Addition on Number Line

Addition on number line helps us to visually perform the addition operation on small numbers. A number line is a visual representation of numbers on a straight line where the value of the numbers increases as we move from left to right. Different arithmetic operations like addition, subtraction, multiplication, and division can be performed on a number line. Let us learn more about addition on number line in this article.

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.

Example: Add 1 + 2

Solution: Let us look into the steps given below to understand addition on a number line.

• Step 1: Consider the first number (1) as the starting point on the number line. In order to add 1 + 2, mark 1 on the number line.
• Step 2: Now, from the first number jump by the number of units equivalent to the second number towards the right. This is because the values on a number increase as we move towards the right-hand side. In this case, we are adding 1 + 2, therefore, we will move 2 steps to the right. This will bring us to number 3. So, 1 + 2 = 3

Addition on a Number Line Using a Negative Number:

To add a negative number to a positive number we always move to the left on the number line. Let us take an example to understand this.

Example: Add 3 + (-4)

Solution: Here, we take 3 as the starting number and move 4 units towards the left on the number line which gives the result as -1.

2-digit addition is the addition of numbers where either one or both the addends are of two digits. Let us understand 2-digit addition using an open number line. An open number line is also known as an empty number line as it does not have any marker or number marked on it. It helps us to create a visual model as per our convenience for performing different arithmetic operations such as addition and subtraction. Let us take an example to understand 2-digit addition on a number line.

Example: Add 35 + 42 using an open number line.

Solution:

Let us do this 2 digit addition on a number line using the following steps:

• Step 1: Draw a straight line which is also known as an open number line and mark the first number (35) on the open number line.
• Step 2: Observe the second addend and identify the number of tens and ones present in it. The second number (addend) here is 42, i.e., it has 4 tens and 2 ones.
• Step 4: Taking the first number as the starting point, jump by the equal number of tens (longer jumps) and ones (shorter jumps) towards the right. Here, we will be jumping by 4 tens (longer jumps) and 2 ones (shorter jumps) towards the right using arrows as shown in the figure.
• Step 5: Each time a jump is made in the forward direction, the results are written on the open number line. In this case, when the first jump was made, the resultant value was 35 + 10 = 45, moving forward, the second jump gave us 45 + 10 = 55, followed by 65, 75 and the final jump of 2 ones was made which gave us the required result 75 + 2 = 77.

☛ Related Articles

• Subtraction on Number Line
• Decimals on Number Line
• Integers on Number Line
• Representation of Real Numbers on Number Line
• Addition on Number Line Worksheets

How to Add on a Number Line?

Addition on a number line is done by the counting logic. To add a positive number, we move towards the right-hand side of the number line, whereas, to add a negative number, we move in the backward direction (left side) on the number line. For example, 3 + 4 can be calculated by taking 3 as the starting number and moving 4 units towards the right on a number line which gives the result as 7. On the other hand, 3 + (-4) can be calculated by taking 3 as the starting point and moving 4 units towards the left on a number line which gives the result as -1.

How to Add Fractions on a Number Line?

Adding fractions on a number line involves the following steps. Let us understand this with an example. Add 1/4 and 2/4.

• If needed, the given fractions are converted into like fractions. In this case, they are like fractions.
• The integers are identified between which these fractions lie and they are marked on the number line. Here, the two integers are 0 and 1.
• The portion between the two integers is divided into an equal number of parts equal to the denominator of the fractions.
• Keeping the first fraction as the starting point, we move by 2 units in the forward direction or right side on the number line since the second fraction is 2/4. Hence, we land on the required result 3/4.

How to Add 3-digit Numbers on a Number Line?

We use an open number line to add 3-digit numbers on a number line. An open number line is an empty straight line where the numbers are marked only when we keep proceeding with the operations. In order to add 3 digit numbers on a number line, we use the following steps:

• Step 1: The first number is marked on the open number line.
• Step 2: Then we observe the second number and identify the number of hundreds, tens, and ones present in it.
• Step 3: Starting from the first number, we move by the equal number of hundreds (longer jumps), tens (medium jumps), and ones (shorter jumps) towards the right. Each time a move is made in the forward direction, the intermediate results are written on the open number line following which we reach the desired result.

How to Add Negative Numbers on a Number Line?

To add negative numbers on a number line, we always move to the left. For example, -5 + (- 4) = -5 - 4 = -9. We take -5 as the starting point and move 4 units towards the left which gives the result as -9.

How to Add and Subtract Integers on a Number Line?

If a positive integer is added, we move towards the right and if a negative integer is added we move towards the left on the number line. For example: 7 + 3 = 10. Taking 7 as the starting point, we move 3 units towards the right on the number line and land on 10 which is the required result. Let us take 7 + (-3) = 4. Taking 7 as the starting point, we move 3 units towards the left on the number line and land on 4 which is the required result.

In case of subtraction, we change the operation from subtraction to addition, and change the sign of the second number and follow the rules of adding integers on a number line. For example: 6 - 2 can be written as 6 + (-2). Now we start from the number 6 and move 2 units towards the left on the number line which gives the result as 4.

What is Double Digit Addition on a Number Line?

Double-Digit addition on a number line is another name given to 2-digit addition on number line. Double-digit addition is performed using an open number line which is also known as an empty number line. We take the numbers as per our convenience and mark them on the open number line as we proceed with the operations.