Class 2
CBSE
UP Board
📘 What's inside:
Concept 1 — What is Multiplication?
```Multiplication is a fast way of adding the same number again and again. Instead of adding equal groups one by one, we use multiplication to find the total in one step.
Multiplication in real life:
Each child gets 3 pencils. There are 4 children. How many pencils in total? → 3 × 4 = 12 A box has 5 chocolates. There are 6 boxes. Total chocolates? → 5 × 6 = 30 A wheel has 4 spokes. A bicycle has 2 wheels. Total spokes? → 4 × 2 = 8
▶ What Happens in Multiplication
- We add the same number a certain number of times.
- The numbers we multiply are called factors.
- The answer is called the product.
- Multiplication is a shortcut for repeated addition.
⚠ Remember
Multiplication means adding equal groups. If the groups are not equal, we cannot use multiplication directly. For example, 3 + 3 + 3 = 3 × 3, but 3 + 4 + 5 cannot be written as a single multiplication.
▶ Solved Example 1
There are 3 bags. Each bag has 4 apples. How many apples are there in all?
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12
3 groups of 4 apples = 12 apples
- 1Each bag has 4 apples. There are 3 bags.
- 2Repeated addition: 4 + 4 + 4 = 12.
- 3Write as multiplication: 4 × 3 = 12.
4 × 3 = 12. There are 12 apples in all.
▶ Solved Example 2
5 children are sitting in a row. Each child has 2 hands. How many hands are there in all?
- 1Each child has 2 hands. There are 5 children.
- 2Repeated addition: 2 + 2 + 2 + 2 + 2 = 10.
- 3Multiplication: 2 × 5 = 10.
2 × 5 = 10. There are 10 hands in all.
✍ Practice — Concept 1
Q1
A box has 6 eggs. There are 3 boxes. How many eggs are there in all? Write as repeated addition and as multiplication.
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Answer
Repeated addition: 6 + 6 + 6 = 18
Multiplication: 6 × 3 = 18
There are 18 eggs in all.
Multiplication: 6 × 3 = 18
There are 18 eggs in all.
Q2
Which of these is multiplication? (a) 3 + 5 + 7 (b) 4 + 4 + 4 + 4
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Answer
(a) 3 + 5 + 7 — the numbers are not equal. This is just addition, not repeated addition.
(b) 4 + 4 + 4 + 4 — the same number (4) is added 4 times. This is multiplication: 4 × 4 = 16.
Answer: (b)
(b) 4 + 4 + 4 + 4 — the same number (4) is added 4 times. This is multiplication: 4 × 4 = 16.
Answer: (b)
Q3
A spider has 8 legs. There are 4 spiders. How many legs in total?
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Answer
Repeated addition: 8 + 8 + 8 + 8 = 32
Multiplication: 8 × 4 = 32
There are 32 legs in total.
Multiplication: 8 × 4 = 32
There are 32 legs in total.
Concept 2 — The × and = Symbols
```Multiplication uses special symbols to write the operation quickly and clearly.
×
Times / Multiply sign
Means “multiplied by” or “times”.
=
Equals sign
Means “is equal to” or “gives”.
3×4=12
Together
3 times 4 equals 12.
▶ Reading the × Symbol
- × is read as “multiplied by”, “times”, or “groups of”.
- 3 × 4 can be read as: 3 times 4, or 3 multiplied by 4, or 3 groups of 4.
- = means both sides have the same value.
- The × symbol is also written as a dot (3 · 4) in higher classes, but at this level we always use ×.
▶ Solved Example 3
Read this multiplication statement and write its meaning in words: 5 × 3 = 15
- 15 is the first factor — the size of each group.
- 2× means “multiplied by” or “times”.
- 33 is the second factor — the number of groups.
- 4= means “equals” or “gives”.
- 515 is the product — the total.
“Five times three equals fifteen.” Meaning: 5 added 3 times gives 15.
