other number is subtracted and subtrahend is the number that is subtracted from the minuend. The symbol (-) indicates the subtraction operation and the difference indicates the result. The example given below shows the subtraction formula.
Now, let us look at 2-digit addition and subtraction.
2-Digit Addition and Subtraction
2-digit addition and subtraction can be performed with and without regrouping. Regrouping takes place when the sum of a column value exceeds 9. In this case, one digit is written under that particular column and the extra digit is carried over to the next column and added along with the addends of that particular column. Let us go through an example of addition without regrouping.
Example: Add the numbers 15 + 24
Solution: Let us add the numbers in the following way.
Here, the place values of the numbers should be taken care of. Numbers with 2-digits have the place value as ones and tens starting from the right side. While adding 2 digits together, we arrange the numbers column-wise as shown above under the respective place values. In the ones column we have 5 + 4 = 9 and in the tens column we have 1 + 2 = 3. Hence, 15 + 24 = 39.
Similar to addition, let us perform 2-digit subtraction without regrouping. Let us subtract 34 from 76 in the following way.
The place value arrangement remains similar as discussed in the addition operation. Thus in ones column, we have 6 - 4 = 2 and in the tens column, we have 7 - 3 = 4. Hence, 76 - 34 = 42.
Addition and Subtraction with Regrouping
In addition, regrouping takes place whenever the sum of a column exceeds 9. Here, the extra digit is carried over to the preceding column and is added along with the addends there. In subtraction, regrouping is done if any digit in the minuend is less than the respective digit in the subtrahend. Let us first learn about addition with regrouping and then we will move on to subtraction with regrouping.
Addition with Regrouping
In addition with regrouping, when we get a sum that exceeds 9 in any of the columns, we carry over the extra digit to the preceding column and add it along with the addends there. Let us understand this with the help of an example.
Example: Add the numbers 355 + 466
- Step 1: Start with the digits in ones column → 6 + 5 = 11. Here the sum is 11. The tens place digit of the sum (i.e., 1) will be carried over to the tens place.
- Step 2: Then we will add the digits in tens place along with the carryover 1 → 1(carry-over) + 5 + 6 = 12. Here the sum is 12. The tens place digit of the sum (i.e., 1) will be carried to the hundreds column.
- Step 3: Now, we will add the digits of hundreds place along with the carryover digit 1 → 1(carry-over) + 3 + 4 = 8. Here the sum is 8.
- Step 4: Thus, 355 + 466 = 821
Below, the regrouping operation is shown for 355 + 466.
Now, let us learn subtraction with regrouping.
Subtraction with Regrouping
Subtraction with regrouping takes place whenever any digit in the minuend is smaller than the corresponding digit in the subtrahend. Here, we borrow 1 from the preceding column and combine it with this minuend so that this becomes greater than the subtrahend. Let us understand this with the help of an example.
Example: Subtract the numbers 432 - 256
Solution: Let us use the following steps to subtract these numbers.
- Step 1: Start with the digits in ones place. We see that 2 is smaller than 6. So, we will borrow 1 from the tens column which will make it 12. Now, 12 - 6 = 6.
- Step 2: After giving 1 to the ones column in step 1, the 3 in the tens column becomes 2. Now, let us subtract the digits in the tens place (2 - 5). Here, 2 is smaller than 5, so we will borrow 1 from the hundreds column. This will make it 12. So, 12 - 5 = 7.
- Step 3: In step 2 we had given 1 to the tens column, so we are left with 3 in the hundreds place. We will now subtract the digits in the hundreds place, i.e., (3 - 2). So, 3 - 2 = 1.
- Step 4: Therefore, the difference between the two given numbers is: 432 - 256 = 176.
Addition and Subtraction on Number Line
Addition and subtraction on a number line can be done using the following rules.
- Addition on a number line is done by starting with the first addend. Then we move towards the right depending on the number of units of the second number to get the sum.
- Subtraction on a number line is done by moving towards the left side of the number line depending on the number of units of the second number.
Let us understand this in detail in the following section.
Addition on Number Line
Addition on number line is as simple as counting positive numbers by moving towards the right-hand side of a number line. It helps us to visually understand the addition operation using small numbers. Let us perform the operation 1 + 2 using a number line as shown below.
We mark the first number (1) and move towards the right by the 2 units using the second number which is 2 here. Thus, we move by 2 units towards the right starting from 1 and land at 3 which gives us the result 1 + 2 = 3.
Subtraction on Number Line
Subtraction on a number line helps to subtract smaller numbers very easily. While subtracting numbers on a number line, we need to jump (move) towards the left-hand side of a number line. Let us subtract 5 - 3 using a number line as shown below.
