Key Learning Outcomes
By the end of this chapter, “Addition and Subtraction”, readers will:
- Addition of Large Numbers
- Properties of Addition
- Subtraction of Large Numbers
- Estimating Sums and Differences
- Checking Subtraction using Addition
- Word Problems – Addition and Subtraction
- Mental Math Tricks
- Practice Exercises with Solutions
- Common Mistakes to Avoid
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Introduction
The chapter “Addition and Subtraction” builds upon the knowledge of numbers and place values. Students learn how to add and subtract large numbers (up to 9 digits), estimate sums/differences, and solve real-life word problems. This chapter also helps in developing mental math skills.
Addition of Large Numbers
In Class 5, you will add numbers having up to 9 digits using the column method.
Example:
Add: 56,74,123 + 38,25,679
56,74,123
+ 38,25,679
------------
95,99,802
Tips: “Add karte waqt right se left jaate hain – ones, tens, hundreds…”
Properties of Addition
1. Order Property:
a + b = b + a
Example: 14 + 9 = 9 + 14 = 23
2. Grouping Property (Associative):
(a + b) + c = a + (b + c)
Example: (10 + 20) + 30 = 10 + (20 + 30) = 60
3. Zero Property:
a + 0 = a
Example: 96 + 0 = 96
Subtraction of Large Numbers
Subtraction is finding the difference between two numbers. Use the column method, borrowing if needed.
Example:
Subtract: 9,84,250 – 5,76,938
9,84,250
– 5,76,938
------------
4,07,312
Estimating Sums and Differences
Estimation helps us quickly guess the result using rounding off.
Rules:
- Round off numbers to nearest 10, 100, 1000, etc.
- Then add or subtract
Example:
Estimate: 5,678 + 2,431
Round to nearest 1000:
6,000 + 2,000 = 8,000
Checking Subtraction Using Addition
To verify subtraction:
Subtracted number + Difference = Bigger number
Example:
9,84,250 – 5,76,938 = 4,07,312
Now, 5,76,938 + 4,07,312 = 9,84,250
Word Problems – Addition and Subtraction
These help students apply concepts to real-life situations.
Example 1: Addition Word Problem
Question:
A school has 1,25,738 students. Another school has 87,654 students. How many students are there in total?
Answer: Add: 1,25,738 + 87,654 = 2,13,392 students
Example 2: Subtraction Word Problem
Question:
A factory produced 9,45,000 items. 6,78,250 items were sold. How many items are left?
Answer: 9,45,000 – 6,78,250 = 2,66,750 items left
Mental Math Tricks
- Add multiples of 10 or 100 first
- Break big numbers into parts
- Use friendly numbers (like 100, 500, 1000)
Example:
395 + 505 = (400 – 5) + (500 + 5) = 900
Common Mistakes to Avoid
❌ Forgetting to carry over in addition
❌ Subtracting a smaller number from a bigger one without borrowing
❌ Writing digits in the wrong columns
✅ Always align numbers by place value
Important Facts
- Addition is commutative but subtraction is not.
- Zero is the identity for addition.
- Always align numbers by place value before operations.
- Subtraction result is called difference.
Activity (Exercise):
A. Add the following:
- 5,62,148 + 3,21,907 = _______
- 76,324 + 14,639 = _____.
B. Subtract the following:
- 8,40,276 – 6,29,834 = _______
- 1,00,000 – 67,890 = _______
C. Solve the Word Problem:
- A company earned ₹6,23,915 in January and ₹5,89,104 in February. How much was earned in total?
D. Compare the numbers using >, < or =
- 6,43,210 _ 6,34,210
Quiz:
Coming Soon…
Supplementary Materials:
Provide downloadable materials for learners to review:
- – PDF Guide: “Coming Soon”
- – Cheat Sheet: “Coming Soon”
- – Video Source: “JNG ACADEMY“
- – Articles: “Blog Page“