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. We will be learning about different methods of addition and subtraction in this article.
|1.||How to do Addition and Subtraction?|
|2.||Addition and Subtraction with Regrouping|
|3.||Addition and Subtraction on Number Line|
|4.||FAQs on Addition and Subtraction|
How to do Addition and Subtraction?
Addition can be done by summing up or putting things together. It is a way to combine numbers, operands, or objects. On the other hand, subtraction can be 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 and subtrahend are the two numbers being subtracted, the symbol (-) indicates the subtraction operation and the difference indicates the result. Below is an example showing the subtraction operation.
It was about the basic terms involved in addition and subtraction and 1-digit addition and subtraction. 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 is defined where the carry is taken forward i.e, the sum of a column value exceeding 9. This will be discussed in the next section. We will be looking into an example of addition without regrouping. Let us add the numbers 15 + 24.
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 in a column-wise manner as shown above under the respective place values. Thus in the ones column we have 5 + 4 = 9 and in the tens column we have 1 + 2 = 3. Hence, 15 + 25 = 39.
Similar to addition, we will now be performing 2-digit subtraction without regrouping. Regrouping in subtraction is seen in subtraction when there's a borrow. Let us subtract 34 from 76.
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
The concept of regrouping comes into the picture whenever there is a carry taken forward in addition or there is a borrow occurring in subtraction. We will be understanding addition and subtraction with regrouping in this section.
Addition with Regrouping
Regrouping is used when the sum of the place digits exceeds 9, the carry is taken forward. We will be taking an example to understand addition with regrouping. Let's add the numbers 355 + 466.
- Step 1: Start with ones place digits → 6 + 5 = 11. Here the sum is 11. The tens place digit of the sum (i.e., 1) will be carried to the tens place.
- Step 2: Add tens place digits along with the carryover 1 → 1(carry) + 5 + 6 = 12. Here the sum is 12. The tens place digit of the sum (i.e., 1) will be carried to the hundreds place.
- Step 3: Now add the digits of hundreds place along with the carryover digit 1 → 1(carry) + 3 + 4 = 8. Here the sum is 8.
- Step 4: Thus, 355 + 466 = 821.
Below, the regrouping operation is shown for 355 + 466.
Subtraction with Regrouping
A greater number cannot be subtracted from a smaller number. Thus, when we have a situation wherein the greater number has to be subtracted from the smaller number, the smaller number borrows 1 from the adjacent place digit, followed by regular subtraction. Let's subtract the numbers 432 - 256.
Step 1: Start with the ones place digits. We see that 6 is greater than 2. 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, 3 becomes 2. Now, let us subtract the digits at the tens place (2 - 5). Here, 5 is greater than 2, so we will borrow 1 from the hundreds column. This will make it 12. Hence, 12 - 5 = 7.
Step 3: In step 2 we had given 1 to the tens column, so we are left with 3 at the hundreds place. We will now subtract the digits on the hundreds place, i.e., (3 - 2). Hence, 3 - 2 = 1.
Step 4: Therefore, the difference between the two given numbers is: 432 - 256 = 176.
Below, the regrouping with subtraction operation is shown for 432 - 256.
Addition and Subtraction on Number Line
Number line can be used to perform different arithmetic operations such as addition, subtraction, multiplication, and division. Now, we will be understanding addition and subtraction on a number line. The rules of addition and subtraction on a number line are given below.
In general, addition on a number line is done by taking the first number as a reference, followed by moving towards the right (if it is a positive number) or towards the left (if it is a negative number) by equivalent units of the second number to get the result.
Similarly, subtraction on a number line is performed by starting with the first number as a reference, followed by moving towards the left (if it is a positive number) or towards the right (if it is a negative number) by equivalent units of the second number to get the result.
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 that is 1 here and move towards the right by the units equivalent to the second number which is 2 here. Thus, we move by 2 units towards the right starting from 1 and land at 3 giving 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 perform 5 - 3 using a number line as shown below.
We mark the first number that is 5 here and move towards the left by the units equivalent to the second number which is 3 here. Thus, we move by 3 units towards the left starting from 5 and land at 2 giving us the result 5 - 3 = 2.
Related Articles on Addition and Subtraction
Check out the following links related to addition and subtraction in math.
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. What is the remaining number of chocolates with Alaina?
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, the number of chocolates remaining with Alaina is 23.
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.
Initial amount 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 amount of water present = 450 - 135 = 315 L. After the leakage was repaired, 55 L of more water was added. Thus, new amount 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. Also, it is given that the resultant number is 118.
Thus, x + 5 = 118
x = 118 - 5
x = 113
Thus, the original number is 113.
FAQs on Addition and Subtraction
What are Addition and Subtraction?
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 parts of our life.
What is Multiplication Division Addition and Subtraction Called?
Multiplication, division, addition, and subtraction are called arithmetic operations.
What is the Relationship between Addition and Subtraction?
Addition and subtraction are inverse operations. This is because they work in completely opposite manner. In addition, we add things and for subtraction, we take away things. For example, I have 10 oranges and my friend gives me 5 more which is an addition operation, but my sister takes away those 5 oranges which is a subtraction operation.
What is Addition and Subtraction of Fractions?
Addition and subtraction of fractions involve the addition or subtraction of numerators if the denominators are the same or the denominators are made to be the same by taking their LCM followed by adding or subtracting the numerators. For example, 3/4 + 5/4 = 8/4 = 2 is the addition of fractions whereas, 7/8 - 5/8 = 2/8 = 1/4 is subtraction of fractions.
Why are Addition and Subtraction Inverse Operations?
Addition and subtraction are inverse operations because it doesn't affect a value as long as the same value is being added and subtracted from it i.e., the operation turns out to be neutral. For example, let's take a number 8, we will add 2 to it i.e., 8 + 2 =10 and now we will subtract 2 from this result i.e., 10 - 2 = 8. Hence, we see that we get back the same number 8.
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 does not affect the result.
- Adding 1 to any number gives its successor while subtracting 1 from any number gives its predecessor.
- Addition and subtraction of the same number to an expression do not change the value.
- Addition and subtraction are inverse operations.