We mark the first number (5) and move towards the left by 3 units which is the second number here. Thus, we move by 3 units towards the left starting from 5 and land at 2 which gives us the result 5 - 3 = 2.
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Addition and Subtraction Word Problems
Example 1: Alaina has 20 chocolates. John gives her 14 more chocolates. After receiving 14 chocolates from John, she gives away 11 chocolates to her sister Daisy. How many chocolates does Alaina have now?
Solution: We will be using the concept of addition and subtraction to calculate the number of chocolates remaining with Alaina.
The initial number of chocolates Alaina had = 20
Number of chocolates given by John to her = 14
New number of chocolates with Alaina = 20 + 14 = 34.
But, she gives away 11 chocolates to her sister Daisy.
Thus, using subtraction,
Remaining number of chocolates with Alaina = 34 - 11 = 23
Hence, Alaina has 23 chocolates now.
Example 2: A water tank has 450 L of water. Due to leakage, there was a flow out of 135 L of water from the tank. After the leakage was repaired, 55 L of more water was added to the tank. What is the new amount of water in the tank?
Solution: We will be using the concept of addition and subtraction to solve this.
The initial quantity of water in the tank = 450 L
Due to leakage, water flowed out. Hence, 135 L will be subtracted from 450 L. After leakage, the quantity of water present = 450 - 135 = 315 L. After the leakage was repaired, 55 L of more water was added. Thus, new quantity of water in the tank = 315 + 55 = 370 L.
Example 3: A number is added to 5 to get the result as 118. Find the original number.
Solution: We will be using the concept of addition and subtraction to solve the question.
Let the original number be x. When 5 is added to this number, the new number is x + 5. It is given that the resultant number is 118.
This can be represented as follows.
x + 5 = 118
x = 118 - 5
x = 113
Therefore, the original number is 113.
Addition and Subtraction Questions
FAQs on Addition and Subtraction
What is Addition and Subtraction?
Addition is an arithmetic operation that is used to find the sum of whole numbers, integers, fractions, and so on. It is represented using the symbol (+). For example, 4 + 7 = 11 which means when 4 is added to 7, it gives 11 as the sum. Subtraction is an arithmetic operation that is used to find the difference of whole numbers, integers, fractions, and so on. It is represented using the symbol (-). For example, 9 - 7 = 2 which means when 7 is subtracted from 9, it gives 2 as the difference.
Why are Addition and Subtraction Important?
Addition and subtraction play a very important role in our daily life activities which involve counting such as billing at the store, buying groceries, traveling, speed of a vehicle, checking weight, and so on. It helps us understand situational-based problems. Hence, addition and subtraction are important in our life.
What is Multiplication Division Addition and Subtraction Called?
Multiplication, division, addition, and subtraction are called arithmetic operations in Mathematics. Multiplication is represented by the symbol (×), division is represented by the symbol (÷), addition is presented by the symbol (+), and subtraction is represented by the symbol (-)
What is the Relationship between Addition and Subtraction?
Addition and subtraction are inverse operations. This means that we can check if our answer is correct by doing the opposite operation. For example, 9 - 6 = 3. Now we can check if our subtraction is correct or not by adding 3 to 6, 3 + 6 = 9. This shows that our calculation is correct.
What is Addition and Subtraction of Fractions?
Addition and subtraction of fractions means adding or subtracting fractions depending on the kind of fractions that they are. In case of like fractions, we work only with the numerators because the denominators are the same. In case of unlike fractions, we have different denominators and we need to make them the same by finding their LCM (Least Common Multiple) and converting them to equivalent fractions in such a way that the denominators remain the same. After this step, we add or subtract the numerators according to the requirement.
What are Addition and Subtraction Facts?
Some of the known facts of addition and subtraction are listed below:
- Adding or subtracting 0 to any number results in the number itself. For example, 6 + 0 = 6
- Adding 1 to any number gives its successor while subtracting 1 from any number gives its predecessor.
- Addition and subtraction are inverse operations.
What is Regrouping in Addition and Subtraction?
In addition with regrouping, if the sum exceeds 9 in any of the place value columns, we carry over the extra digit to the preceding column and add it along with the addends there. Subtraction with regrouping takes place whenever any digit in the minuend is smaller than the corresponding digit in the subtrahend. In this case, we borrow 1 from the preceding column and combine it with this minuend so that this becomes greater than the subtrahend. Then we continue the subtraction keeping in mind that the number that had given 1 to its following column gets reduced by 1.