Table of 8
The Table of 8 is essential for fast mental calculations in competitive exams. Mastering this table helps solve questions involving multiplication, division, fractions, and percentage calculations quickly. The table of 8 follows a clear pattern and can be learned using simple doubling techniques from easier tables.
1. Complete Table of 8 (Multiplication Facts)
Below is the complete multiplication table of 8 from 1 to 20. Memorizing these facts enables rapid calculation without counting or repeated addition.
- 8 × 1 = 8
- 8 × 2 = 16
- 8 × 3 = 24
- 8 × 4 = 32
- 8 × 5 = 40
- 8 × 6 = 48
- 8 × 7 = 56
- 8 × 8 = 64
- 8 × 9 = 72
- 8 × 10 = 80
- 8 × 11 = 88
- 8 × 12 = 96
- 8 × 13 = 104
- 8 × 14 = 112
- 8 × 15 = 120
- 8 × 16 = 128
- 8 × 17 = 136
- 8 × 18 = 144
- 8 × 19 = 152
- 8 × 20 = 160
1.1 Pattern Recognition in Table of 8
Understanding patterns helps in quick recall and verification of answers during exams.
- Even Number Pattern: All products in the table of 8 are even numbers. This is because 8 itself is an even number.
- Unit Digit Pattern: The unit digits repeat in a cycle: 8, 6, 4, 2, 0, 8, 6, 4, 2, 0... This five-digit cycle repeats throughout.
- Addition Pattern: Each successive product increases by 8. For example, 16 + 8 = 24, then 24 + 8 = 32.
- Divisibility Rule: Any number in the table of 8 is divisible by 8, 4, 2, and 1.
1.2 Key Benchmark Values
Certain multiplication facts serve as reference points for quick mental calculation.
- 8 × 5 = 40: Half of 80, useful for percentage calculations (8% of 50)
- 8 × 10 = 80: Foundation for calculating 8 times any multiple of 10
- 8 × 12 = 96: Frequently appears in time calculations (8 dozen)
- 8 × 15 = 120: Useful for converting minutes (8 quarters of an hour = 2 hours)
2. Doubling Method (Building from Table of 4)
The Doubling Method is the most efficient trick for learning the table of 8. Since 8 = 2 × 4, every value in the table of 8 is exactly double the corresponding value in the table of 4.
2.1 Step-by-Step Doubling Technique
This method reduces memorization load by using a simpler table you already know.
- Start with Table of 4: First recall or calculate 4 times the number
- Double the Result: Multiply the result by 2 to get 8 times the number
- Formula: 8 × n = 2 × (4 × n)
2.2 Worked Examples Using Doubling
- Example 1 - Finding 8 × 7:
- Step 1: Calculate 4 × 7 = 28
- Step 2: Double the result: 28 × 2 = 56
- Answer: 8 × 7 = 56
- Example 2 - Finding 8 × 13:
- Step 1: Calculate 4 × 13 = 52
- Step 2: Double the result: 52 × 2 = 104
- Answer: 8 × 13 = 104
- Example 3 - Finding 8 × 18:
- Step 1: Calculate 4 × 18 = 72
- Step 2: Double the result: 72 × 2 = 144
- Answer: 8 × 18 = 144
2.3 Alternative Doubling Chain Method
For students who know the table of 2 very well, you can use three successive doublings.
- Formula: 8 × n = 2 × 2 × 2 × n (since 8 = 2³)
- Process: Double the number, then double the result, then double again
- Example - Finding 8 × 9:
- First doubling: 9 × 2 = 18
- Second doubling: 18 × 2 = 36
- Third doubling: 36 × 2 = 72
- Answer: 8 × 9 = 72
3. Additional Mental Calculation Tricks
These alternative methods provide flexibility when solving problems under time pressure.
3.1 Breaking Down Method (Distributive Property)
Break the multiplier into convenient parts and add the results. This uses the Distributive Property: a × (b + c) = (a × b) + (a × c).
- Example - Finding 8 × 17:
- Break 17 as (10 + 7)
- Calculate: 8 × 10 = 80
- Calculate: 8 × 7 = 56
- Add results: 80 + 56 = 136
- Example - Finding 8 × 25:
- Break 25 as (20 + 5)
- Calculate: 8 × 20 = 160
- Calculate: 8 × 5 = 40
- Add results: 160 + 40 = 200
3.2 Using Table of 10 Method
This method works well when multiplying 8 by numbers close to multiples of 10.
- Formula: 8 × n = (8 × 10) - (8 × (10 - n)) for numbers less than 10
- Example - Finding 8 × 9:
- Calculate: 8 × 10 = 80
- Calculate: 8 × 1 = 8
- Subtract: 80 - 8 = 72
3.3 Shortcut for Multiples of 5
When multiplying 8 by any multiple of 5, use this quick method.
- Formula: 8 × (5n) = 40n
- Example 1: 8 × 15 = 8 × (5 × 3) = 40 × 3 = 120
- Example 2: 8 × 20 = 8 × (5 × 4) = 40 × 4 = 160
4. Common Student Mistakes (Trap Alerts)
Being aware of typical errors helps avoid silly mistakes during exams under time pressure.
- Confusion with Table of 6: Students often mix 8 × 7 = 56 with 6 × 8 = 48. Remember the unit digit pattern (8's table has 6 as unit digit here).
