Multiplying by 0 and 1
What happens when you multiply a number by 0? What happens when you multiply by 1? These are two special rules in multiplication that every Class 3 student must know.
These rules are called the zero property and the identity property (or multiplicative identity). They work for every number — small or big.
What is Multiplying by 0 and 1 - Class 3 Maths (Multiplication)?
Zero Property: When you multiply any number by 0, the answer is always 0.
Identity Property: When you multiply any number by 1, the answer is the number itself.
a × 0 = 0 | a × 1 = a
Types and Properties
Why does multiplying by 0 give 0?
Multiplication means repeated addition. If you add a number 0 times, you have nothing.
- 5 × 0 means: add 5 zero times → 0
- 0 × 7 means: add 0 seven times → 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
Why does multiplying by 1 give the same number?
If you add a number 1 time, you just have that number.
- 8 × 1 means: add 8 one time → 8
- 1 × 6 means: add 1 six times → 1 + 1 + 1 + 1 + 1 + 1 = 6
Solved Examples
Example 1: Multiply by 0 — Small Number
Question: Find 7 × 0.
Think:
- Any number times 0 = 0
- 7 × 0 = 0
Answer: 7 × 0 = 0.
Example 2: Multiply by 0 — Larger Number
Question: Find 258 × 0.
Think:
- It does not matter how big the number is.
- Any number × 0 = 0
Answer: 258 × 0 = 0.
Example 3: Multiply by 0 — Word Problem
Question: Aman has 6 empty boxes. Each box has 0 chocolates. How many chocolates does he have?
Think:
- Chocolates per box = 0
- Total = 6 × 0 = 0
Answer: Aman has 0 chocolates.
Example 4: Multiply by 1 — Small Number
Question: Find 9 × 1.
Think:
- Any number times 1 = the number itself
- 9 × 1 = 9
Answer: 9 × 1 = 9.
Example 5: Multiply by 1 — Larger Number
Question: Find 1 × 463.
Think:
- 1 × any number = that number
- 1 × 463 = 463
Answer: 1 × 463 = 463.
Example 6: Multiply by 1 — Word Problem
Question: Priya has 1 basket with 12 mangoes. How many mangoes does she have?
Think:
- Baskets = 1, mangoes per basket = 12
- 1 × 12 = 12
Answer: Priya has 12 mangoes.
Example 7: Fill in the Blank
Question: 0 × ___ = 0. What number goes in the blank?
Think:
- 0 multiplied by any number gives 0.
- Any number can go in the blank.
Answer: Any number works. 0 × 5 = 0, 0 × 100 = 0, 0 × 999 = 0.
Example 8: Compare Products
Question: Which is greater: 45 × 0 or 1 × 1?
Think:
- 45 × 0 = 0
- 1 × 1 = 1
- 1 > 0
Answer: 1 × 1 = 1 is greater.
Example 9: Pattern with 0 and 1
Question: Complete the pattern: 5 × 3 = 15, 5 × 2 = 10, 5 × 1 = ?, 5 × 0 = ?
Think:
- 5 × 1 = 5 (identity property)
- 5 × 0 = 0 (zero property)
- Notice: each time the multiplier decreases by 1, the product decreases by 5.
Answer: 5 × 1 = 5 and 5 × 0 = 0.
Key Points to Remember
- Zero property: Any number × 0 = 0. This is always true.
- Identity property: Any number × 1 = the number itself.
- These two rules work for all numbers — even very large numbers.
- 0 × 0 = 0 (both properties apply).
- 1 × 1 = 1 (identity property).
- Multiplying by 0 gives the smallest possible product (0).
- Multiplying by 1 does not change the number at all.
Practice Problems
- Find 14 × 0.
- Find 1 × 37.
- Meera has 8 plates. Each plate has 0 sweets. How many sweets are there?
- Dev has 1 bag with 25 marbles. How many marbles does he have?
- Which is greater: 100 × 0 or 0 × 100?
- Fill in the blank: ___ × 1 = 56.
- Complete the pattern: 4 × 2 = 8, 4 × 1 = ?, 4 × 0 = ?
Frequently Asked Questions
Q1. Why is any number multiplied by 0 equal to 0?
Multiplication means adding a number repeatedly. If you repeat it 0 times, you have nothing at all. So the answer is 0.
Q2. Is 0 × 0 equal to 0?
Yes. 0 × 0 = 0. The zero property says any number multiplied by 0 is 0, and 0 is a number too.
Q3. Why is multiplying by 1 called the identity property?
Because the number keeps its identity — it remains unchanged. 7 × 1 = 7. The number 7 stays as 7.
Q4. Does the order matter when multiplying by 0 or 1?
No. 0 × 5 = 5 × 0 = 0, and 1 × 9 = 9 × 1 = 9. The commutative property applies here too.
Q5. Is 1 × 1 equal to 1 or 2?
1 × 1 = 1. Multiplying by 1 keeps the number the same, so 1 stays as 1.
Q6. Can a number multiplied by 0 ever give something other than 0?
No. The zero property is an absolute rule. No matter how large the number is, multiplying it by 0 always gives 0.
Q7. What is 0 × 1?
0 × 1 = 0. The identity property says 0 × 1 = 0 (the number itself), and the zero property says 0 × anything = 0. Both give the same answer.
Q8. How do these properties help in solving problems?
They let you skip calculations. If you see any number multiplied by 0, you instantly know the answer is 0. If you see any number multiplied by 1, the answer is that number. No working needed.
Q9. Are these properties covered in NCERT Class 3?
Yes. NCERT Class 3 Maths covers multiplying by 0 and 1 as part of the multiplication chapter, teaching students to recognise patterns and properties.
Related Topics
- Properties of Multiplication
- Multiplication Concept (Grade 3)
- Multiplication Tables of 3 and 4
- Multiplication Tables of 6 and 7
- Multiplication Tables of 8 and 9
- Multiplication by 10 and 100
- Multiplication of 2-Digit by 1-Digit
- Multiplication Word Problems (Grade 3)
- Multiplication Tables (2 to 10)
- Multiplication of 2-Digit Numbers (Grade 3)
