Multiplication Tables of 8 and 9
The multiplication tables of 8 and 9 complete the single-digit multiplication tables. These tables have some of the largest products in single-digit multiplication (up to 9 × 10 = 90).
The table of 8 is related to the table of 4 (double it), and the table of 9 has a special pattern — the digits of each product always add up to 9.
What is Multiplication Tables of 8 and 9 - Class 3 Maths (Multiplication (Grade 3))?
Table of 8:
| 8 × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| = | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |
Table of 9:
| 9 × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| = | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
Special pattern in table of 9: The tens digit goes up by 1 (0, 1, 2, 3...) and the ones digit goes down by 1 (9, 8, 7, 6...). The sum of digits always equals 9. Example: 9 × 4 = 36 → 3 + 6 = 9.
Solved Examples
Example 1: Product from Table of 8
Question: What is 8 × 7?
Think:
- 8 × 7 = (4 × 7) × 2 = 28 × 2 = 56
Answer: 8 × 7 = 56
Example 2: Product from Table of 9 Using the Pattern
Question: What is 9 × 6?
Think:
- Tens digit = 6 − 1 = 5
- Ones digit = 9 − 5 = 4
- So 9 × 6 = 54
- Check: 5 + 4 = 9 ✓
Answer: 9 × 6 = 54
Example 3: The Finger Trick for 9
Question: Use the finger trick to find 9 × 4.
Think:
- Hold up 10 fingers. Put down finger number 4 (from the left).
- Count fingers before the bent finger: 3
- Count fingers after the bent finger: 6
- Read as 36
Answer: 9 × 4 = 36
Example 4: Word Problem — Octopus Legs
Question: An octopus has 8 legs. How many legs do 5 octopuses have?
Think:
- 5 × 8 = 40
Answer: 5 octopuses have 40 legs.
Example 5: Word Problem — Cricket Overs
Question: In a cricket match, 9 overs were bowled. Each over has 6 balls. How many balls were bowled?
Think:
- 9 × 6 = 54
Answer: 54 balls were bowled.
Example 6: Missing Factor — Table of 8
Question: 8 × ___ = 64.
Think:
- 8, 16, 24, 32, 40, 48, 56, 64
- 64 is the 8th multiple
Answer: 8 × 8 = 64.
Example 7: Missing Factor — Table of 9
Question: 9 × ___ = 81.
Think:
- 81 → 8 + 1 = 9 ✓ (it is a multiple of 9)
- Tens digit is 8, so the multiplier is 8 + 1 = 9
Answer: 9 × 9 = 81.
Example 8: Table of 9 as 10 Minus 1
Question: Find 9 × 7 using the (10 − 1) trick.
Think:
- 9 × 7 = (10 − 1) × 7 = 10 × 7 − 1 × 7 = 70 − 7 = 63
Answer: 9 × 7 = 63
Example 9: Doubling Table of 4 for Table of 8
Question: If 4 × 9 = 36, what is 8 × 9?
Think:
- 8 = 2 × 4
- 8 × 9 = 2 × (4 × 9) = 2 × 36 = 72
Answer: 8 × 9 = 72
Example 10: Word Problem — Saving Money
Question: Dev saves ₹9 every day. How much does he save in 8 days?
Think:
- 8 × 9 = 72
Answer: Dev saves ₹72 in 8 days.
Real-World Applications
Where are tables of 8 and 9 used?
- Table of 8: An octopus has 8 arms → 3 octopuses = 3 × 8 = 24 arms. A spider has 8 legs. A chess board has 8 rows.
- Table of 9: A cricket team has 9 fielders (plus bowler and keeper). Planets in the solar system (excluding Pluto): approximately 8-9 depending on definition.
- Multiplication shortcut for 9: The finger trick and the (10 − 1) method make table of 9 one of the easiest once you know the trick.
- Money: If a pencil costs ₹8, buying 9 pencils = 9 × 8 = ₹72.
- Time: 9 hours of sleep per night × 7 nights = 63 hours of sleep per week.
Tables of 8 and 9 produce the largest single-digit products (up to 81 and 80). Mastering them completes your single-digit multiplication knowledge.
Key Points to Remember
- Table of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
- Table of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
- Table of 8 = double of table of 4.
- Table of 9: digits of each product add to 9.
- Table of 9 shortcut: 9 × n = (10 × n) − n.
- All products in table of 8 are even.
- The finger trick works for the entire table of 9.
Practice Problems
- What is 8 × 6?
- What is 9 × 8?
- Fill in: 8 × ___ = 48.
- Fill in: 9 × ___ = 45.
- Use the finger trick to find 9 × 7.
- If 4 × 6 = 24, what is 8 × 6?
- Ria earns ₹8 per day. How much in 9 days?
- Which is greater: 8 × 8 or 9 × 7?
Frequently Asked Questions
Q1. What is the finger trick for the table of 9?
Hold up 10 fingers. To find 9 × n, put down finger number n (from left). The fingers before the bent finger give the tens digit, and the fingers after give the ones digit.
Q2. Why do the digits of table-of-9 products always add to 9?
This is a mathematical property of 9. Since 9 = 10 − 1, multiplying by 9 creates a pattern where the tens digit increases by 1 and the ones digit decreases by 1, keeping their sum at 9.
Q3. How can I use the table of 4 to find table of 8?
Double each product of table of 4. For example, 4 × 7 = 28, so 8 × 7 = 56 (28 × 2).
Q4. What is 8 × 8?
8 × 8 = 64. This is a perfect square.
Q5. What is 9 × 9?
9 × 9 = 81. This is a perfect square. Check: 8 + 1 = 9.
Q6. How is 9 × n related to 10 × n?
9 × n = (10 × n) − n. For example, 9 × 7 = 70 − 7 = 63. This is a useful shortcut.
Q7. Which number is in both the tables of 8 and 9?
72 is the smallest common multiple in both tables. 8 × 9 = 72 and 9 × 8 = 72.
Q8. Are the tables of 8 and 9 the hardest to learn?
Many students find them challenging because the products are larger. Using shortcuts (doubling table of 4 for 8, digit-sum trick for 9) makes them much easier.
Related Topics
- Multiplication Tables of 6 and 7
- Multiplication Tables of 3 and 4
- Multiplication Concept (Grade 3)
- Multiplication by 10 and 100
- Multiplication of 2-Digit by 1-Digit
- Multiplication Word Problems (Grade 3)
- Properties of Multiplication
- Multiplying by 0 and 1
- Multiplication Tables (2 to 10)
- Multiplication of 2-Digit Numbers (Grade 3)
