Multiplication — 3-Digit × 2-Digit

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Multiply 3-digit numbers by 2-digit numbers using the standard algorithm
Understand and apply properties of multiplication (commutative, associative, distributive, identity, zero)
Multiply numbers by 10, 100, and 1000 using shortcut rules
Estimate products by rounding numbers before multiplying
Handle multiplication with zeros in the middle (e.g., 305 × 42)
Solve real-life word problems involving multiplication in Indian contexts
Extend multiplication skills to 4-digit × 2-digit numbers

Introduction — Multiplication in Daily Life

In Class 4, you learned to multiply 2-digit numbers by 2-digit numbers. Now in Class 5, we take it further — you will learn to multiply 3-digit numbers by 2-digit numbers and even begin working with 4-digit numbers!

Think about these real-life situations:

A school orders 48 boxes of notebooks, and each box has 125 notebooks. How many notebooks in total? (125 × 48)
A train travels 345 km every day. How far does it travel in 28 days? (345 × 28)
Arjun's father buys 36 bags of rice at ₹750 per bag. What is the total cost? (750 × 36)
A farmer plants 64 rows of mango saplings with 215 saplings in each row. How many saplings in all? (215 × 64)

All of these need 3-digit × 2-digit multiplication. Let us learn how to do it step by step!

Quick Revision — What You Already Know

Before we begin, let us quickly revise what multiplication means and some facts you already know:

What is Multiplication?

Multiplication is repeated addition. For example: 5 × 3 = 5 + 5 + 5 = 15
The numbers being multiplied are called factors. The answer is called the product.
In 345 × 23 = 7,935 → 345 and 23 are factors; 7,935 is the product.
The larger number is usually called the multiplicand and the smaller one the multiplier.

Multiplication Tables — Quick Check

You must know your tables from 2 to 12 by heart. Here is a quick check:

×	6	7	8	9	12
7	42	49	56	63	84
8	48	56	64	72	96
9	54	63	72	81	108
12	72	84	96	108	144

Think About It: Why do we need tables? Because every big multiplication problem breaks down into smaller multiplications from the tables! When we multiply 345 × 23, we actually use tables of 3, 2, and single-digit multiplication many times.

Multiplying by 10, 100, and 1000

Before we learn long multiplication, here is a powerful shortcut that makes many calculations easy:

The Zero Rule

Multiply by 10: Add one zero at the end of the number.
Multiply by 100: Add two zeros at the end of the number.
Multiply by 1000: Add three zeros at the end of the number.

Examples:

Multiplication	Result	How?
346 × 10	3,460	Write 346, add one zero → 3460
346 × 100	34,600	Write 346, add two zeros → 34600
346 × 1000	3,46,000	Write 346, add three zeros → 346000
250 × 10	2,500	Write 250, add one zero → 2500
250 × 100	25,000	Write 250, add two zeros → 25000
480 × 1000	4,80,000	Write 480, add three zeros → 480000

Multiplying by Multiples of 10 (20, 30, 40...)

To multiply by 20, 30, 40, etc., first multiply by the non-zero digit, then add the zero(s):

Examples:
345 × 20: First, 345 × 2 = 690. Then add one zero → 6,900
250 × 60: First, 250 × 6 = 1,500. Then add one zero → 15,000
178 × 300: First, 178 × 3 = 534. Then add two zeros → 53,400
465 × 40: First, 465 × 4 = 1,860. Then add one zero → 18,600

Image needed: A visual showing the pattern of multiplying by 10, 100, 1000. Show a number (e.g., 345) with zeros being added at the end step by step. Use arrows and colour-coded zeros (green for ×10, blue for ×100, red for ×1000).
Style: Clean diagram, colourful arrows, child-friendly, step-by-step visual
Size: 700×350px

Standard Algorithm — Long Multiplication (3-Digit × 2-Digit)

The standard algorithm (also called long multiplication or column method) breaks the multiplication into simple steps. Here is how it works:

Steps for 3-Digit × 2-Digit Multiplication

Step 1: Write the 3-digit number (multiplicand) on top and the 2-digit number (multiplier) below it, aligned to the right.
Step 2: Multiply the multiplicand by the ones digit of the multiplier. Write this as the first partial product.
Step 3: Write a zero placeholder in the ones place of the next line. Then multiply the multiplicand by the tens digit of the multiplier. Write this as the second partial product.
Step 4: Add both partial products to get the final answer (product).

