Multiplication of Whole Numbers

P6 Mathematics - Term I, Topic 3

Lesson 3 of 5

Learning Objectives:

• Multiply whole numbers (product ≤ 9,999,999)
• Use multiplication tables effectively
• Solve multiplication word problems

Mental Warm-Up!

1. 7 × 8 = ?
2. 12 × 5 = ?
3. 20 × 30 = ?
4. 100 × 50 = ?

Answers

1. 7 × 8 = 56
2. 12 × 5 = 60
3. 20 × 30 = 600
4. 100 × 50 = 5,000

When Do We Multiply?

• Shopping: Price × Quantity
• Work: Daily rate × Days
• Farming: Per acre × Number of acres
• School: Students per class × Number of classes
• Business: Units sold × Price per unit

Multiplying by Powers of 10

Quick Rule: Add Zeros!

• 456 × 10 = 4,560
• 456 × 100 = 45,600
• 456 × 1,000 = 456,000

Each zero in the multiplier adds one zero to the answer!

Multiplication by Single Digit

Example: 234,567 × 8

  234,567
×       8
---------

Work from right to left, just like addition!

Example Solution

  234,567
×       8
---------
1,876,536

• 7 × 8 = 56 (write 6, carry 5)
• 6 × 8 = 48 + 5 = 53 (write 3, carry 5)
• 5 × 8 = 40 + 5 = 45 (write 5, carry 4)
• 4 × 8 = 32 + 4 = 36 (write 6, carry 3)
• 3 × 8 = 24 + 3 = 27 (write 7, carry 2)
• 2 × 8 = 16 + 2 = 18

Multiplication by Two Digits

Example: 4,567 × 23

We multiply in TWO steps:

1. Multiply by 3 (ones)
2. Multiply by 20 (tens)
3. Add the results

Example: 4,567 × 23 (Step 1)

     4,567
   ×    23
   -------
    13,701  ← (4,567 × 3)

First: Multiply 4,567 by 3

Example: 4,567 × 23 (Step 2)

     4,567
   ×    23
   -------
    13,701  ← (4,567 × 3)
+   91,340  ← (4,567 × 20)

Second: Multiply 4,567 by 20
Remember to shift left one place!

Example: 4,567 × 23 (Final)

     4,567
   ×    23
   -------
    13,701  ← (4,567 × 3)
+   91,340  ← (4,567 × 20)
   -------
   105,041  ← Final answer

Third: Add the partial products

Another Example: 12,345 × 67

     12,345
   ×     67
   --------

Let's work through this together!

Solution: 12,345 × 67

     12,345
   ×     67
   --------
     86,415  ← (12,345 × 7)
+   740,700  ← (12,345 × 60)
   --------
    827,115  ← Final answer

Key Steps for Two-Digit Multiplication

1. Multiply by the ones digit
2. Multiply by the tens digit (shift left)
3. Add the partial products
4. Check by estimating

Practice Problem 1

Calculate: 8,976 × 7

  8,976
×     7
-------
   ?

Practice Problem 1: Answer

  8,976
×     7
-------
 62,832

Practice Problem 2

Calculate: 5,678 × 9

  5,678
×     9
-------
   ?

Practice Problem 2: Answer

  5,678
×     9
-------
 51,102

Word Problem 1

Books in Boxes

Problem: A box contains 24 books. How many books are in 345 boxes?

What operation? MULTIPLICATION!

24 × 345 = ?

Word Problem 1: Solution

      24
   × 345
   -----
     120  ← (24 × 5)
     960  ← (24 × 40)
+  7,200  ← (24 × 300)
   -----
   8,280 books

Answer: 8,280 books

Word Problem 2

Tree Planting

Problem: A farmer plants 2,345 trees per day. How many trees in 15 days?

2,345 × 15 = ?

Word Problem 2: Solution

    2,345
  ×    15
  -------
   11,725  ← (2,345 × 5)
+  23,450  ← (2,345 × 10)
  -------
   35,175 trees

Answer: 35,175 trees

Estimation: Checking Your Answer

Example: Is 4,567 × 23 ≈ 105,041?

Round to estimate:

• 4,567 ≈ 5,000
• 23 ≈ 20
• 5,000 × 20 = 100,000

Our answer (105,041) is close to 100,000 ✓

Common Mistakes to Avoid!

• Forgetting to carry
• Not shifting partial products left
• Poor alignment of numbers
• Multiplication table errors
• Adding partial products incorrectly

Be careful and systematic!

Summary: What We Learned

• Multiply by powers of 10 (add zeros)
• Multiply large numbers by single digits
• Multiply by two-digit numbers (partial products)
• Solve real-life multiplication problems
• Check answers by estimation

Homework

1. 7,890 × 6 = ?
2. 4,567 × 34 = ?
3. 98,765 × 8 = ?
4. Word problem: Each classroom has 45 desks. How many desks in 78 classrooms?

Show all working!

Remember!

Multiplication Steps:

1. Know your tables (1-12)
2. Work from right to left
3. Carry carefully
4. Shift partial products
5. Add accurately
6. Check by estimating

Well Done!

You can now multiply large numbers!

Next lesson: Division by Two-Digit Numbers

Keep practicing!