Operations on Number Line (Grade 3)
A number line is a straight line with numbers placed at equal intervals. It helps you see addition, subtraction, and even simple multiplication and division.
In Class 3, you use the number line to add and subtract numbers by making jumps forward or backward. Moving to the right means adding (getting bigger), and moving to the left means subtracting (getting smaller).
The number line makes operations visual, helping you understand what happens when you add or take away.
What is Operations on Number Line - Class 3 Maths (Numbers up to 1000)?
A number line is a line with equally spaced points labelled with numbers in order.
0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10
Operations on a number line:
- Addition: Start at the first number, jump RIGHT by the second number.
- Subtraction: Start at the first number, jump LEFT by the second number.
- Multiplication: Make equal jumps from 0 (e.g., 3 × 4 = three jumps of 4).
Right = Add (+) | Left = Subtract (−)
Types and Properties
Types of Operations on a Number Line
1. Addition on the Number Line
Start at the first number. Jump right by the amount you are adding.
Example: 5 + 3
0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10
Start at 5, jump 3 to the right → land on 8
2. Subtraction on the Number Line
Start at the first number. Jump left by the amount you are subtracting.
Example: 9 − 4
0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10
Start at 9, jump 4 to the left → land on 5
3. Multiplication as Repeated Jumps
Start at 0 and make equal jumps.
Example: 4 × 3 = four jumps of 3: 0 → 3 → 6 → 9 → 12
Solved Examples
Example 1: Example 1: Addition on Number Line
Question: Show 6 + 4 on a number line.
Think:
- Start at 6
- Jump 4 places to the right
- 6 → 7 → 8 → 9 → 10
0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10
Answer: 6 + 4 = 10
Example 2: Example 2: Subtraction on Number Line
Question: Show 8 − 3 on a number line.
Think:
- Start at 8
- Jump 3 places to the left
- 8 → 7 → 6 → 5
0 — 1 — 2 — 3 — 4 — 5 — 6 — 7 — 8 — 9 — 10
Answer: 8 − 3 = 5
Example 3: Example 3: Adding Larger Numbers
Question: Use a number line to find 15 + 8.
Think:
- Start at 15
- Jump 5 to reach 20 (easy landmark), then 3 more to reach 23
- Or: jump 8 from 15 → 23
Answer: 15 + 8 = 23
Example 4: Example 4: Subtracting Larger Numbers
Question: Use a number line to find 32 − 7.
Think:
- Start at 32
- Jump 2 left to reach 30, then 5 more to reach 25
- Total jumped = 2 + 5 = 7
Answer: 32 − 7 = 25
Example 5: Example 5: Multiplication as Jumps
Question: Show 3 × 5 on a number line.
Think:
- Start at 0
- Make 3 jumps of 5 each
- 0 → 5 → 10 → 15
0 — — — — — 5 — — — — — 10 — — — — — 15
Answer: 3 × 5 = 15
Example 6: Example 6: Finding the Difference
Question: Use a number line to find the difference between 14 and 9.
Think:
- Count the jumps from 9 to 14
- 9 → 10 → 11 → 12 → 13 → 14 = 5 jumps
Answer: The difference is 5.
Example 7: Example 7: Adding by Tens
Question: Use a number line to find 45 + 30.
Think:
- Start at 45
- Jump by 10 three times: 45 → 55 → 65 → 75
Answer: 45 + 30 = 75
Example 8: Example 8: Word Problem
Question: Aditi is on page 18 of a book. She reads 12 more pages. What page is she on now? Use a number line.
Think:
- Start at 18, jump 12 to the right
- 18 + 12 = 30
Answer: Aditi is on page 30.
Example 9: Example 9: Skip Counting on Number Line
Question: Skip count by 4 starting from 0. Write the first 6 numbers.
Think:
- 0, 4, 8, 12, 16, 20
- Each jump is +4 on the number line
0 — — — — 4 — — — — 8 — — — — 12 — — — — 16 — — — — 20
Answer: 0, 4, 8, 12, 16, 20
Example 10: Example 10: Two Operations on Number Line
Question: Start at 10. Add 5. Then subtract 3. Where do you end?
Think:
- Start at 10
- Add 5: 10 + 5 = 15 (jump right)
- Subtract 3: 15 − 3 = 12 (jump left)
Answer: You end at 12.
Real-World Applications
Where Do We Use Number Lines?
- Addition and subtraction: Visualising what it means to add or take away.
- Skip counting: Counting by 2s, 3s, 5s, 10s on a number line.
- Comparing numbers: Numbers further right are greater.
- Measuring: A ruler is a number line! Each cm mark is like a point on the line.
- Temperature: A thermometer is a vertical number line.
Key Points to Remember
- A number line has numbers at equal intervals in order.
- Addition = move RIGHT on the number line.
- Subtraction = move LEFT on the number line.
- Multiplication = make equal jumps from 0.
- You can break jumps into easier steps (e.g., jump to the nearest 10 first).
- The number line helps you see operations and understand place value.
- Numbers to the right are greater; numbers to the left are smaller.
Practice Problems
- Show 7 + 5 on a number line. What is the answer?
- Show 15 − 6 on a number line. What is the answer?
- Use a number line to find 23 + 9.
- Use a number line to find 40 − 15.
- Show 4 × 3 as jumps on a number line.
- Start at 20. Add 10. Subtract 8. Where do you end?
- Skip count by 6 from 0. Write the first 5 numbers and show on a number line.
- Aman is on step 14 of a staircase. He goes up 7 steps. What step is he on now?
Frequently Asked Questions
Q1. What is a number line?
A number line is a straight line with numbers placed at equal gaps in order. It goes on forever in both directions. It is used to show addition, subtraction, and compare numbers.
Q2. How do I add on a number line?
Start at the first number. Jump to the right by the number you are adding. The point where you land is the answer.
Q3. How do I subtract on a number line?
Start at the first number. Jump to the left by the number you are subtracting. The point where you land is the answer.
Q4. Can I multiply on a number line?
Yes. Start at 0 and make equal jumps. For example, 4 × 3 means 4 jumps of 3: 0 → 3 → 6 → 9 → 12.
Q5. Why are number lines useful?
Number lines make operations visual. You can see what it means to add (move right), subtract (move left), and compare numbers (check position).
Q6. Can number lines have negative numbers?
Yes, number lines extend to the left with negative numbers. In Class 3, you mainly use the positive side (0, 1, 2, 3, ...).
Q7. How do I use a number line for large numbers?
You do not need to draw every number. Mark key numbers (like multiples of 10) and make jumps of 10 or other convenient amounts.
Q8. Is a ruler a number line?
Yes. A ruler is a number line marked in centimetres (and millimetres). The 0 mark is the starting point, and numbers increase to the right.
Q9. How do I find the difference between two numbers on a number line?
Count the jumps from the smaller number to the larger number. The number of jumps equals the difference.