Worked Example 1: 345 × 23

Let us multiply 345 × 23 step by step:

      3 4 5
    ×   2 3
    -------
    1 0 3 5   ← 345 × 3 (ones digit)
  6 9 0 0     ← 345 × 2 (tens digit), shifted one place left
    -------
  7 9 3 5     ← Add: 1035 + 6900 = 7935

Step 1: 345 × 3 = 1,035 (multiply by ones digit 3)
→ 5×3=15, write 5 carry 1. 4×3=12, +1=13, write 3 carry 1. 3×3=9, +1=10, write 10.
First partial product = 1,035

Step 2: 345 × 2 = 690, but since 2 is in the tens place, write it as 6,900 (add a zero)
→ 5×2=10, write 0 carry 1. 4×2=8, +1=9. 3×2=6.
Second partial product = 6,900

Step 3: Add: 1,035 + 6,900 = 7,935

Therefore, 345 × 23 = 7,935

Image needed: A clear step-by-step long multiplication visual showing 345 × 23. Show the column layout with the multiplicand on top, multiplier below, partial products clearly labelled with arrows showing "multiply by ones" and "multiply by tens (shift left)". Final addition shown with carrying marks.
Style: Clean diagram on grid paper background, colour-coded steps (blue for first partial product, green for second), child-friendly
Size: 600×500px

Worked Example 2: 567 × 48

      5 6 7
    ×   4 8
    -------
    4 5 3 6   ← 567 × 8 (ones digit)
  2 2 6 8 0   ← 567 × 4 (tens digit), shifted left
    -------
  2 7 2 1 6   ← Add: 4536 + 22680 = 27216

Step 1: 567 × 8:
→ 7×8=56, write 6 carry 5. 6×8=48, +5=53, write 3 carry 5. 5×8=40, +5=45, write 45.
First partial product = 4,536

Step 2: 567 × 4 = 2,268, write as 22,680 (shifted left by one place)
→ 7×4=28, write 8 carry 2. 6×4=24, +2=26, write 6 carry 2. 5×4=20, +2=22, write 22.
Second partial product = 22,680

Step 3: Add: 4,536 + 22,680 = 27,216

Therefore, 567 × 48 = 27,216

Worked Example 3: 904 × 76

      9 0 4
    ×   7 6
    -------
    5 4 2 4   ← 904 × 6 (ones digit)
  6 3 2 8 0   ← 904 × 7 (tens digit), shifted left
    -------
  6 8 7 0 4   ← Add: 5424 + 63280 = 68704

Step 1: 904 × 6:
→ 4×6=24, write 4 carry 2. 0×6=0, +2=2, write 2. 9×6=54, write 54.
First partial product = 5,424

Step 2: 904 × 7 = 6,328, write as 63,280
→ 4×7=28, write 8 carry 2. 0×7=0, +2=2, write 2. 9×7=63, write 63.
Second partial product = 63,280

Step 3: Add: 5,424 + 63,280 = 68,704

Therefore, 904 × 76 = 68,704

Worked Example 4: 250 × 60

When the multiplier ends in zero, we can use the shortcut:

250 × 60 = 250 × 6 × 10

250 × 6: → 0×6=0. 5×6=30, write 0 carry 3. 2×6=12, +3=15. So 250 × 6 = 1,500

Now multiply by 10: 1,500 × 10 = 15,000

Therefore, 250 × 60 = 15,000

Multiplying Larger Numbers — 4-Digit × 2-Digit

The same method works for 4-digit numbers too! You just have more digits to multiply in each step.

Example: 2,345 × 67

      2 3 4 5
    ×     6 7
    ---------
    1 6 4 1 5   ← 2345 × 7 (ones digit)
  1 4 0 7 0 0   ← 2345 × 6 (tens digit), shifted left
    ---------
  1 5 7 1 1 5   ← Add: 16415 + 140700 = 157115

Step 1: 2345 × 7 = 16,415
→ 5×7=35, write 5 carry 3. 4×7=28, +3=31, write 1 carry 3. 3×7=21, +3=24, write 4 carry 2. 2×7=14, +2=16.

