Subtraction on Number Line
Subtraction on number line helps us to visually perform the subtraction operation on small numbers. A number line is a visual representation of numbers on a straight line that can be used to perform different arithmetic operations like addition, subtraction, multiplication, and division. Let us learn more about subtraction on a number line by taking various examples.
| 1. | What is Subtraction on Number Line? |
| 2. | 2 digit Subtraction on a Number Line |
| 3. | 3 digit Subtraction on a Number Line |
| 4. | FAQs on Subtraction on Number Line |
What is 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. We always start with the minuend and move towards the left according to the number given as the subtrahend. 'Minuend' is the number from which we subtract and 'subtrahend' is the number which is subtracted.
Example: Subtract 3 from 5 using a number line.
According to the subtraction formula, Difference = Minuend - Subtrahend. Thus, 5 - 3 = 2. Now, let's perform the subtraction using a number line shown below.
Let us go through the steps that are used to perform subtraction using the number line.
- Step 1: Mark the minuend (5) on the number line.
- Step 2: Move towards the left-hand side of the number line according to the number given in the subtrahend. In this case, the subtrahend is 3, so we will move 3 units to the left as shown by the arrows. Hence, we land on 2, which is the answer.
Subtraction on Number Line Using a Negative Number
When we subtract on a number line using negative numbers, there can be two scenarios.
Case I: Subtracting a positive number from a negative number.
Example: Subtract 3 from -4 using a number line.
We know that (- 4) - 3 = - 7. Let's perform the subtraction using a number as shown below.
We start with -4 on the number line as shown and move by 3 units towards the left and reach on -7. Thus, we see that the subtraction - 4 - 3 = - 7 is shown on the number line.
Case II: Subtracting a negative number from a negative number.
Example: Subtract - 4 from - 5 using a number line.
We know that - 5 - (- 4) = - 5 + 4 = -1. Let's solve this using a number line as shown below.
NOTE: Subtracting a negative number changes the operation to addition. To perform addition on a number line, we move towards the right-hand side. We start with - 5 on the number line as shown and move by 4 units towards the right and land on -1. Hence, - 5 - (- 4) = - 5 + 4 = - 1. Thus, we can conclude that subtracting negative numbers is the same as performing an addition operation.
2 digit Subtraction on a Number Line
We will be learning about 2 digit subtraction using an open number line followed by a certain set of rules. An open number line is defined as an empty number line that does not have any number marked on it. We use an open number line to create a visual model as per our convenience for performing different arithmetic operations such as addition and subtraction.
Example: Subtract 45 from 78 using a number line.
We know that, 78 - 45 = 33. Let's solve this using a number line as shown below.
- Step 1: Mark the minuend (78) on the open number line as shown.
- Step 2: Count the number of tens and ones in the subtrahend (45). Here, we have 4 tens and 5 ones.
- Step 3: Move towards the left according to the number of tens (longer jumps) and ones (shorter jumps) obtained in the previous step and mark the numbers simultaneously after every move (68, 58,..., 33) on the number line. The last number that we arrive at will be the difference (33). Thus, we get the result as, 78 - 45 = 33 using a number line.
3 digit Subtraction on a Number Line
3 digit subtraction on a number line is quite similar to 2 digit subtraction that is done using an open number line. Let's take an example to understand this concept.
Example: Subtract 368 from 585 using a number line.
We know that, 585 - 368 = 217. Let's understand this using a number line as shown below.
- Step 1: Mark the minuend (585) on the open number line as shown.
- Step 2: Count the number of hundreds, tens, and ones in the subtrahend (368). Here we have 3 hundreds, 6 tens, and 8 ones.
- Step 3: Move towards the left according to the number of hundreds (longer jumps), tens (moderate jumps), and ones (shorter jumps) obtained in the previous step and mark the numbers simultaneously after every move (285, 225, 217) on the number line. The last number that we arrive at will be the difference (217). Thus, we obtain the result 585 - 368 = 217 using a number line.
