Step-by-Step Guide: Subtraction with Addition Explained
The concept of Subtraction Of Numbers Using Addition Of Numbers is an important skill in arithmetic. It allows students to use their knowledge of addition for subtraction tasks, making calculations easier, especially in mental math. Mastering this method supports exam success, daily life problem-solving, and quick verification of answers.
Understanding Subtraction Of Numbers Using Addition Of Numbers
Subtraction of numbers using addition means finding the value that, when added to the subtracted number, gives the original number. This is based on the idea that subtraction is the inverse (or opposite) operation of addition. For example, if you know that 13 – 8 = 5, you also know that 8 + 5 = 13. This connection helps in both solving subtraction problems and checking your work.
The Inverse Relationship: Addition and Subtraction
Addition and subtraction are closely connected mathematical operations and are called inverse operations. This means one operation can "undo" the other:
- If you have A – B = C, then you also know that B + C = A.
- This relationship is used in "fact families": sets of related addition and subtraction equations using the same numbers.
- Number lines are great tools to visualize this connection—moving forward is adding, and moving backward is subtracting.
Understanding this relationship is vital in learning mental math strategies and helps avoid confusion between addition and subtraction.
How to Subtract Using Addition: Step-by-Step Methods
Let’s break down the methods for subtraction by addition:
- Rewrite the subtraction equation as a missing addend problem (e.g., 15 – 9 = ? becomes 9 + ? = 15).
- Find the number that, when added to the subtracted number, results in the original number.
- Use a number line, or simply count up.
- Optionally, check your answer by reversing the equation (add your answer to the subtracted number).
This technique works well for whole numbers, decimals, and even negative numbers.
Key Formula
The general formula is:
If A – B = C, then B + C = A.
So to find C (the difference), solve for C such that B + C = A.
Worked Examples
Example 1: Single-Digit Numbers
What is 12 – 7?
- Change to addition: 7 + ? = 12
- Think: 7 + 5 = 12
- So, 12 – 7 = 5
Example 2: Higher Numbers
What is 41 – 27?
- Change to addition: 27 + ? = 41
- Count up from 27: 27 + 3 = 30, 30 + 11 = 41 (3 + 11 = 14)
- So, 41 – 27 = 14
Example 3: Using Number Line
Find 18 – 13 using a number line:
- Place 13 on a number line.
- Count on from 13 up to 18: 14, 15, 16, 17, 18 (that’s 5 steps).
- So, 18 – 13 = 5
Example 4: Checking Subtraction with Addition
If 35 – 19 = 16, check your answer:
- 19 + 16 = 35? Yes!
- Your subtraction is correct.
Example 5: Subtracting Decimals
What is 4.5 – 2.7?
- 2.7 + ? = 4.5
- 2.7 + 1.8 = 4.5
- So, 4.5 – 2.7 = 1.8
Practice Problems
- 1. Find the missing number: 6 + ? = 14
- 2. What is 25 – 13? (Hint: 13 + ? = 25)
- 3. Solve: 8.3 – 4.7
- 4. 45 – 28 = ? (use addition to check)
- 5. What number, added to 19, gives 27?
- 6. Work out 100 – 77 by addition.
- 7. 22 – 18 = ? (think: 18 + ? = 22)
Common Mistakes to Avoid
- Not matching the numbers correctly in the rewritten addition problem (e.g., swapping minuend and subtrahend).
- Forgetting to check using addition after solving a subtraction problem.
- Miscounting when using the number line (missing a step, or double-counting start/end).
- Confusing addition "sum" with subtraction "difference".
Real-World Applications
Subtraction using addition is used in everyday situations like:
- Checking bills and change: “Given ₹500 and spent ₹320, how much is left?” (Think: 320 + ? = 500).
- Finding the difference in scores or measurements: “Team A scored 36, Team B 22. By how much did A win?”
- Distance calculations: "You started at 480 km and now are at 525 km. How far did you travel? (480 + ? = 525)"
At Vedantu, we help students practice these mental math techniques to solve problems faster and more accurately.
In this topic, we explored how to perform Subtraction Of Numbers Using Addition Of Numbers through stepwise strategies, worked examples, and practice problems. Understanding this inverse relationship not only builds arithmetic confidence for exams, but also sharpens day-to-day calculation skills. For more concepts and worksheets, explore other addition and subtraction resources on Vedantu.