Step 2: 2345 × 6 = 14,070, write as 1,40,700
→ 5×6=30, write 0 carry 3. 4×6=24, +3=27, write 7 carry 2. 3×6=18, +2=20, write 0 carry 2. 2×6=12, +2=14.

Step 3: Add: 16,415 + 1,40,700 = 1,57,115

Therefore, 2,345 × 67 = 1,57,115

Think About It: Notice that when we multiply a 3-digit number by a 2-digit number, the answer can be a 4-digit or 5-digit number. When we multiply a 4-digit number by a 2-digit number, the answer can be a 5-digit or 6-digit number! Can you figure out why?

Properties of Multiplication

Multiplication has some special properties (rules) that always work, no matter what numbers you use. These properties make calculations easier and help us check our answers.

Property	Rule	Example
Commutative Property (Order Property)	a × b = b × a Changing the order of factors does not change the product.	345 × 23 = 23 × 345 = 7,935 126 × 45 = 45 × 126 = 5,670
Associative Property (Grouping Property)	(a × b) × c = a × (b × c) Changing the grouping of factors does not change the product.	(5 × 4) × 25 = 20 × 25 = 500 5 × (4 × 25) = 5 × 100 = 500
Distributive Property (Breaking apart)	a × (b + c) = a×b + a×c a × (b − c) = a×b − a×c You can break one factor into parts, multiply separately, then add/subtract.	345 × 23 = 345 × (20 + 3) = 345×20 + 345×3 = 6,900 + 1,035 = 7,935
Identity Property (Multiplying by 1)	a × 1 = a Any number multiplied by 1 stays the same.	567 × 1 = 567 9,999 × 1 = 9,999
Zero Property	a × 0 = 0 Any number multiplied by 0 equals 0.	345 × 0 = 0 99,999 × 0 = 0

Image needed: A visual showing the Distributive Property of multiplication. Show 345 × 23 being broken into 345 × 20 + 345 × 3, with rectangular area models. One large rectangle split into two smaller rectangles showing how the areas add up to the total product.
Style: Area model diagram, colour-coded sections (blue and green), labels with numbers, child-friendly
Size: 700×400px

Using the Distributive Property to Multiply Mentally:

Example 1: 125 × 12 = 125 × (10 + 2) = 1,250 + 250 = 1,500
Example 2: 99 × 45 = (100 − 1) × 45 = 4,500 − 45 = 4,455
Example 3: 198 × 25 = (200 − 2) × 25 = 5,000 − 50 = 4,950
Example 4: 350 × 14 = 350 × (10 + 4) = 3,500 + 1,400 = 4,900

Estimation of Products

Estimation means finding an approximate answer quickly by rounding numbers before multiplying. This is useful to:

Check if your answer is reasonable (not too big or too small)
Get a quick rough answer when an exact answer is not needed
Spot mistakes in your calculation

How to Estimate a Product

Step 1: Round each factor to the nearest ten, hundred, or leading digit.
Step 2: Multiply the rounded numbers.
The estimated product will be close to the actual product.

Examples:

Actual Problem	Round to	Estimated Product	Actual Product
489 × 52	500 × 50	25,000	25,428
312 × 48	300 × 50	15,000	14,976
678 × 23	700 × 20	14,000	15,594
195 × 41	200 × 40	8,000	7,995
845 × 67	850 × 70	59,500	56,615

Think About It: Meena calculated 345 × 23 and got 79,350. Can she use estimation to check? Round: 350 × 20 = 7,000. Her answer of 79,350 is about 10 times too big! She probably made a mistake. (The correct answer is 7,935.)

Multiplication with Zero in the Middle

When a number has a zero in the middle (like 305, 700, 408), the multiplication works the same way — just remember that any digit multiplied by 0 gives 0.