- Doubling Error: When using doubling method, students sometimes forget to double or double incorrectly. Always verify: 8 × 7 = 2 × (4 × 7) = 2 × 28 = 56, not 46.
- Carry-Over Mistakes: In 8 × 13 = 104, students sometimes write 94 by forgetting to carry over properly when doubling 52.
- Unit Digit Confusion: Remember the unit digit cycle: 8, 6, 4, 2, 0. If your answer doesn't follow this pattern, recheck your calculation.
- Mixing with Table of 9: 8 × 9 = 72, not 81 (which is 9 × 9). Cross-verify using the doubling method if unsure.
5. Strategic Practice Approach
Systematic practice with focus on weak areas ensures mastery before the exam.
5.1 Three-Stage Practice Method
- Stage 1 - Sequential Learning (Days 1-2):
- Write the table 5 times daily in sequence from 8 × 1 to 8 × 20
- Recite aloud while writing to engage auditory memory
- Focus on correct spelling of numbers (e.g., forty, not fourty)
- Stage 2 - Random Recall (Days 3-4):
- Solve random multiplication problems: 8 × 14, 8 × 7, 8 × 19, etc.
- Use flashcards or have someone quiz you in random order
- Time yourself - aim for instant recall within 2-3 seconds per fact
- Stage 3 - Application Practice (Days 5-7):
- Solve word problems requiring table of 8
- Practice division problems (inverse of multiplication)
- Mix with other tables in combined practice tests
5.2 Priority Focus Areas
Certain facts are more frequently used and deserve extra attention.
- High-Priority Facts (Memorize First): 8 × 5, 8 × 10, 8 × 8, 8 × 12, 8 × 15
- Commonly Confused Facts (Practice More): 8 × 7 = 56, 8 × 9 = 72, 8 × 13 = 104
- Extension Range (For Advanced Calculations): 8 × 16 to 8 × 20
5.3 Daily Revision Schedule
- Morning Revision: Recite the complete table once (1 minute)
- Mid-Day Practice: Solve 10 random multiplication problems (3 minutes)
- Evening Review: Test yourself on problem areas identified during the day (2 minutes)
- Weekly Test: Take a timed test mixing table of 8 with other tables
6. Division Facts (Inverse Operations)
Understanding division as the inverse of multiplication strengthens overall number sense and helps solve various exam problems.
6.1 Key Division Facts from Table of 8
- 16 ÷ 8 = 2 (because 8 × 2 = 16)
- 24 ÷ 8 = 3 (because 8 × 3 = 24)
- 32 ÷ 8 = 4 (because 8 × 4 = 32)
- 40 ÷ 8 = 5 (because 8 × 5 = 40)
- 56 ÷ 8 = 7 (because 8 × 7 = 56)
- 64 ÷ 8 = 8 (because 8 × 8 = 64)
- 72 ÷ 8 = 9 (because 8 × 9 = 72)
- 80 ÷ 8 = 10 (because 8 × 10 = 80)
- 96 ÷ 8 = 12 (because 8 × 12 = 96)
- 120 ÷ 8 = 15 (because 8 × 15 = 120)
6.2 Checking Divisibility by 8
A number is divisible by 8 if its last three digits form a number divisible by 8.
- Example 1: Is 5,128 divisible by 8? Check last three digits: 128 ÷ 8 = 16. Yes, divisible.
- Example 2: Is 3,456 divisible by 8? Check last three digits: 456 ÷ 8 = 57. Yes, divisible.
- Quick Mental Check: Divide the last three digits by 2 three times. If result is a whole number, original number is divisible by 8.
7. Exam Application Strategies
Knowing when and how to apply the table of 8 in different question types maximizes speed and accuracy.
7.1 Common Question Types
- Direct Multiplication: "What is 8 times 17?" Use doubling method or direct recall.
- Word Problems: "A box contains 8 pens. How many pens are in 15 boxes?" Apply 8 × 15 = 120.
- Time Calculations: "An event repeats every 8 hours. How many hours in 12 repetitions?" Use 8 × 12 = 96.
- Price Calculations: "If one item costs ₹8, what is the cost of 18 items?" Apply 8 × 18 = 144.
- Pattern Recognition: "Fill in the blank: 32, 40, 48, __, 64." Answer: 56 (table of 8 sequence).
7.2 Speed Calculation Tips
- For numbers 1-10: Use direct memorization (fastest method)
- For numbers 11-15: Use doubling method from table of 4
- For numbers 16-20: Use breaking down method (10 + remaining part)
- For larger numbers: Break into (multiple of 10) + (single digit) and apply distributive property
7.3 Verification Techniques
Always verify your answer using a different method to catch calculation errors.
- Unit Digit Check: Verify the unit digit follows the pattern (8, 6, 4, 2, 0)
- Reverse Division: Divide your answer by 8; you should get the original multiplier
- Approximation Check: Round to nearest 10 and see if answer is reasonable (8 × 17 ≈ 8 × 20 = 160, so 136 is reasonable)
- Doubling Verification: Check if your answer is exactly double the table of 4 value
Mastering the table of 8 through the doubling method and consistent practice enables rapid mental calculation essential for competitive exams. Focus on the high-priority facts, practice random recall daily, and apply verification techniques to ensure accuracy. Remember that 8 = 2 × 4, making the doubling method your most reliable tool for quick calculations involving 8.
