Hello, young mathematician! Multiplication is not just a table to memorise. It is a way to count equal groups, compare clever methods, estimate a sensible answer, and solve large calculations without feeling rushed.
Caregiver: Ask the learner to explain why a method works before asking for a faster method. Clear thinking matters more than speed.
This original PrincipalSaab guide follows Chapter 6, The Dairy Farm, from NCERT’s Maths Mela for Class 5. The official chapter develops multiplication through equal groups, place value, flexible strategies, estimation, and patterns. Every explanation, example, activity, and question below is newly written.
If rows and columns feel unfamiliar, the pictures and grouping language in Shapes Around Us can help you notice organised arrangements before you multiply.
Words to Know
Factor
a number being multiplied
6 and 8 in 6 × 8
Product
the answer to a multiplication
48 in 6 × 8 = 48
Place value
the value of a digit because of its position
3 means 300 in 342
Estimate
a nearby answer used for checking
39 × 21 is close to 40 × 20
Strategy
a planned way to solve
split 23 into 20 and 3
Your Learning Plan
- Picture the equal groups.
- Choose a strategy that makes the numbers friendly.
- Write each partial product clearly.
- Estimate before accepting the answer.
- Explain why the method works.
Equal Groups And Order
Multiplication describes equal groups. In 7 × 13, there are 7 groups with 13 objects in each group. Turning the same rectangular arrangement gives 13 groups with 7 objects in each group. The product stays 91.
This order rule is useful because one direction may be easier to calculate. For example, 25 × 4 and 4 × 25 describe the same total, but many learners recognise 4 groups of 25 as 100 immediately.
A display has 7 rows with 13 cards in each row.
- Write 7 × 13.
- Split 13 into 10 + 3.
- 7 × 10 = 70 and 7 × 3 = 21.
- 70 + 21 = 91.
Answer: There are 91 cards. Reading 13 × 7 gives the same product.
Multiplying By 10, 100, And 1,000
When a whole number is multiplied by 10, each digit becomes ten times as valuable and moves one place to the left in a place-value chart. Multiplying by 100 moves each digit two places; multiplying by 1,000 moves it three places.
It is tempting to say “just add zeros”, but place value explains why the shortcut works. The digit changes position before zeroes fill the newly empty places.
- 34 × 10 = 340
- 26 × 100 = 2,600
- 8 × 1,000 = 8,000
In each case, every digit becomes 10, 100, or 1,000 times its earlier value.
Split And Combine
A large factor can be split into tens and ones. Multiply each part, then combine the partial products. This is called using place-value decomposition.
The method works because 14 really means 10 + 4. Therefore, 23 × 14 is the same as 23 × 10 plus 23 × 4.
- 23 × 14 = 23 × (10 + 4).
- 23 × 10 = 230.
- 23 × 4 = 92.
- 230 + 92 = 322.
Answer: 23 × 14 = 322.
- 64 × 37 = 64 × (30 + 7).
- 64 × 30 = 1,920.
- 64 × 7 = 448.
- 1,920 + 448 = 2,368.
Answer: 64 × 37 = 2,368.
A written vertical method records the same partial products in a compact form. If you understand the split method first, the zeros and shifted rows in the vertical method make sense.
If regrouping across place values feels rusty, revisit Measuring Length for Class 4, where larger and smaller units also depend on careful place-value thinking.
Double And Half
Sometimes you can halve one factor and double the other without changing the product. This works especially well when one factor can become 10, 50, or 100.
- 48 × 25
- Half 48 and double 25: 24 × 50.
- Half 24 and double 50: 12 × 100.
- 12 × 100 = 1,200.
Answer: 48 × 25 = 1,200.
Why does this work? One group becomes half as large while the other group becomes twice as large. The total quantity stays unchanged. You can check by splitting: 48 × 25 = 48 × (100 ÷ 4) = 4,800 ÷ 4 = 1,200.
Use A Nearby Multiple
Numbers such as 19, 29, 49, or 101 sit close to friendly multiples of ten or one hundred. Multiply with the friendly number first, then correct the difference.
- 17 × 29 = 17 × (30 − 1).
- 17 × 30 = 510.
- Subtract one extra group of 17.
- 510 − 17 = 493.
Answer: 17 × 29 = 493.
Estimate And Check
An estimate is not a guess. It is a nearby calculation that tells you the expected size of the exact answer. Round each factor to a friendly number, multiply, and then compare.
- 39 × 62 is close to 40 × 60.
- 40 × 60 = 2,400, so expect an answer near 2,400.
- Exact: 39 × 62 = 39 × (60 + 2).
- 2,340 + 78 = 2,418.
Answer: The exact product is 2,418, which is close to the estimate.
Estimation catches many errors. An answer of 24,180 would be ten times too large; an answer of 241 would be about ten times too small.
Careful estimation later supports science measurement too. The Class 6 Measurement and Motion guide shows how sensible size checks strengthen observations.
Multiplication Patterns
Patterns help you predict related products. If 6 × 7 = 42, then 6 × 70 = 420 because one factor is ten times as large. Also, 60 × 70 = 4,200 because both factors have become ten times as large, making the product one hundred times as large.
Equivalent products create another pattern. Halving one factor and doubling the other gives a different-looking expression with the same answer.