Example 1: 305 × 42

      3 0 5
    ×   4 2
    -------
      6 1 0   ← 305 × 2: (5×2=10, 0×2=0+1=1, 3×2=6)
  1 2 2 0 0   ← 305 × 4: (5×4=20, 0×4=0+2=2, 3×4=12), shifted left
    -------
  1 2 8 1 0   ← Add: 610 + 12200 = 12810

Therefore, 305 × 42 = 12,810

Example 2: 700 × 86

Shortcut: 7 × 86 = 602. Then add two zeros → 60,200

Or the long way:

      7 0 0
    ×   8 6
    -------
    4 2 0 0   ← 700 × 6
  5 6 0 0 0   ← 700 × 8, shifted left
    -------
  6 0 2 0 0   ← Add: 4200 + 56000 = 60200

Therefore, 700 × 86 = 60,200

Example 3: 408 × 35

      4 0 8
    ×   3 5
    -------
    2 0 4 0   ← 408 × 5: (8×5=40, 0×5=0+4=4, 4×5=20)
  1 2 2 4 0   ← 408 × 3: (8×3=24, 0×3=0+2=2, 4×3=12), shifted
    -------
  1 4 2 8 0   ← Add: 2040 + 12240 = 14280

Therefore, 408 × 35 = 14,280

Word Problems — Indian Context

Let us solve some real-life word problems that use 3-digit × 2-digit multiplication:

Problem 1: Priya's school ordered 36 boxes of colour pencils. Each box contains 144 pencils. How many colour pencils were ordered in total?

Solution: Total pencils = 144 × 36

    144 × 36:  144 × 6 = 864  |  144 × 3 = 432 → 4320  |  864 + 4320 = 5,184

Answer: 5,184 colour pencils were ordered.

Problem 2: The Rajdhani Express travels 675 km every day between Delhi and Mumbai. How many kilometres does it travel in 24 days?

Solution: Total distance = 675 × 24
675 × 4 = 2,700 | 675 × 2 = 1,350 → 13,500 | 2,700 + 13,500 = 16,200
Answer: The train travels 16,200 km in 24 days.

Problem 3: A mango farmer in Ratnagiri packs 48 crates of mangoes. Each crate holds 250 mangoes. How many mangoes does he pack in total?

Solution: Total mangoes = 250 × 48
250 × 8 = 2,000 | 250 × 4 = 1,000 → 10,000 | 2,000 + 10,000 = 12,000
Answer: The farmer packs 12,000 mangoes.

Problem 4: Arjun's father buys 52 bags of wheat at ₹485 per bag for their ration shop. What is the total cost?

Solution: Total cost = ₹485 × 52
485 × 2 = 970 | 485 × 5 = 2,425 → 24,250 | 970 + 24,250 = 25,220
Answer: The total cost is ₹25,220.

Problem 5: A school has 38 classrooms. Each classroom has 45 desks. The school wants to buy new chairs at ₹375 per chair (one chair per desk). What is the total cost of chairs?

Solution:
Step 1: Total chairs needed = 38 × 45 = 1,710
Step 2: Total cost = 1,710 × 375
This is a bigger multiplication! Let us use the distributive property:
1,710 × 375 = 1,710 × (400 − 25) = 6,84,000 − 42,750 = ₹6,41,250
Answer: The total cost of chairs is ₹6,41,250.

Image needed: A colourful illustration of an Indian market/shop scene showing: bags of rice/wheat with price tags (₹485), crates of mangoes, boxes of school supplies. A shopkeeper with a calculator. Numbers and multiplication symbols visible to show the math connection to real life.
Style: Warm, colourful cartoon illustration, Indian setting, child-friendly characters
Size: 750×450px

Key Words

Term	Meaning
Multiplicand	The number being multiplied (the larger number, written on top)
Multiplier	The number you multiply by (the smaller number, written below)
Product	The answer you get after multiplying
Factors	Numbers that are multiplied together to give a product
Partial Product	The result of multiplying by one digit of the multiplier (an intermediate step)
Estimate	An approximate answer found by rounding before calculating
Commutative	Order does not matter: a × b = b × a
Associative	Grouping does not matter: (a×b)×c = a×(b×c)
Distributive	Break apart: a×(b+c) = a×b + a×c
Identity (×1)	Any number × 1 = the same number
Zero Property	Any number × 0 = 0

Key Points to Remember

To multiply a 3-digit number by a 2-digit number: multiply by ones digit, then by tens digit (with a zero placeholder), then add both partial products.
Multiplying by 10: add one zero. By 100: add two zeros. By 1000: add three zeros.
For multiples of 10 (20, 30, 40...): multiply by the non-zero digit first, then add the zero(s).
Use estimation (rounding) to quickly check if your answer is reasonable.
The distributive property lets you break hard multiplications into easier parts.
The commutative property means you can swap the order: 345 × 23 = 23 × 345.
When there is a zero in the middle of a number, multiply normally — 0 times anything is 0.
A 3-digit × 2-digit product can be 4 digits (100×10=1,000) or 5 digits (999×99=98,901).
Always carry over when a single-digit multiplication gives a 2-digit result.
Check word problems: identify which numbers to multiply, solve, and write the answer with correct units.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. 345 × 10 = ?