✍ Practice — Concept 2
Q4
Read aloud and write in words: 7 × 2 = 14
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Answer
“Seven times two equals fourteen.”
Meaning: 7 added 2 times gives 14. (7 + 7 = 14)
Meaning: 7 added 2 times gives 14. (7 + 7 = 14)
Q5
Fill in the symbol (× or =): (a) 4 ___ 3 ___ 12 (b) 6 ___ 2 ___ 12
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Answer
(a) 4 × 3 = 12
(b) 6 × 2 = 12
(b) 6 × 2 = 12
Concept 3 — The Multiplication Sentence
```When we write a multiplication using numbers and symbols, it is called a multiplication sentence. Every multiplication sentence has three parts.
3
×
4
=
12
▲ Factor 1
▲ Factor 2
▲ Product
▶ Parts of a Multiplication Sentence
- Factor — each number being multiplied. There are two factors.
- Product — the answer; the total when groups are combined.
- Structure: Factor × Factor = Product
- The first factor often tells the size of each group; the second factor tells the number of groups.
▶ Solved Example 4
Identify the factors and product in: 6 × 4 = 24
6
×
4
=
24
▲ Factor 1 = 6
▲ Factor 2 = 4
▲ Product = 24
Factor 1 = 6 Factor 2 = 4 Product = 24
▶ Solved Example 5
Write a multiplication sentence: “There are 5 plates. Each plate has 3 biscuits. Total biscuits = 15.”
- 1Factor 1: 3 (biscuits per plate).
- 2Factor 2: 5 (number of plates).
- 3Product: 15 (total biscuits).
3
×
5
=
15
Multiplication sentence: 3 × 5 = 15
✍ Practice — Concept 3
Q6
In 8 × 3 = 24, name the factors and product.
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Answer
Factor 1: 8 Factor 2: 3 Product: 24
Q7
Write a multiplication sentence: A flower has 5 petals. There are 4 flowers. Total petals = 20.
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Answer
Factor 1 = 5 (petals per flower). Factor 2 = 4 (flowers).
Multiplication sentence: 5 × 4 = 20
Multiplication sentence: 5 × 4 = 20
Q8
Find the missing product: (a) 3 × 7 = ___ (b) 9 × 2 = ___ (c) 5 × 5 = ___
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Answer
(a) 3 × 7 = 21 (3+3+3+3+3+3+3)
(b) 9 × 2 = 18 (9+9)
(c) 5 × 5 = 25 (5+5+5+5+5)
(b) 9 × 2 = 18 (9+9)
(c) 5 × 5 = 25 (5+5+5+5+5)
Concept 4 — Multiplication as Repeated Addition
```Every multiplication fact can be written as a repeated addition. Understanding this connection is the key to learning multiplication tables later.
▶ Converting Between Repeated Addition and Multiplication
- Repeated addition → multiplication: Count how many times the number repeats → that is the second factor.
- Multiplication → repeated addition: Write the first factor the number of times shown by the second factor.
- Example: 5 + 5 + 5 = 5 × 3 = 15
- Example: 6 × 4 = 6 + 6 + 6 + 6 = 24
▶ Solved Example 6
Write the repeated addition for 4 × 5 and find the product.
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20
5 groups of 4 = 20
4 + 4 + 4 + 4 + 4 = 20
⇨
4 × 5 = 20
4 × 5 = 20
▶ Solved Example 7
Write as a multiplication sentence: 7 + 7 + 7 = 21
- 1The number being repeated is 7 → first factor.
- 2It appears 3 times → second factor.
- 3Multiplication sentence: 7 × 3 = 21.
7 + 7 + 7 = 21
⇨
7 × 3 = 21
7 + 7 + 7 = 7 × 3 = 21
▶ Solved Example 8
Write as repeated addition: 9 × 4. Find the product.
- 19 × 4 means: add 9 a total of 4 times.
- 2Repeated addition: 9 + 9 + 9 + 9.
- 3Add step by step: 9 + 9 = 18, 18 + 9 = 27, 27 + 9 = 36.
