How To Solve Multiplication And Division Questions Step By Step With Examples
The concept of multiplication and division questions is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Whether in school, competitive exams, or daily life, knowing how to approach these questions quickly and accurately can make maths far less daunting.
Understanding Multiplication and Division Questions
Multiplication and division questions refer to problems where you need to find the product (multiplication) or quotient (division) of given numbers. These concepts are widely used in arithmetic, money problems, and time or quantity calculations. Multiplication is used to find the total of equal groups, while division is about splitting into equal parts or groups. Typical terms include multiplier, multiplicand, quotient, remainder, dividend, and divisor.
Key Formulae Used in Multiplication and Division Questions
Multiplication formula: Product = Multiplicand × Multiplier
Division formula: Dividend = Divisor × Quotient + Remainder
Here’s a helpful table to understand multiplication and division questions more clearly:
Multiplication and Division Table
| Type | Sample Problem | Result |
|---|---|---|
| Multiplication | 14 × 7 | 98 |
| Division | 98 ÷ 7 | 14 |
| Word Problem (Multiplication) | Cost of 1 chair is ₹300. What is the cost of 12 such chairs? | ₹3,600 |
| Word Problem (Division) | Divide 120 apples into boxes of 10 each. How many boxes? | 12 |
This table shows how multiplication and division patterns appear regularly in test and real-life situations.
Solved Examples of Multiplication and Division Questions
Let’s go step by step to solve a few typical multiplication and division questions:
1. If the cost of one vehicle is ₹35,780, what is the cost of 100 vehicles?
Step 1: Multiply cost of 1 vehicle by 100.
Step 2: 35,780 × 100 = 35,78,000
Answer: The cost of 100 vehicles is ₹35,78,000.
Example 2 – Division:
2. Find the quotient and remainder if 4050 is divided by 3.
Step 1: Divide 4050 by 3.
Step 2: 4050 ÷ 3 = 1350, remainder = 0
Answer: Quotient = 1350, Remainder = 0.
Example 3 – Missing Number in Division:
3. ____ ÷ 10 = 13. Find the missing number.
Step 1: Multiply 13 by 10.
Step 2: 13 × 10 = 130
Check: 130 ÷ 10 = 13.
Final Answer: The missing number is 130.
Practice Multiplication and Division Questions
Now try solving these multiplication and division questions for more practice:
2. A group of women has 715 notes of ₹500 each. What is their total amount?
3. The monthly production of a toy factory is 5,376 toys. How many toys does it produce in a year?
4. The result of multiplying two numbers is 4,131. If one number is 27, what is the other?
5. The total cost of 15 cycles is ₹24,405. What is the cost of each cycle?
Common Mistakes to Avoid
- Mixing up the order of numbers (especially in division – always check which is the dividend and which is the divisor).
- Forgetting place value when multiplying or dividing large numbers.
- Skipping step-by-step checks (especially in word problems).
- Not checking for remainder in division questions.
Real-World Applications
The concept of multiplication and division questions appears in many real-life areas: shopping (finding total price), event planning (dividing guests into groups), manufacturing (finding total production), and banking tasks (counting bundles of notes). Practicing such questions on Vedantu helps students see the real value of maths in daily life and exams.
Quick Revision Tips for Multiplication and Division Questions
- Always align numbers by place value columns before multiplying or dividing.
- Practice with multiplication tables up to 20 for faster calculations. Try Multiplication Tables for Kids to improve speed.
- Break big numbers into smaller parts for easier calculations.
- Use estimation to quickly check if your answers are reasonable.
- Double-check with the formula: Dividend = (Divisor × Quotient) + Remainder.
More Multiplication and Division Practice
To deepen your understanding, try these resources on Vedantu:
- Multiplication Questions – Extra sums and solved examples.
- Division Questions – Focused division-only practice.
- Multiplication and Division Methods – Compare different calculation methods and tricks.
- Long Division – Stepwise solutions for bigger numbers.