- 18 × 45
- Half 18 and double 45: 9 × 90.
- 9 × 90 = 810.
- Check by splitting: 18 × 40 + 18 × 5 = 720 + 90 = 810.
Answer: 18 × 45 = 810.
Do not copy a pattern from one line without asking what changed. Say whether a factor was doubled, made ten times larger, or split into parts.
If a method still feels confusing after a second careful try, use Ask a Doubt and show the step where your product stopped matching your estimate.
Practice Time
Solve each original question. Estimate first when the factors are large, and open the answer only after your own attempt.
Practice 1. Find 14 × 9 by splitting 14.
Answer: (10 × 9) + (4 × 9) = 90 + 36 = 126.
Practice 2. Find 36 × 10 and 36 × 100.
Answer: 36 × 10 = 360 and 36 × 100 = 3,600.
Practice 3. Use place-value splitting to find 27 × 13.
Answer: 27 × (10 + 3) = 270 + 81 = 351.
Practice 4. Use doubling and halving to find 25 × 48.
Answer: 25 × 48 = 50 × 24 = 100 × 12 = 1,200.
Practice 5. Use a nearby multiple to find 23 × 39.
Answer: 23 × 40 − 23 = 920 − 23 = 897.
Practice 6. Estimate 51 × 19, then find the exact product.
Answer: Estimate: 50 × 20 = 1,000. Exact: 51 × (20 − 1) = 1,020 − 51 = 969.
Practice 7. Find 42 × 35 by splitting 35 into 30 + 5.
Answer: 42 × 30 + 42 × 5 = 1,260 + 210 = 1,470.
Practice 8. Find 72 × 18 and show two partial products.
Answer: 72 × 10 + 72 × 8 = 720 + 576 = 1,296.
Practice 9. If 6 × 7 = 42, find 6 × 70 and 60 × 70.
Answer: 6 × 70 = 420. Then 60 × 70 = 4,200.
Practice 10. A storeroom has 24 trays with 36 sealed packets on each tray. How many packets are there?
Answer: 24 × 36 = 24 × (30 + 6) = 720 + 144 = 864 packets.
Quick Self-Check
Use these five questions to check both your calculation and your explanation.
Self-check 1. What is the product in 8 × 12 = 96?
Answer: 96 is the product.
Self-check 2. Why are 7 × 13 and 13 × 7 equal?
Answer: They count the same equal-group arrangement in two orders.
Self-check 3. What happens to each digit when a whole number is multiplied by 100?
Answer: Each digit moves two place-value positions to the left and becomes 100 times as valuable.
Self-check 4. What correction is needed when 29 is replaced by 30?
Answer: Subtract one extra group of the other factor.
Self-check 5. Why estimate before accepting an exact product?
Answer: The estimate shows the expected size and helps catch place-value or arithmetic errors.
How To Choose A Good Strategy
Look at the factors before you calculate. A factor ending in 9 may invite a nearby multiple: 32 × 19 can become 32 × 20 − 32. A factor of 25 may invite doubling and halving: 16 × 25 can become 8 × 50 and then 4 × 100. Two ordinary two-digit factors often suit the split method.
No single strategy is always best. The useful question is, “Which change makes this product easier while keeping its value the same?” If your change is difficult to explain, return to place-value splitting. It is slower than a clever shortcut sometimes, but it is dependable.
After solving, check in a different way. If you split for the exact calculation, use rounding for the estimate. If you doubled and halved, multiply by place-value parts as a check. Two methods that agree give stronger evidence than repeating one method twice.
Keep the written work lined up. Name the factor you split, show every partial product, and include the final addition or subtraction. Neat steps are not decoration; they let you find the exact line where an error entered.
Method check: A correct multiplication answer should come with an explainable path. You may split a factor, double and halve, use a nearby multiple, or use a written algorithm, but every step must keep the value of the product unchanged.
When one method becomes messy, pause and choose another. For 48 × 25, splitting works, but doubling and halving reaches 12 × 100 quickly. For 64 × 37, splitting 37 into 30 + 7 is easier to explain.
Place-value language prevents a common mistake in two-digit multiplication. In 64 × 30, the 3 means three tens, not three ones. That is why 64 × 30 equals 1,920 rather than 192.
Estimate after choosing the factors but before trusting the exact answer. If both factors are around 40, the product should be around 1,600. A result near 160 or 16,000 needs another look.
A multiplication pattern is useful only when you can state the change. If one factor becomes ten times as large and the other stays the same, the product becomes ten times as large. If both factors become ten times as large, the product becomes one hundred times as large.
The activity with a 6-by-8 array is safe because it uses ordinary small objects on a table. Keep tiny objects away from younger children, or use paper squares instead.
To revise, choose one product and solve it in two ways. For example, solve 24 × 15 by splitting 15 into 10 + 5, then solve it again by halving 24 and doubling 15. Both paths should give 360.
Finally, write a sentence answer for every story problem. “864 packets” communicates more than the number 864 alone because it connects the product back to the question.
Kaizen step: Practise one strategy clearly today. Add a second strategy tomorrow. Small improvements make multiplication flexible.
Continue Learning
- Explore Class 5 Mathematics guides
- Browse PrincipalSaab Study Notes
- Open the CBSE learning hub
- Next in Maths Mela: continue with Chapter 7, Shapes and Patterns.