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CBSE Class 5 Mathematics★ 5-7 marks in Class 5 Mathematics assessments; multiplication, division, and estimation

Ways to Multiply and Divide

Ways to Multiply and Divide is a current Class 5 CBSE Mathematics chapter from NCERT Math Magic. These notes cover multiplication and division algorithms, word problems, mental math strategies, and estimation with tables and practice.

⏱ 12 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Multiply large numbers by 1- and 2-digit numbers
2Divide large numbers by 1- and 2-digit numbers
3Check answers using the reverse operation
4Use mental-math tricks for quick calculation
5Estimate products and quotients

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Why this chapter matters

'Ways to Multiply and Divide' teaches efficient methods for multiplying and dividing larger numbers, along with mental-math tricks and estimation. These operations are used daily for bills, sharing, budgets, and measuring, and accuracy with them is essential for higher maths.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 4 Mathematics: Multiplication and division

Times tables and basic operations

Ways to Multiply and Divide — Class 5 Mathematics (CBSE)

Based on the NCERT Math Magic Grade 5 textbook. Master multiplication and division skills, then solve the practice set without looking at the answers.

1. Why this chapter matters

Multiplication and division are the most used operations in daily life — calculating bills, sharing items equally, planning budgets, and measuring quantities. This chapter goes beyond basic tables to teach students efficient algorithms for multiplying and dividing larger numbers. Students also learn mental math strategies, estimation, and real-world problem solving. Speed and accuracy with these operations are essential for success in higher mathematics.

2. Multiplication of large numbers

Multiplication by a 1-digit number

Example 1: 3,456 x 7

  3,456
x     7
-------
 24,192

Working: 7 x 6 = 42 (write 2, carry 4) 7 x 5 = 35 + 4 = 39 (write 9, carry 3) 7 x 4 = 28 + 3 = 31 (write 1, carry 3) 7 x 3 = 21 + 3 = 24 (write 24)

Multiplication by a 2-digit number

Example 2: 1,234 x 23

Method: Multiply by 3 (ones digit), then by 20 (tens digit), then add.

    1,234
x      23
---------
    3,702   (1,234 x 3)
+ 24,680   (1,234 x 20)
---------
  28,382

Lattice multiplication (alternative method)

Draw a grid with the number of rows = digits of first number, columns = digits of second number.
Split each cell diagonally.
Multiply the digit at the top of each column by the digit at the left of each row.
Write the product in the cell (tens above diagonal, ones below).
Add diagonally, carrying when needed.

Example: 45 x 37

    4   5
  +---+---+
3 |1 /|1 /|
  | / | / |
  |/ 2|/ 5|
  +---+---+
7 |2 /|3 /|
  | / | / |
  |/ 8|/ 5|
  +---+---+

Adding diagonally from bottom-right: 5, then 5+3+8=16 (carry 1), then 1+1+2+1=5... = 1,665

3. Division of large numbers

Division by a 1-digit number

Example: 6,432 / 8

    804
  ------
8 | 6,432
  - 6,400 (8 x 800)
  ------
       32
     - 32 (8 x 4)
     ----
        0

Answer: 804

Division by a 2-digit number

Example: 3,456 / 12

    288
  ------
12 | 3,456
   - 2,400 (12 x 200)
   ------
     1,056
   - 960 (12 x 80)
   ------
        96
      - 96 (12 x 8)
      ----
         0

Answer: 288

Checking division

Dividend = Divisor x Quotient + Remainder

For the above: 12 x 288 + 0 = 3,456. Correct.

4. Word problems

Problem 1: A factory produces 2,450 notebooks each day. How many notebooks does it produce in 25 days? 2,450 x 25 = 2,450 x 20 + 2,450 x 5 = 49,000 + 12,250 = 61,250 notebooks.

Problem 2: 5,760 pencils are packed equally into 24 boxes. How many pencils in each box? 5,760 / 24 = 240 pencils per box.

Problem 3: A train travels 1,250 km in 5 hours. What is its speed per hour? 1,250 / 5 = 250 km per hour.

Problem 4: A book costs Rs 185. What is the cost of 36 such books? 185 x 36 = 185 x 30 + 185 x 6 = 5,550 + 1,110 = Rs 6,660.

5. Mental math strategies

Multiplication tricks

Strategy	Example	Working
Multiply by 10	45 x 10	Add a zero: 450
Multiply by 100	45 x 100	Add two zeros: 4,500
Multiply by 5	46 x 5	Half and then x10: 46/2=23, 23x10=230
Multiply by 25	48 x 25	Quarter and then x100: 48/4=12, 12x100=1,200
Multiply by 9	36 x 9	(36 x 10) — 36 = 360 — 36 = 324
Multiply by 11	42 x 11	4(4+2)2 = 462

Division tricks

Strategy	Example	Working
Divide by 10	450 / 10	Remove a zero: 45
Divide by 100	4,500 / 100	Remove two zeros: 45
Divide by 5	240 / 5	Double then /10: 240x2=480, 480/10=48
Divide by 25	600 / 25	Times 4 then /100: 600x4=2,400, 2,400/100=24

6. Estimation

Before calculating exactly, estimate to check if the answer is reasonable.

Example: Estimate 4,890 x 32.

Round 4,890 to 5,000. Round 32 to 30. Estimated product = 5,000 x 30 = 1,50,000. The actual answer should be close to 1,50,000.

Example: Estimate 5,720 / 28.

Round 5,720 to 6,000. Round 28 to 30. Estimated quotient = 6,000 / 30 = 200. Actual answer: 5,720 / 28 = 204.2... Close to 200.

7. Activity corner

Activity 1: Find the total number of pages in 12 notebooks if each notebook has 168 pages. Estimate first, then calculate exactly.

