Subtraction on Number Line

Subtraction on a number line refers to the process of subtracting the subtrahend from the minuend. The process involves moving to the left on the number line. For example, if we need to subtract 7 from 9, we need to start at 9 on the line and move 7 steps to the left to arrive at 2, which is the answer. 

A number line is a visual representation of numbers that extends infinitely in both directions. It consists of a horizontal line with evenly spaced markings that represent integers, and it can include fractions and decimals as well.

Let us take a closer look at the steps involved in subtracting numbers on a number line: 
 

• Begin by drawing a horizontal line that extends infinitely in both directions.
   
• Make markings at regular intervals on top of the line. 
   
• Choose a midpoint and mark it as 0. The markings on the right will have positive integers starting from 1, and the markings on the left will have their negative counterparts.
   
• Now that we have created a number line, let us use it to subtract 5 from 6. Start at 6 and move 5 steps to the left. We will reach 1, which is the correct answer;
  6 - 5 = 1.

Follow these steps to subtract negative numbers using a number-line. Let us consider the subtraction of -9 - 5.


Step 1: Start at the integer -9

Step 2: Since we need to subtract a positive number (5), we must move 5 steps to the left.

Step 3: Verify the answer. We must end up at -14. 

To subtract two-digit numbers, we must follow the steps mentioned below:

Step 1: Draw a number line.

Step 2: Subtract the tens first.

Step 3: Subtract the ones.

Step 4: Write the final answer.

Example: Subtract 47 from 82.


1. Draw a horizontal line and mark 82 as the starting point.

2. 47 has 4 tens, so move 40 steps towards the left of 82.

3. 47 has 7 ones, so move 7 steps left.

4. The final answer is 35.

To subtract three-digit numbers, we must follow the following steps:

Step 1: Draw a number line.

Step 2: Subtract hundreds using jump steps.

Step 3: Subtract the tens place.

Step 4: Subtract the ones.

Step 5: Write the final answer.

Example: Subtract 276 from 532.
 

1. Draw a horizontal line and mark the starting point at 532.

2. Look at the hundreds place of 276, it's 2 hundreds, so move one jump step of 200 steps.

3. The tens place has 7 tens, so take a jump 70 steps to the left.

4. There are 6 ones, so move 6 steps to the left.

5. The final answer is 256.

Subtraction on a number line helps students visualize and solve subtraction problems more easily and accurately.
 

• Always begin at the number you are subtracting from on the number line.
   
• Subtract by moving the required number of steps to the left.
   
• Break larger subtractions into smaller, equal jumps for easier calculation.
   
• Extend the number line to the left to handle subtraction that results in negative values.
   
• Draw the number line to represent real-life scenarios like money spent or distance traveled.

The subtraction on the number line has numerous applications across various fields. Let us explore how subtraction on the number line is used in different areas:
 

• Financial transactions: For financial management, it is helpful to use subtraction on the number line. If a person starts with $100 and spends $35 on groceries, they can visualize the subtraction on a number line by moving 35 steps to the left from 100, landing at $65. This method is useful for budgeting, keeping track of expenses, and ensuring financial stability.

• Distance and navigation: Subtraction on a number line is essential in determining distances traveled or remaining. If a hiker plans a 20-mile trek and has already walked 7 miles, they can subtract 7 from 20 on a number line to see that 13 miles remain. This helps estimate the remaining distance in travel or logistics.

• Temperature changes: Subtraction on a number line helps track temperature changes, such as drops or rises. If the temperature in the morning is 15°C and drops to -5°C at night, the number line helps visualize this change by moving 20 steps left from 15 to -5. This concept is crucial for meteorologists and everyday life, helping people dress appropriately and prepare for weather changes.
   
• Sports scoring: Subtraction on a number line helps track points or scores in games. For example, if a basketball team has 78 points and loses 12 points due to penalties, moving 12 steps left on a number line shows the new score as 66. This helps coaches and players quickly understand score changes.
   
• Inventory management: Businesses use subtraction on a number line to monitor stock levels. If a store has 150 items and sells 45, moving 45 steps left from 150 shows that 105 items remain. This method helps in planning restocking and avoiding shortages.