Multiplying by 10 adds one zero: 3,450.

2. 25 × 16 = ?

25 × 16 = 25 × 4 × 4 = 100 × 4 = 400.

3. Any number multiplied by 0 gives:

Zero property: any number × 0 = 0.

4. 123 × 45 is closest to which estimate?

120 × 45 ≈ 5,400, closest to 5,000. (Exact: 5,535.)

5. 345 × 23 = ? (digits only)

345 × 23 = 345 × 20 + 345 × 3 = 6,900 + 1,035 = 7,935.

6. 48 × 1000 = ? (digits only)

Multiplying by 1000 adds three zeros: 48,000.

7. A shop sells 6 boxes of 485 pens each. How many pens in total? (digits only)

485 × 6 = 2,910 pens.

8. 99 × 100 = ? (digits only)

99 × 100 = 9,900.

Practice Questions

A. Multiply (3-Digit × 2-Digit):

1. 234 × 15 =

2. 456 × 23 =

3. 678 × 34 =

4. 512 × 47 =

5. 809 × 56 =

6. 375 × 68 =

7. 943 × 72 =

8. 607 × 89 =

B. Multiply by 10, 100, 1000:

1. 456 × 10 =

2. 789 × 100 =

3. 325 × 1000 =

4. 670 × 100 =

5. 208 × 1000 =

C. Estimate the product (round and multiply):

1. 387 × 42 ≈ × =

2. 612 × 58 ≈ × =

3. 195 × 31 ≈ × =

4. 749 × 88 ≈ × =

D. Fill in the blanks using properties of multiplication:

1. 245 × 36 = 36 × (Property: )

2. 500 × 0 = (Property: )

3. 678 × 1 = (Property: )

4. 125 × 48 = 125 × (50 − 2) = 125 × 50 − 125 × (Property: )

5. (4 × 25) × 37 = 4 × ( × 37) (Property: )

E. Find the missing number:

1. ___ × 25 = 7,500

2. 450 × ___ = 13,500

3. ___ × 12 = 3,600

4. 375 × ___ = 37,500

F. True or False:

1. 345 × 23 = 23 × 345

2. Any number multiplied by 0 equals that number.

3. 250 × 40 = 250 × 4 × 10

4. The product of two 2-digit numbers is always a 4-digit number.

5. Estimation gives us the exact answer.

G. Choose the correct answer (MCQ):

1. What is 345 × 20?

a) 690 b) 6,900 c) 69,000 d) 3,450

2. Which property says a × b = b × a?

a) Associative b) Distributive c) Commutative d) Identity

3. The estimated product of 489 × 52 (rounding to nearest tens) is approximately:

a) 20,000 b) 25,000 c) 30,000 d) 2,500

4. What is the second partial product when multiplying 567 × 48?

a) 4,536 b) 2,268 c) 22,680 d) 27,216

H. Word Problems:

1. Ravi's school library has 48 shelves. Each shelf holds 175 books. How many books are in the library?

2. A train ticket from Delhi to Jaipur costs ₹345. If 56 passengers buy tickets, how much money does the railway collect?

3. Sita's mother buys 24 packets of biscuits for a school picnic. Each packet costs ₹125. What is the total cost?

4. A farmer has 72 rows of coconut trees. Each row has 135 trees. How many coconut trees does the farmer have?

5. An auto-rickshaw travels 185 km every day. How many kilometres does it travel in 31 days?

6. Meena's father orders 65 cartons of mangoes for his shop. Each carton weighs 12 kg and costs ₹480. Find: (a) the total weight of all cartons, and (b) the total cost.

Activity — Shopping Bill Calculator

Imagine you are helping at a stationery shop. A school has placed a bulk order. Calculate the total bill:

Item	Quantity	Price per Item (₹)
Notebooks (single line)	48	₹65
Pencil boxes	36	₹125
Geometry boxes	24	₹185
Erasers (packets)	15	₹240
Drawing sheets (bundles)	12	₹350
Grand Total:

Challenge: First estimate the grand total by rounding each price to the nearest hundred. Then calculate the exact total. How close was your estimate?