Activity 2: A school has 960 students. They are divided into 24 equal sections. How many students in each section? Check by multiplying.

Activity 3: Practice mental math with a partner. Take turns giving each other problems like 50 x 30, 120 x 5, 400 / 20, 3,600 / 12. Time each other.

8. Common mistakes

Mistake: Forgetting to carry in multiplication Fix: Write the carry digit clearly above the next column. Double-check each step.
Mistake: Misaligning digits in the partial products Fix: When multiplying by the tens digit, start writing the result below the tens place.
Mistake: Forgetting to bring down digits in long division Fix: Bring down one digit at a time. If the divisor cannot divide, write 0 in the quotient and bring down the next digit.
Mistake: Not checking the answer Fix: Always check: Product ÷ Multiplier = Multiplicand. Or: Divisor x Quotient + Remainder = Dividend.

9. Key facts

Multiply large numbers step by step, starting from the ones digit.
In division, remember: Dividend = Divisor x Quotient + Remainder.
Estimate before calculating to check if the answer is reasonable.
Use mental math tricks for quick calculations with 5, 9, 10, 11, 25, etc.
Always align digits correctly in the ones, tens, hundreds columns.
Check your answers by performing the reverse operation.

10. Self-test

Multiply: 2,345 x 6.
Multiply: 1,256 x 34.
Divide: 4,896 / 8.
Divide: 7,200 / 24.
Estimate: 6,120 x 48. Round to the nearest thousand and ten.

11. Answer key

Multiply: 2,345 x 6. Answer: 2,345 x 6 = 14,070.
Multiply: 1,256 x 34. Answer: 1,256 x 34 = 1,256 x 30 + 1,256 x 4 = 37,680 + 5,024 = 42,704.
Divide: 4,896 / 8. Answer: 4,896 / 8 = 612. Check: 612 x 8 = 4,896.
Divide: 7,200 / 24. Answer: 7,200 / 24 = 300. Check: 300 x 24 = 7,200.
Estimate: 6,120 x 48. Answer: Round 6,120 to 6,000. Round 48 to 50. Estimate = 6,000 x 50 = 3,00,000. Actual = 6,120 x 48 = 2,93,760. The estimate is close.

12. Quick revision

Multiply: align digits, multiply each place, add partial products.
Divide: find how many times the divisor fits into the dividend.
Estimate first, calculate exactly, then check.
Use mental math tricks for speed.
Practise word problems by reading carefully and identifying the operation.
Always check: reverse operation verifies your answer.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Division check

Dividend = Divisor x Quotient + Remainder

Use it to verify division answers.

Estimation

Round the numbers, then multiply or divide

Checks if the exact answer is reasonable.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Forgetting to carry in multiplication

✓ Write the carry digit clearly above the next column and add it in.

WATCH OUT

✗ Misaligning partial products

✓ When multiplying by the tens digit, start writing the result one place to the left (under the tens).

WATCH OUT

✗ Not checking the answer

✓ Verify with the reverse operation: Divisor x Quotient + Remainder = Dividend.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiply and Divide

Algorithms for larger numbers

Questions

Word problems and estimation

Real-life problems and estimating answers

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Multiply

Multiply 2,345 x 6.

▶ Show solution

14,070.

Q2MEDIUM· Multiply

Multiply 1,256 x 34.

▶ Show solution

1,256 x 30 + 1,256 x 4 = 37,680 + 5,024 = 42,704.

Q3EASY· Divide

Divide 4,896 / 8.

▶ Show solution

612 (check: 612 x 8 = 4,896).

Q4MEDIUM· Estimate

Estimate 6,120 x 48 by rounding.

▶ Show solution

Round to 6,000 x 50 = 3,00,000 (the exact answer 2,93,760 is close).

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Multiply starting from the ones digit, carrying as needed.
•Align partial products correctly when multiplying by 2-digit numbers.
•Division: Dividend = Divisor x Quotient + Remainder.
•Estimate by rounding before calculating exactly.
•Use tricks: x10 adds a zero, x5 is half then x10, x9 is x10 minus the number.
•Bring down one digit at a time in long division.
•Check answers with the reverse operation.

CBSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 5-7 marks, depending on the school paper

Question type	Marks each	Typical count	What it tests
Multiplication / division	3-4	1-2	Algorithms with larger numbers
Word problems / estimation	2-3	1	Real-life problems and estimating

Prep strategy

Practise carrying and aligning digits
Master long division step by step
Learn mental-math tricks for 5, 9, 10, 11, 25
Always estimate and then check answers

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Shopping and bills

Multiplication and division work out totals, change, and unit prices.

Sharing equally

Division splits items fairly among people or boxes.

Quick mental maths

Tricks help calculate fast without paper.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Carry carefully and align digits in multiplication
Show each step in long division
Estimate first to predict the answer
Verify with the reverse operation

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Try lattice multiplication for large numbers.
Solve multi-step word problems mixing multiplication and division.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

CBSE Class 5 School ExamHigh

Maths Olympiad / IMOMedium

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Estimation gives you a quick, rough idea of what the answer should be, so you can tell whether your exact calculation is reasonable. For example, to multiply 4,890 by 32 you can round to 5,000 times 30, which is 1,50,000. If your exact answer is wildly different from this, you know you have made a mistake somewhere. Estimating first is a simple but powerful way to catch errors.

Use the relationship Dividend = Divisor x Quotient + Remainder. Multiply the divisor by the quotient you found, then add any remainder; the result should equal the original number you divided (the dividend). For example, if 3,456 divided by 12 gives 288 with no remainder, then 12 x 288 + 0 = 3,456, which matches, so the answer is correct.

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