Patterns in Multiplication Tables
Multiplication tables are not just lists to memorise -- they are full of patterns. In Class 3, students explore patterns in the products of multiplication tables to understand how numbers behave and to remember tables faster.
Spotting patterns in tables helps build number sense, mental maths skills, and makes multiplication easier.
What is Patterns in Multiplication Tables - Class 3 Maths (Patterns)?
A pattern in multiplication tables is a repeating or predictable feature found in the products (answers) of a times table. These patterns relate to even/odd numbers, digit sums, last digits, and relationships between different tables.
Types and Properties
Common patterns in multiplication tables:
- Table of 2: All products are even numbers. Last digits repeat: 2, 4, 6, 8, 0.
- Table of 5: Products always end in 0 or 5.
- Table of 9: The digits of each product add up to 9 (e.g., 18 → 1+8=9, 27 → 2+7=9).
- Table of 10: Just add a 0 at the end of the number.
- Even tables (2, 4, 6, 8, 10): All products are even.
- Odd tables (3, 5, 7, 9): Products alternate between odd and even.
Solved Examples
Example 1: Pattern in Table of 2
Question: Write the first 10 multiples of 2 and find the pattern in the last digit.
Think:
- 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
- Last digits: 2, 4, 6, 8, 0, 2, 4, 6, 8, 0
Answer: The last digits repeat in a cycle: 2, 4, 6, 8, 0.
Example 2: Pattern in Table of 5
Question: What pattern do you see in the table of 5?
Think:
- 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
- Last digits alternate: 5, 0, 5, 0, 5, 0, ...
Answer: Products of 5 always end in 5 or 0.
Example 3: Digit Sum Pattern in Table of 9
Question: Find the digit sum of each product in the table of 9 (from 9 x 1 to 9 x 10).
Think:
- 9→9, 18→1+8=9, 27→2+7=9, 36→3+6=9, 45→4+5=9
- 54→5+4=9, 63→6+3=9, 72→7+2=9, 81→8+1=9, 90→9+0=9
Answer: The digit sum is always 9.
Example 4: Finger Trick for Table of 9
Question: Use the finger trick to find 9 x 4.
Think:
- Hold up 10 fingers. Fold down the 4th finger from the left.
- Fingers before the folded one = 3 (tens digit)
- Fingers after the folded one = 6 (ones digit)
- Answer = 36
Answer: 9 x 4 = 36.
Example 5: Even and Odd Products
Question: In the table of 3, are the products always even, always odd, or mixed?
Think:
- 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- Odd: 3, 9, 15, 21, 27. Even: 6, 12, 18, 24, 30.
- They alternate: odd, even, odd, even, ...
Answer: Products of 3 alternate between odd and even.
Example 6: Pattern in Table of 10
Question: What is the pattern in the table of 10?
Think:
- 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
- Each product is the number with a 0 at the end.
Answer: To multiply by 10, add a zero at the end of the number.
Example 7: Relationship Between Table of 4 and Table of 2
Question: Compare the table of 4 with the table of 2. What do you notice?
Think:
- Table of 2: 2, 4, 6, 8, 10, ...
- Table of 4: 4, 8, 12, 16, 20, ...
- Each product of 4 is double the corresponding product of 2.
Answer: The table of 4 is double the table of 2.
Example 8: Last Digit Pattern in Table of 6
Question: Write the last digits of the first 10 multiples of 6.
Think:
- 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
- Last digits: 6, 2, 8, 4, 0, 6, 2, 8, 4, 0
Answer: The last digits repeat: 6, 2, 8, 4, 0.
Example 9: Commutative Property Pattern
Question: Aman notices that 3 x 7 = 21 and 7 x 3 = 21. Is this always true?
Think:
- 4 x 5 = 20 and 5 x 4 = 20 ✓
- 6 x 2 = 12 and 2 x 6 = 12 ✓
- Swapping the numbers gives the same product.
Answer: Yes, this is always true. This is the commutative property: a x b = b x a.
Key Points to Remember
- Table of 2: Last digits cycle through 2, 4, 6, 8, 0. All products are even.
- Table of 5: Products end in 0 or 5.
- Table of 9: Digit sums always equal 9. The tens digit goes up and the ones digit goes down.
- Table of 10: Add a zero to the number.
- Odd number tables produce alternating odd and even products.
- Even number tables produce only even products.
- The commutative property (a x b = b x a) means you only need to learn half the tables.
- Table of 4 = double the table of 2. Table of 8 = double the table of 4.
Practice Problems
- Write the last digits of the first 10 multiples of 3. Do they repeat?
- In the table of 7, list the odd products from 7 x 1 to 7 x 10.
- Use the digit sum pattern to check if 54 is a multiple of 9.
- The table of 6 is double which table?
- Use the finger trick to find 9 x 7.
- Write the first 10 multiples of 4. Compare with the table of 2.
- Is 35 a multiple of 5? How can you tell without dividing?
Frequently Asked Questions
Q1. What patterns are found in multiplication tables?
Common patterns include repeating last digits (table of 2: 2,4,6,8,0), products ending in 0 or 5 (table of 5), digit sums equalling 9 (table of 9), and even/odd alternation.
Q2. Why are patterns in multiplication tables useful?
Patterns help memorise tables faster, check answers quickly, and understand how numbers relate to each other. For example, knowing products of 5 end in 0 or 5 helps verify answers.
Q3. What is the digit sum rule for 9?
The digits of any multiple of 9 add up to 9 (or a multiple of 9). For example, 27: 2+7=9; 63: 6+3=9; 81: 8+1=9.
Q4. What is the commutative property of multiplication?
The commutative property states that changing the order of factors does not change the product. So 3 x 5 = 5 x 3 = 15.
Q5. Are all multiples of 2 even numbers?
Yes. Every multiple of 2 is an even number. The table of 2 produces: 2, 4, 6, 8, 10, 12, and so on -- all even.
Q6. How is the table of 4 related to the table of 2?
Each product in the table of 4 is double the corresponding product in the table of 2. For example, 2 x 3 = 6 and 4 x 3 = 12 (double of 6).
Q7. Do odd tables give only odd products?
No. Odd tables (like 3, 5, 7, 9) give products that alternate between odd and even. For example, 3 x 1 = 3 (odd), 3 x 2 = 6 (even), 3 x 3 = 9 (odd).
Q8. Are patterns in multiplication tables covered in NCERT Class 3?
Yes. Exploring patterns in multiplication tables is part of the Patterns chapter in NCERT Class 3 Maths.