9 × 4
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9 + 9 + 9 + 9 = 36
9 × 4 = 36
✍ Practice — Concept 4
Q9
Write as multiplication: 6 + 6 + 6 + 6 = 24
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Answer
6 is repeated 4 times.
6 × 4 = 24
6 × 4 = 24
Q10
Write as repeated addition: 8 × 3. Find the product.
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Answer
8 × 3 means add 8 three times:
8 + 8 + 8 = 24
Product = 24
8 + 8 + 8 = 24
Product = 24
Q11
Fill in: (a) 5 × 6 = 5 + 5 + 5 + ___ + ___ + ___ = ___ (b) ___ + ___ + ___ = 4 × 3 = ___
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Answer
(a) 5 × 6 = 5 + 5 + 5 + 5 + 5 + 5 = 30
(b) 4 + 4 + 4 = 4 × 3 = 12
(b) 4 + 4 + 4 = 4 × 3 = 12
Q12
Anu says 3 + 3 + 3 + 3 = 3 × 4. Is she correct? Why?
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Answer
Yes, Anu is correct.
3 is added 4 times, so: 3 + 3 + 3 + 3 = 3 × 4 = 12. ✓
3 is added 4 times, so: 3 + 3 + 3 + 3 = 3 × 4 = 12. ✓
Concept 5 — Properties of Multiplication
```Multiplication has some very useful properties that make calculations easier. Learning these now will help greatly with multiplication tables.
Multiply by 1
Any number multiplied by 1 gives the same number.
7 × 1 = 7
1 × 9 = 9
1 group of anything = that thing itself.
7 × 1 = 7
1 × 9 = 9
1 group of anything = that thing itself.
Multiply by 0
Any number multiplied by 0 is always 0.
8 × 0 = 0
0 × 5 = 0
0 groups of anything = nothing.
8 × 0 = 0
0 × 5 = 0
0 groups of anything = nothing.
Commutative Property
Changing the order of factors does not change the product.
3 × 4 = 4 × 3 = 12
6 × 2 = 2 × 6 = 12
Order does not matter in multiplication.
3 × 4 = 4 × 3 = 12
6 × 2 = 2 × 6 = 12
Order does not matter in multiplication.
Multiply by 2
Any number multiplied by 2 is the same as doubling it.
6 × 2 = 12 (double 6)
9 × 2 = 18 (double 9)
Multiply by 2 = add the number to itself.
6 × 2 = 12 (double 6)
9 × 2 = 18 (double 9)
Multiply by 2 = add the number to itself.
▶ Solved Example 9
Show that 3 × 5 = 5 × 3. What property is this?
- 13 × 5 = 3 + 3 + 3 + 3 + 3 = 15.
- 25 × 3 = 5 + 5 + 5 = 15.
- 3Both give 15. The product is the same even when the order of factors is swapped.
3 × 5 = 5 × 3 = 15. This is the Commutative Property of multiplication.
✍ Practice — Concept 5
Q13
Fill in: (a) 6 × 0 = ___ (b) ___ × 1 = 9 (c) 4 × 2 = ___
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Answer
(a) 6 × 0 = 0 (multiply by zero)
(b) 9 × 1 = 9 (multiply by one)
(c) 4 × 2 = 8 (double 4)
(b) 9 × 1 = 9 (multiply by one)
(c) 4 × 2 = 8 (double 4)
Q14
True or False: 7 × 3 = 3 × 7. Show working.
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Answer
True. 7 × 3 = 7+7+7 = 21. 3 × 7 = 3+3+3+3+3+3+3 = 21.
Both equal 21. This is the Commutative Property.
Both equal 21. This is the Commutative Property.
Concept 6 — Multiplication on a Number Line
```Just like addition uses forward jumps on a number line, multiplication uses equal forward jumps. Each jump is the same size (the first factor), and we make as many jumps as the second factor tells us.
▶ Steps to Show Multiplication on a Number Line
- Start at 0.