- Multiplication and Division of Integers – Learn how to handle negative and positive numbers.
- Maths Worksheets – Download for extra home revision.
- Multiplication and Division of Decimals – Tackle decimal-based problems.
We explored the idea of multiplication and division questions, how to apply it, solve related problems, and understand its real-life relevance. Practice more with Vedantu to build confidence in these maths skills for your class and exams.
FAQs on Multiplication And Division Questions Explained With Solutions
1. What is multiplication in maths?
Multiplication is the mathematical operation of finding the total of equal groups. It is written using the symbol × or * and represents repeated addition.
- For example: 4 × 3 = 12
- This means 4 groups of 3: 3 + 3 + 3 + 3 = 12
- The numbers being multiplied are called factors
- The answer is called the product
2. What is division in maths?
Division is the mathematical operation of splitting a number into equal parts or finding how many times one number fits into another. It is written using the symbol ÷ or /.
- For example: 12 ÷ 3 = 4
- This means 12 is divided into 3 equal groups of 4
- The number being divided is the dividend
- The number you divide by is the divisor
- The answer is the quotient
3. What is the relationship between multiplication and division?
Multiplication and division are inverse operations, meaning one undoes the other. If you know a multiplication fact, you can find related division facts.
- Example: 5 × 6 = 30
- So, 30 ÷ 6 = 5
- And, 30 ÷ 5 = 6
- This connection is called a fact family
4. How do you solve multiplication questions step by step?
To solve multiplication questions, multiply each digit carefully and combine the results correctly. Follow these steps for multi-digit multiplication:
- Write numbers in column form
- Multiply the bottom number by each digit of the top number
- Add partial products if needed
- Example: 23 × 4
- 4 × 3 = 12 (write 2, carry 1)
- 4 × 2 = 8, plus 1 = 9
- Final answer: 92
5. How do you solve long division step by step?
Long division is solved using the Divide, Multiply, Subtract, Bring Down method. These steps help break large division problems into smaller parts.
- Example: 84 ÷ 4
- 4 goes into 8 → 2 times
- Multiply: 2 × 4 = 8
- Subtract: 8 − 8 = 0
- Bring down 4 → 4 ÷ 4 = 1
- Final answer: 21
6. What are the properties of multiplication?
The main properties of multiplication are the commutative, associative, distributive, and identity properties. These rules make calculations easier.
- Commutative: a × b = b × a
- Associative: (a × b) × c = a × (b × c)
- Distributive: a × (b + c) = ab + ac
- Identity: a × 1 = a
7. What happens when you multiply or divide by zero?
Multiplying any number by zero gives 0, but division by zero is undefined. These are important rules in arithmetic.
- 7 × 0 = 0
- 0 ÷ 5 = 0
- 5 ÷ 0 is undefined because division by zero is not possible
8. What is the formula for multiplication and division of fractions?
To multiply fractions, multiply numerators and denominators; to divide fractions, multiply by the reciprocal. These are standard fraction rules.
- Multiplication: (a/b) × (c/d) = ac/bd
- Example: 2/3 × 4/5 = 8/15
- Division: (a/b) ÷ (c/d) = (a/b) × (d/c)
- Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
9. What is the difference between multiplication and division?
Multiplication combines equal groups, while division separates a quantity into equal parts. They perform opposite functions in arithmetic.
- Multiplication: 6 × 4 = 24 (combining groups)
- Division: 24 ÷ 4 = 6 (splitting into groups)
- Multiplication increases value (except by fractions)
- Division usually reduces value (except when dividing by fractions)
10. What are common mistakes in multiplication and division questions?
Common mistakes in multiplication and division include place value errors, sign mistakes, and incorrect handling of remainders. Avoiding these improves accuracy.
- Forgetting to carry digits in multiplication
- Misplacing decimals in decimal multiplication or division
- Ignoring remainders in long division
- Dividing by zero, which is undefined
- Not simplifying final answers