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Subtraction on Number Line Examples
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Example 1: Perform the subtraction on number line for the given numbers: 9 - 4
Solution:
Let us find the difference of 9 and 4 by performing subtraction on the number line.
We start by marking 9 on the number line. Then, we move towards the left by 4 units and we reach 5.
Thus, we get the result, 9 - 4 = 5
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Example 2: Subtract 29 from 54 using 2 digit subtraction on a number line.
Solution:
Let's draw an open number line as shown below and follow the steps of 2 digit subtraction on number line.
a) Consider the first number 54 and mark it on the open number line.
b) The second number here is 29, i.e., it has 2 tens and 9 ones.
c) Taking 54 as the starting point, we will be moving by 2 tens (longer jumps) and 9 ones (shorter jumps) towards the left as shown in the figure.
Thus, we get the result, 54 - 29 = 25
FAQs on Subtraction on Number Line
What is Subtraction on Number Line?
Subtraction on a number line is done by the counting logic. To subtract a positive number, we move towards the left-hand side of the number line. For example, 6 - 2 can be calculated by taking 6 as the starting number and moving 2 units towards the left on a number line which gives the result as 4. Whereas, to subtract a negative number, we move towards the right-hand side on the number line because the subtraction operation changes to addition. For example, 9 - (- 3) can be calculated by taking 9 as the starting point and moving 3 units towards the right on a number line since the subtraction operation changes to addition, that is, 9 - (-3) = 9 + 3 which gives the result as 12.
How to Subtract Fractions on a Number Line?
In order to subtract fractions on a number line, we always check if the fractions to be subtracted are like fractions. If not, then they are converted to like fractions. After this step, the integers between which the fractions lie are identified and marked on the number line. The portion between the integers is divided into parts equal to the denominator of the fractions. Now, keeping the minuend as the starting point, we move towards the left according to the number of units in the subtrahend to get the result. For example: To subtract 3/7 from 5/7 we mark the integers 0 and 1, and divide the portion into 7 equal parts. Starting with 5, we move 3 units towards the left on the number line and land on 2, which gives 2/7 as the result. Hence, 5/7 - 3/7 = 2/7.
How to Subtract Decimals on a Number Line?
Subtraction of decimals on a number line is done by first marking the minuend. Then, according to the number of hundredths, tenths, and ones present in the subtrahend we move towards the left of a number line. For example, for subtracting 0.8 from 5.9, we will start by marking 5.9 on the number line and move towards the left by 8 times tenths to land on 5.1. Thus, the operation 5.9 - 0.8 = 5.1 is verified.
How to Subtract Negative Numbers on a Number Line?
When negative numbers are subtracted using a number line, we move towards the right-hand side because according to the rules of integers when a negative number is subtracted, the operation turns into addition. For example, - 8 - (-2) = - 8 + 2 = - 6. This can be shown by starting with - 8 on the number line and moving by 2 units towards the right and landing on - 6. This shows that subtracting negative numbers is similar to the addition operation.
Which way do you Jump to use a Number Line for Subtraction?
We jump towards the left of a number line while performing subtraction on a number line. For example, to subtract 7 from 10, we start with 10 and move towards the left by 7 units to get the result 3.
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's 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 the case of subtraction, to subtract a positive number, we move towards the left-hand side of the number line. For example, 5 - 2 = 3, this can be shown by starting with 5 and moving towards the left by 2 units to land on 3 which shows that 5 - 2 = 3. Whereas, to subtract a negative number, we move towards the right-hand side on the number line because in this case, the operation changes to addition. For example, 6 - (-3) = 6 + 3 = 9, this can be shown by starting with 6 and moving towards the right by 3 units to get 9.
How to Subtract 7-2 on a Number Line?
When we subtract a positive number, we move towards the left-hand side of the number line. Here 7 - 2 can be calculated by taking 7 as the starting number and moving 2 units towards the left on a number line which gives the result as 5.