Subtraction On number Line
Subtraction on number line makes it easier to see how to take away from small numbers. A number line is a visual representation of numbers on a straight line that can be used to add, subtract, multiply, and divide. Let’s look at some examples to learn more about subtraction on a number line.
What is Subtraction on Number Line?
Using a number line to do subtraction makes it easy to take away smaller numbers. When subtracting numbers on a number line, we need to jump to the left. We always start with the minuend and move to the left based on the number given as the subtrahend. The number we take away is called the “minuend,” and the number we take away is called the “subtrahend.”
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 numbers 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 number line using negative numbers, there are two possible outcomes.
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.
On the number line, we start at -4, move 3 units to the left, and end up at -7. On the number line, we can see that the subtraction -4 -3 = -7 is shown.
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: When you subtract a negative number, the operation changes from subtraction to addition. On a number line, we move to the right to add numbers. On the number line, we start at -5 and move 4 spaces to the right to get to -1. Hence, – 5 – (- 4) = – 5 + 4 = – 1. So, we can say that subtracting negative numbers is the same as doing an addition operation.
2 digit Subtraction on a Number Line
We will learn how to subtract with two digits by using an open number line and a set of rules. An empty number line with no numbers written on it is called a “open number line.” We can use an open number line to make a visual model for different math operations, like adding and taking away, that works for us.
- 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
Three-digit subtraction on a number line is a lot like subtracting two-digit numbers on an open number line. Let’s look at an example to see how this works.
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.
Solved Examples of Subtraction on Number Line
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
Example 2 : 7 students are visiting a zoo. 3 of them later decided not to go. How many students are going to the zoo now?
Answer: Number of students visiting the zoo = 7
Number of students who decided not to visit = 3
We can use the number line to find the answer.
So, in the given number line, we will begin at 7 and then move 3 times to the left. This is because we are subtracting on a number line. So, that will give us 7 – 3 = 4
Thus, 4 students are visiting the zoo now.
FAQs ( Frequently Asked Questions )
Q.1 What is Subtraction on Number Line?
The counting method is used to figure out how to subtract on a number line. To take away a positive number, we move the number line towards the left. For example, 6 – 2 can be found by starting with the number 6 and moving 2 units to the left on a number line. This gives the answer of 4 as the result. When subtracting a negative number, on the other hand, we move to the right on the number line because subtraction becomes addition. For example, 9 – (- 3) can be found by starting with 9 and moving 3 units to the right on a number line. This is because subtraction changes to addition when the minus sign is added, so 9 – (-3) = 9 + 3, which equals 12.
Q.2 How to Subtract Fractions on a Number Line?
On a number line, to subtract fractions, we always check to see if the fractions to be subtracted are the same. If not, they are changed into fractions that are the same size. After this step, the integers on the number line between which the fractions lie are found and marked. The space between the integers is split into parts that are the same size as the fractions’ denominators. Now, with the minuend as the starting point, we move to the left by the number of units in the subtrahend to get the answer. For example, to subtract 3/7 from 5/7, we mark the 0 and 1 and divide the portion into 7 equal parts. When we start with 5, we move 3 units to the left on the number line until we reach 2. This gives us 2/7. Hence, 5/7 – 3/7 = 2/7.
Q.3 How to Subtract Negative Numbers on a Number Line?
When subtracting negative numbers on a number line, we move to the right because, according to the rules of integers, subtracting a negative number is the same as adding that number. For example, -8 minus (-2) equals -8 plus 2 equals -6. This can be seen by starting at -8 on the number line, moving right by 2 units, and ending up at -6. This shows that taking away negative numbers is like adding positive numbers.