- Make equal jumps to the right, each of size equal to the first factor.
- Make as many jumps as the second factor.
- The number you land on is the product.
▶ Solved Example 10
Show 3 × 4 = 12 on a number line.
- 1Start at 0.
- 2Jump 3 steps forward, 4 times: 0→3→6→9→12.
- 3Land on 12. That is the product.
3 × 4 = 12
▶ Solved Example 11
Show 5 × 3 = 15 on a number line.
- 1Start at 0. Jump 5 steps, 3 times.
- 20 → 5 → 10 → 15.
5 × 3 = 15
✍ Practice — Concept 6
Q15
A number line shows 4 equal jumps of 2 each starting from 0. What multiplication does this show?
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Answer
Jump size = 2. Number of jumps = 4. Lands on 8.
2 × 4 = 8
2 × 4 = 8
Q16
Show 6 × 2 = 12 using a number line. Describe the jumps.
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Answer
Start at 0. Make 2 jumps of 6 each: 0 → 6 → 12.
6 × 2 = 12
6 × 2 = 12
★ Key Points to Remember
- Multiplication is a shortcut for repeated addition of equal groups.
- The numbers being multiplied are called factors. The answer is the product.
- Structure: Factor × Factor = Product.
- Any number × 0 = 0. Any number × 1 = that number.
- Multiplication is commutative — swapping the factors does not change the product. (3 × 4 = 4 × 3)
- Multiplying by 2 = doubling the number.
- On a number line, multiplication means making equal jumps to the right starting from 0.
Exam Style — Class 2
6 Questions on What is Multiplication
Q1
Name the factors and product in: 9 × 3 = 27. Write this sentence in words.
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Answer
Factor 1: 9 Factor 2: 3 Product: 27
In words: “Nine times three equals twenty-seven.”
In words: “Nine times three equals twenty-seven.”
Q2
Write as multiplication and find the product: 5 + 5 + 5 + 5 + 5 + 5
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Answer
5 is added 6 times.
Multiplication: 5 × 6 = 30
Repeated addition check: 5+5=10, 10+5=15, 15+5=20, 20+5=25, 25+5=30. ✓
Multiplication: 5 × 6 = 30
Repeated addition check: 5+5=10, 10+5=15, 15+5=20, 20+5=25, 25+5=30. ✓
Q3
Fill in using properties: (a) 12 × 0 = ___ (b) ___ × 1 = 7 (c) 4 × 3 = 3 × ___
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Answer
(a) 12 × 0 = 0 (multiply by zero)
(b) 7 × 1 = 7 (multiply by one)
(c) 4 × 3 = 3 × 4 (commutative property)
(b) 7 × 1 = 7 (multiply by one)
(c) 4 × 3 = 3 × 4 (commutative property)
Q4
A rickshaw has 3 wheels. There are 8 rickshaws. How many wheels are there in total? Write the repeated addition and the multiplication sentence.
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Answer
Repeated addition: 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
Multiplication sentence: 3 × 8 = 24
There are 24 wheels in total.
Multiplication sentence: 3 × 8 = 24
There are 24 wheels in total.
Q5
A number line shows 3 equal jumps of 4. Write the multiplication sentence and the product.
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Answer
Jump size = 4. Number of jumps = 3. Lands on 12.
Multiplication sentence: 4 × 3 = 12
Multiplication sentence: 4 × 3 = 12
Q6
Ravi writes 2 × 8 = 8 × 2. Is he correct? Name the property and verify by finding both products.
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Answer
Yes, Ravi is correct.
2 × 8 = 2+2+2+2+2+2+2+2 = 16
8 × 2 = 8+8 = 16
Both give 16. This is the Commutative Property of multiplication — the order of factors does not change the product.
2 × 8 = 2+2+2+2+2+2+2+2 = 16
8 × 2 = 8+8 = 16
Both give 16. This is the Commutative Property of multiplication — the order of factors does not change the product.
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