Want to review the lesson again?

Mathematics

Multiplication — 3-Digit × 2-Digit

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Multiply 3-digit numbers by 2-digit numbers using the standard algorithm
Understand properties of multiplication (commutative, associative, distributive)
Multiply by 10, 100, and 1000 using shortcut rules
Estimate products by rounding
Solve real-life word problems involving multiplication

Introduction

In Class 4, you multiplied 2-digit × 2-digit numbers. Now in Class 5, we extend to 3-digit × 2-digit multiplication. Real-life examples: buying 48 boxes of 125 notebooks (125×48), a train travelling 345 km/day for 28 days (345×28), buying 36 bags of rice at ₹750 each (750×36).

Quick Revision

What is Multiplication? Repeated addition. 5×3 = 5+5+5 = 15.
Vocabulary: Multiplicand × Multiplier = Product. Both are called Factors.

×	6	7	8	9	12
7	42	49	56	63	84
8	48	56	64	72	96
9	54	63	72	81	108
12	72	84	96	108	144

Multiplying by 10, 100, 1000

×10: Add one zero | ×100: Add two zeros | ×1000: Add three zeros
Multiples of 10: Multiply by non-zero digit first, then add the zero(s).

Problem	Result	Problem	Result
346 × 10	3,460	345 × 20	6,900
346 × 100	34,600	250 × 60	15,000
346 × 1000	3,46,000	178 × 300	53,400

[Image: Visual showing pattern of multiplying by 10/100/1000 — zeros being added with colour-coded arrows]

Standard Algorithm — Long Multiplication

Steps:
1. Multiply multiplicand by ones digit of multiplier → First partial product
2. Write zero placeholder, multiply by tens digit → Second partial product
3. Add both partial products → Final product

Example 1: 345 × 23
345 × 3 = 1,035 (first partial product)
345 × 20 = 6,900 (second partial product — shifted left)
Add: 1,035 + 6,900 = 7,935

[Image: Step-by-step long multiplication visual — 345 × 23 with colour-coded partial products on grid paper]

Example 2: 567 × 48
567 × 8 = 4,536 (first partial product)
567 × 40 = 22,680 (second partial product)
Add: 4,536 + 22,680 = 27,216

Example 3: 904 × 76
904 × 6 = 5,424 | 904 × 70 = 63,280
Add: 5,424 + 63,280 = 68,704

Example 4: 250 × 60 (shortcut — ends in zero)
250 × 6 = 1,500. Add one zero → 15,000

4-Digit × 2-Digit (Extension)

Example: 2,345 × 67
2345 × 7 = 16,415 | 2345 × 60 = 1,40,700
Add: 16,415 + 1,40,700 = 1,57,115

Properties of Multiplication

Property	Rule	Example
Commutative	a × b = b × a	345 × 23 = 23 × 345 = 7,935
Associative	(a×b)×c = a×(b×c)	(5×4)×25 = 20×25 = 500 = 5×(4×25) = 5×100
Distributive	a×(b+c) = a×b + a×c	345×23 = 345×20 + 345×3 = 6900+1035 = 7935
Identity	a × 1 = a	567 × 1 = 567
Zero	a × 0 = 0	999 × 0 = 0

[Image: Distributive property area model — 345×23 split into 345×20 + 345×3 as two rectangles]

Using Distributive Property mentally:
125 × 12 = 125×(10+2) = 1,250 + 250 = 1,500
99 × 45 = (100−1)×45 = 4,500 − 45 = 4,455
198 × 25 = (200−2)×25 = 5,000 − 50 = 4,950

Estimation of Products

How to estimate: Round each factor → Multiply the rounded numbers → Get approximate answer.

Problem	Rounded	Estimate	Actual
489 × 52	500 × 50	25,000	25,428
312 × 48	300 × 50	15,000	14,976
678 × 23	700 × 20	14,000	15,594
195 × 41	200 × 40	8,000	7,995

Tip: Use estimation to check your answer! If your calculation gives 79,350 for 345×23, estimate: 350×20 = 7,000. Your answer is 10× too big — check again!

