DAV Board Class 3 Mathematics (Primary Mathematics) | 100% Authentic Textbook Solutions
DAV Class 3 Maths Unit 3 Solutions Subtraction
Get complete, step-by-step textbook solutions for DAV Class 3 Primary Mathematics Unit 3: Subtraction. This unit covers all worksheets including subtraction without borrowing, subtraction with borrowing (regrouping), subtracting across zeros, verifying answers using addition ($text{Difference} + text{Subtrahend} = text{Minuend}$), and real-life statement word problems strictly aligned with the DAV CMC syllabus.
| Class | Subject | Textbook | Unit Number & Title | Key Mathematical Concepts |
|---|---|---|---|---|
| Class 3 | Mathematics | Primary Mathematics | Unit 3: Subtraction | 4-digit subtraction, borrowing (regrouping), subtracting across zeros, checking subtraction |
Worksheet 1: Subtraction Without Borrowing
| Problem | Working in Columns (Th H T O) | Step-by-Step Subtraction | Difference |
|---|---|---|---|
| (a) $7685 – 3241$ |
7 6 8 5 – 3 2 4 1 ——— 4 4 4 4 |
• Ones: $5 – 1 = 4$ • Tens: $8 – 4 = 4$ • Hundreds: $6 – 2 = 4$ • Thousands: $7 – 3 = 4$ | 4444 |
| (b) $8976 – 4523$ |
8 9 7 6 – 4 5 2 3 ——— 4 4 5 3 |
• Ones: $6 – 3 = 3$ • Tens: $7 – 2 = 5$ • Hundreds: $9 – 5 = 4$ • Thousands: $8 – 4 = 4$ | 4453 |
| (c) $6543 – 2102$ |
6 5 4 3 – 2 1 0 2 ——— 4 4 4 1 |
• Ones: $3 – 2 = 1$ • Tens: $4 – 0 = 4$ • Hundreds: $5 – 1 = 4$ • Thousands: $6 – 2 = 4$ | 4441 |
Worksheet 2: Subtraction With Regrouping (Borrowing)
Rule: When the top digit (minuend) is smaller than the bottom digit (subtrahend), borrow 1 from the next higher place to the left ($1 text{ Ten} = 10 text{ Ones}$, $1 text{ Hundred} = 10 text{ Tens}$, etc.).
| Problem | Regrouping Columns | Step-by-Step Borrowing Steps | Difference |
|---|---|---|---|
| (a) $5432 – 2768$ |
(4)(13)(12)(12) 5 4 3 2 – 2 7 6 8 ———— 2 6 6 4 |
• Ones: Cannot do $2 – 8$. Borrow 1 Ten from 3 (leaving 2). $12 – 8 = 4$ • Tens: Left with 2. Borrow 1 Hundred from 4 (leaving 3). $12 – 6 = 6$ • Hundreds: Left with 3. Borrow 1 Thousand from 5 (leaving 4). $13 – 7 = 6$ • Thousands: $4 – 2 = 2$ | 2664 |
| (b) $8000 – 3456$ (Across Zeros) |
(7)(9)(9)(10) 8 0 0 0 – 3 4 5 6 ——— 4 5 4 4 |
• Borrow from 8 Thousands (leaving 7). • Hundreds become 9, Tens become 9, Ones become 10. • $10 – 6 = 4$, $9 – 5 = 4$, $9 – 4 = 5$, $7 – 3 = 4$ | 4544 |
| (c) $7205 – 4387$ |
(6)(11)(9)(15) 7 2 0 5 – 4 3 8 7 ——— 2 8 1 8 |
• Ones: $15 – 7 = 8$ • Tens: $9 – 8 = 1$ • Hundreds: $11 – 3 = 8$ • Thousands: $6 – 4 = 2$ | 2818 |
Worksheet 3: Checking Subtraction Using Addition
Fundamental Mathematical Rule:
$$mathbf{text{Difference} + text{Subtrahend} = text{Minuend}}$$
Example: Subtract $6789 – 2345$ and check the answer:
| Step 1: Perform Subtraction | Step 2: Check by Addition ($text{Difference} + text{Subtrahend}$) | Verification Result |
|---|---|---|
|
6 7 8 9 (Minuend) – 2 3 4 5 (Subtrahend) ——— 4 4 4 4 (Difference) |
4 4 4 4 (Difference) + 2 3 4 5 (Subtrahend) ——— 6 7 8 9 (Equals Minuend!) | ✓ Verified Correct! |
Worksheet 4: Word Problems on Subtraction (With Statements)
Problem 1: A poultry farm produced 4,500 eggs. Out of these, 1,250 eggs were sold. How many eggs are left?
Solution:
Total eggs produced = 4500
Eggs sold = 1250
Eggs remaining = $4500 – 1250$
4 5 0 0
– 1 2 5 0
———
3 2 5 0
Answer: There are 3,250 eggs left in the poultry farm.
Problem 2: Out of 8,250 students in a school, 4,120 are boys. How many girls are studying in the school?
Solution:
Total number of students = 8250
Number of boys = 4120
Number of girls = $8250 – 4120$
8 2 5 0
– 4 1 2 0
———
4 1 3 0
Answer: There are 4,130 girls studying in the school.
Problem 3: A grain godown had 6,300 bags of wheat. If 2,875 bags were dispatched to fair price shops, find the remaining number of bags.
Solution:
Initial bags of wheat = 6300
Bags dispatched = 2875
Remaining bags = $6300 – 2875$
6 3 0 0
– 2 8 7 5
———
3 4 2 5
Answer: 3,425 bags of wheat are left in the godown.
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