DAV Board Class 3 Mathematics (Primary Mathematics) | 100% Authentic Textbook Solutions
DAV Class 3 Maths Unit 5 Solutions Division
Get complete, step-by-step textbook solutions for DAV Class 3 Primary Mathematics Unit 5: Division. This comprehensive guide covers all worksheets including division as equal distribution and repeated subtraction, division terms (Dividend, Divisor, Quotient, Remainder), relation between multiplication and division facts, properties of division, long division calculations, and 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 5: Division | Equal sharing, division terms, division facts, long division, word problems |
Worksheet 1: Division as Equal Distribution & Terms
Core Concept: Division means splitting a quantity into equal groups or finding how many times one number is contained in another.
In the division equation: $mathbf{45 div 5 = 9}$:
• Dividend: The number to be divided ($45$).
• Divisor: The number by which we divide ($5$).
• Quotient: The answer obtained after division ($9$).
• Remainder: The leftover number that cannot be divided further ($0$).
Fundamental Verification Formula:
$$mathbf{text{Dividend} = (text{Divisor} times text{Quotient}) + text{Remainder}}$$
Worksheet 2: Multiplication Facts and Division Facts
Rule: For every multiplication fact of two distinct numbers, there are two corresponding division facts. For square numbers, there is only one division fact.
| Multiplication Fact | First Division Fact | Second Division Fact |
|---|---|---|
| $6 times 7 = 42$ | $42 div 7 = mathbf{6}$ | $42 div 6 = mathbf{7}$ |
| $8 times 9 = 72$ | $72 div 9 = mathbf{8}$ | $72 div 8 = mathbf{9}$ |
| $4 times 5 = 20$ | $20 div 5 = mathbf{4}$ | $20 div 4 = mathbf{5}$ |
| $5 times 5 = 25$ | $25 div 5 = mathbf{5}$ | (Only one division fact exists) |
| $9 times 9 = 81$ | $81 div 9 = mathbf{9}$ | (Only one division fact exists) |
Worksheet 3: Properties of Division
- 1. Division by 1: When any number is divided by 1, the quotient is the number itself.
Examples: $38 div 1 = mathbf{38}$; $546 div 1 = mathbf{546}$ - 2. Division by Itself: When a non-zero number is divided by itself, the quotient is always 1.
Examples: $29 div 29 = mathbf{1}$; $175 div 175 = mathbf{1}$ - 3. Zero Divided by a Number: Zero divided by any number is always 0.
Examples: $0 div 8 = mathbf{0}$; $0 div 45 = mathbf{0}$ - 4. Division by Zero: Division of any number by zero is not possible (undefined).
Worksheet 4: Long Division (Finding Quotient and Remainder)
| Problem | Step-by-Step Long Division Working | Quotient (Q) | Remainder (R) | Verification Check |
|---|---|---|---|---|
| (a) $84 div 4$ |
• Divide 8: $4 times 2 = 8$. $8 – 8 = 0$. • Bring down 4: $4 times 1 = 4$. $4 – 4 = 0$. | Q = 21 | R = 0 | $(4 times 21) + 0 = 84$ ✓ |
| (b) $75 div 6$ |
• Divide 7: $6 times 1 = 6$. $7 – 6 = 1$. • Bring down 5 to make 15: $6 times 2 = 12$. $15 – 12 = 3$. | Q = 12 | R = 3 | $(6 times 12) + 3 = 72 + 3 = 75$ ✓ |
| (c) $369 div 3$ |
• Divide 3: $3 times 1 = 3$. Remainder 0. • Divide 6: $3 times 2 = 6$. Remainder 0. • Divide 9: $3 times 3 = 9$. Remainder 0. | Q = 123 | R = 0 | $(3 times 123) + 0 = 369$ ✓ |
| (d) $548 div 5$ |
• Divide 5: $5 times 1 = 5$. Remainder 0. • Bring down 4: 4 cannot be divided by 5 ($5 times 0 = 0$). Write 0 in quotient. • Bring down 8 to make 48: $5 times 9 = 45$. $48 – 45 = 3$. | Q = 109 | R = 3 | $(5 times 109) + 3 = 545 + 3 = 548$ ✓ |
Worksheet 5: Word Problems on Division (With Proper Statements)
Problem 1: 48 pencils are distributed equally among 6 children. How many pencils will each child receive?
Solution:
Total number of pencils = 48
Total number of children = 6
Pencils each child gets = $48 div 6 = mathbf{8}$
Answer: Each child receives 8 pencils.
Problem 2: 72 juicy apples are packed equally into 8 wooden boxes. Find the number of apples in each box.
Solution:
Total apples = 72
Total boxes = 8
Apples in each box = $72 div 8 = mathbf{9}$
Answer: There are 9 apples in each box.
Problem 3: A long rope of length 95 meters is cut into 5 equal smaller pieces. What is the length of each piece?
Solution:
Total length of rope = 95 m
Number of equal pieces = 5
Length of each piece = $95 div 5$
1 9
——-
5 ) 9 5
– 5
—
4 5
– 4 5
—–
0
Answer: The length of each piece of rope is 19 meters.
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