Multiplication with Zero in the Middle

305 × 42: 305×2 = 610 | 305×40 = 12,200 | Add: 12,810
700 × 86: 7×86 = 602, add two zeros → 60,200
408 × 35: 408×5 = 2,040 | 408×30 = 12,240 | Add: 14,280

Word Problems (Indian Context)

1. School ordered 36 boxes × 144 pencils = 144×36 = 5,184 pencils
2. Train travels 675 km/day × 24 days = 675×24 = 16,200 km
3. Farmer packs 48 crates × 250 mangoes = 250×48 = 12,000 mangoes
4. 52 bags × ₹485/bag = 485×52 = ₹25,220

[Image: Indian market scene — bags of rice with price tags, crates of mangoes, school supplies, showing multiplication in real life]

Key Words

Term	Meaning
Multiplicand	Number being multiplied (on top)
Multiplier	Number you multiply by (below)
Product	The answer after multiplying
Partial Product	Result of multiplying by one digit of the multiplier
Estimate	Approximate answer by rounding
Commutative	a × b = b × a
Distributive	a×(b+c) = a×b + a×c

Key Points:
• Multiply by ones digit → partial product 1. Shift left, multiply by tens digit → partial product 2. Add both.
• ×10: add 1 zero | ×100: add 2 zeros | ×1000: add 3 zeros
• Use estimation to check answers. Use distributive property for mental maths.
• Zero in the middle: multiply normally (0 × anything = 0, but don't forget to carry!)
• 3-digit × 2-digit → answer is 4 or 5 digits. 4-digit × 2-digit → answer is 5 or 6 digits.

Practice Questions

A. Multiply (3-Digit × 2-Digit):

1. 234 × 15 =

2. 456 × 23 =

3. 678 × 34 =

4. 512 × 47 =

5. 809 × 56 =

6. 375 × 68 =

7. 943 × 72 =

8. 607 × 89 =

B. Multiply by 10, 100, 1000:

1. 456 × 10 =

2. 789 × 100 =

3. 325 × 1000 =

4. 670 × 100 =

5. 208 × 1000 =

C. Estimate the product:

1. 387 × 42 ≈ × =

2. 612 × 58 ≈ × =

3. 195 × 31 ≈ × =

4. 749 × 88 ≈ × =

D. Fill in the blanks using properties:

1. 245 × 36 = 36 × (Property: )

2. 500 × 0 = (Property: )

3. 678 × 1 = (Property: )

4. 125 × 48 = 125×50 − 125× (Property: )

5. (4×25) × 37 = 4 × (×37) (Property: )

E. Find the missing number:

1. ___ × 25 = 7,500 →

2. 450 × ___ = 13,500 →

3. ___ × 12 = 3,600 →

4. 375 × ___ = 37,500 →

F. True or False:

1. 345 × 23 = 23 × 345

2. Any number × 0 = that number

3. 250 × 40 = 250 × 4 × 10

4. Product of two 2-digit numbers is always 4 digits

5. Estimation gives exact answer

G. Choose the correct answer (MCQ):

1. 345 × 20 = ?

a) 690 b) 6,900 c) 69,000 d) 3,450

2. Which property: a × b = b × a?

a) Associative b) Distributive c) Commutative d) Identity

3. Estimated product of 489 × 52 ≈

a) 20,000 b) 25,000 c) 30,000 d) 2,500

4. Second partial product of 567 × 48?

a) 4,536 b) 2,268 c) 22,680 d) 27,216

H. Word Problems:

1. Ravi's school library has 48 shelves with 175 books each. Total books?

2. Train ticket Delhi→Jaipur: ₹345. 56 passengers buy tickets. Total collection?

3. Sita's mother buys 24 packets of biscuits at ₹125 each. Total cost?

4. Farmer has 72 rows × 135 coconut trees per row. Total trees?

5. Auto-rickshaw travels 185 km/day. Distance in 31 days?

6. Meena's father orders 65 cartons at ₹480 each (12 kg each). Find: (a) total weight (b) total cost.

Activity — Shopping Bill Calculator

Calculate the total bill for this school order:

Item	Qty	Price (₹)
Notebooks	48	₹65
Pencil boxes	36	₹125
Geometry boxes	24	₹185
Erasers (packets)	15	₹240
Drawing sheets	12	₹350
Grand Total:

Challenge: First estimate the grand total by rounding prices, then calculate exact. How close was your estimate?

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