Ways to Multiply and Divide Class 5 NCERT

Chapter Overview: Why Different Methods Help

Multiplication and division become easier when we understand the number instead of memorising only one fixed method. For example, 23 × 6 can be seen as 20 × 6 plus 3 × 6. This uses place value: 23 has 2 tens and 3 ones. Similarly, 96 ÷ 4 can be split as 80 ÷ 4 and 16 ÷ 4. Both parts are easy, so the final answer is easy. Class 5 students should practise choosing friendly splits, estimating before solving, and checking multiplication by division. This helps in word problems where the main challenge is deciding which operation is needed.

Important Meanings in This Chapter

Multiplication

A quick way of adding the same number again and again. For example, 7 × 5 means 7 groups of 5 or 5 groups of 7.

Division

A way to share equally or make equal groups. For example, 36 ÷ 6 means sharing 36 into 6 equal parts or making groups of 6.

Factor

A number that is multiplied with another number to get a product. In 8 × 9 = 72, both 8 and 9 are factors.

Remainder

The amount left after making equal groups. In 29 ÷ 5, we can make 5 groups of 5 and 4 is left, so the remainder is 4.

A Reliable Method for Multiplication and Division

1. Read the question carefully — Find what is being asked: total amount, equal sharing, number of groups, cost, distance, or time. Underline the important numbers and words such as each, total, equally, left, rows, or packets.
2. Choose the operation — Use multiplication when equal groups are being joined. Use division when a total is being shared equally or when you need to find how many equal groups can be made.
3. Break numbers using place value — Split larger numbers into easier parts. For example, 47 × 5 becomes 40 × 5 plus 7 × 5. This keeps the calculation simple and reduces mistakes.
4. Check the answer — Use the opposite operation to check. If 168 ÷ 7 = 24, then 24 × 7 should give 168. Also estimate to see if the answer is close to what you expected.

Worked Examples with Place-Value Thinking

• Example 1: Find 36 × 8. Step 1: Split 36 into 30 + 6. Step 2: Multiply each part: 30 × 8 = 240 and 6 × 8 = 48. Step 3: Add the partial products: 240 + 48 = 288. Final answer: 36 × 8 = 288.
• Example 2: Divide 156 by 6. Step 1: Split 156 into friendly parts: 120 + 36. Step 2: Divide each part by 6: 120 ÷ 6 = 20 and 36 ÷ 6 = 6. Step 3: Add the quotients: 20 + 6 = 26. Final answer: 156 ÷ 6 = 26.
• Example 3: A notebook costs ₹18. What is the cost of 25 notebooks? Step 1: We need the cost of many equal items, so multiply 18 × 25. Step 2: Split 25 as 100 ÷ 4, or use 18 × 20 + 18 × 5. Step 3: 18 × 20 = 360 and 18 × 5 = 90. Add: 360 + 90 = 450. Final answer: The cost is ₹450.

Common Mistakes to Avoid

• Do not ignore place value. In 42 × 6, 4 means 40, so 40 × 6 is 240, not 24.
• In division, write the remainder only when something is left after making equal groups. Always check whether the question wants the remainder included.
• Do not multiply just because a word problem has big numbers. If it asks for equal sharing, division is usually needed.
• After solving, check by the opposite operation: multiplication checks division, and division can check multiplication.
• When using splitting, add all parts. For example, in 57 × 4, calculate both 50 × 4 and 7 × 4, then add them.

Exam Tip: Show Your Steps Neatly

In CBSE Class 5 maths, marks are often given for correct method, not only the final answer. Write the operation, split the numbers clearly, and show each step. For word problems, include a short statement like Total cost = 24 × 15. This makes your thinking easy to follow and helps you catch errors before submitting.

Practice Questions with Solutions

• Q: Find 48 × 7 using place value. A: Step 1: Split 48 into 40 + 8. Step 2: Multiply each part: 40 × 7 = 280 and 8 × 7 = 56. Step 3: Add 280 + 56 = 336. Final answer: 48 × 7 = 336.
• Q: 192 sweets are packed equally into 8 boxes. How many sweets are in each box? A: Step 1: Since sweets are shared equally, use division: 192 ÷ 8. Step 2: Split 192 as 160 + 32. Step 3: 160 ÷ 8 = 20 and 32 ÷ 8 = 4, so 20 + 4 = 24. Final answer: Each box has 24 sweets.
• Q: A bus has 42 seats. How many seats are there in 9 such buses? A: Step 1: Each bus has the same number of seats, so multiply 42 × 9. Step 2: Split 42 into 40 + 2. Step 3: 40 × 9 = 360 and 2 × 9 = 18. Add 360 + 18 = 378. Final answer: There are 378 seats.
• Q: Divide 275 by 5 and check your answer. A: Step 1: Split 275 into 250 + 25. Step 2: Divide each part: 250 ÷ 5 = 50 and 25 ÷ 5 = 5. Step 3: Add 50 + 5 = 55. Check: 55 × 5 = 275. Final answer: 275 ÷ 5 = 55.

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