Solved Exercises on Multiplication to Solve in Grade 2

Master multiplication foundations: using multiplication to solve problems, repeated addition, and number patterns through these 3 detailed exercises with complete answers.

Solution: Exercises 1 to 3
1 Basic Multiplication
Exercise 1
Solve: 4 × 6 using repeated addition
Definition:

Multiplication: Repeated addition of the same number

Formula: a × b = adding 'a' to itself 'b' times

Multiplication method:
  1. Identify the number being added (first factor)
  2. Identify how many times it's added (second factor)
  3. Add the first number to itself the specified number of times
Expression
4 × 6
Repeated Addition
4 + 4 + 4 + 4 + 4 + 4
Result
24
Step 1: Understand the problem

4 × 6 means adding 4 to itself 6 times

Step 2: Write repeated addition

4 + 4 + 4 + 4 + 4 + 4

Step 3: Add step by step

4 + 4 = 8, then 8 + 4 = 12, then 12 + 4 = 16, then 16 + 4 = 20, then 20 + 4 = 24

4 × 6 = 24
Final answer:

4 × 6 = 24

Applied rules:

• Multiplication as repeated addition: a × b = a + a + ... (b times)

• Commutative property: 4 × 6 = 6 × 4

• Counting: Keep track of additions made

2 Multiplication Pattern
Exercise 2
Find the missing number: 8 × ? = 32
Definition:

Multiplication Pattern: Using known facts to find missing numbers

Problem
8 × ? = 32
Solution
32 ÷ 8 = 4
Result
4
Step 1: Understand the problem

We need to find how many times 8 goes into 32

Step 2: Think about multiplication facts

What number times 8 equals 32?

Step 3: Use division to check

32 ÷ 8 = 4, so 8 × 4 = 32

Step 4: Verify with repeated addition

8 + 8 + 8 + 8 = 32

8 × 4 = 32
Final answer:

The missing number is 4

Applied rules:

• Division as inverse of multiplication: If a × b = c, then c ÷ a = b

• Pattern recognition: Notice that 8 × 4 = 32

• Verification: Check with repeated addition

3 Word Problem
Exercise 3
There are 5 rows of chairs in a classroom. Each row has 6 chairs. How many chairs are there in total?
Definition:

Word Problem: Real-life situation requiring mathematical solution

Problem
5 rows × 6 chairs
Expression
5 × 6
Result
30
Step 1: Identify key information

5 rows, 6 chairs per row

Step 2: Set up multiplication

Number of rows × Chairs per row = Total chairs

5 × 6 = ?

Step 3: Calculate

5 × 6 = 6 + 6 + 6 + 6 + 6 = 30

Step 4: Answer the question

There are 30 chairs in total

5 × 6 = 30 chairs
Final answer:

There are 30 chairs in total

Applied rules:

• Word problem solving: Identify numbers and operation needed

• Multiplication context: Groups of equal size

• Units: Include units in final answer

Multiplication Rules and Methods
\(a \times b = \underbrace{a + a + a + \ldots + a}_{b \text{ times}}\)
Multiplication as Repeated Addition
Rule 1
Any number × 0 = 0
Multiplying by zero
Rule 2
Any number × 1 = number
Multiplying by one
Rule 3
a × b = b × a
Commutative property
× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100
Key definitions:

Multiplication: Adding the same number multiple times

Factors: Numbers being multiplied together

Product: Result of multiplication

Multiplication strategies:
  1. Repeated Addition: Add the first number to itself the second number of times
  2. Counting by Multiples: Skip count (2, 4, 6, 8...)
  3. Visual Arrays: Organize items in rows and columns
  4. Using Known Facts: Build on familiar multiplication facts
Tip 1: Remember the zero rule: any number times 0 equals 0.
Tip 2: The identity rule: any number times 1 equals itself.
Tip 3: Order doesn't matter: 3×4 = 4×3.
Tip 4: Draw pictures to visualize multiplication problems.
Common errors: Confusing multiplication with addition, forgetting to count all groups.
Practice tips: Use objects like counters, practice with small numbers first.
Multiplication facts for 1-10:

• 1's: 1×1=1, 1×2=2, 1×3=3, ..., 1×10=10

• 2's: 2×1=2, 2×2=4, 2×3=6, ..., 2×10=20

• 3's: 3×1=3, 3×2=6, 3×3=9, ..., 3×10=30

• 4's: 4×1=4, 4×2=8, 4×3=12, ..., 4×10=40

• 5's: 5×1=5, 5×2=10, 5×3=15, ..., 5×10=50

• 6's: 6×1=6, 6×2=12, 6×3=18, ..., 6×10=60

• 7's: 7×1=7, 7×2=14, 7×3=21, ..., 7×10=70

• 8's: 8×1=8, 8×2=16, 8×3=24, ..., 8×10=80

• 9's: 9×1=9, 9×2=18, 9×3=27, ..., 9×10=90

• 10's: 10×1=10, 10×2=20, 10×3=30, ..., 10×10=100

Multiplication Summary: Key Concepts & Strategies

This comprehensive summary covers all essential concepts for using multiplication to solve problems in 2nd grade.

Definitions

Multiplication: A mathematical operation that represents repeated addition of the same number. It's faster than adding the same number multiple times.

Factors: The numbers being multiplied together (in 3×4, the factors are 3 and 4).

Product: The result of multiplying two or more numbers (in 3×4=12, the product is 12).

Groups: Sets of equal amounts (3 groups of 4 means 3 sets with 4 items in each set).

Patterns: Regular sequences in multiplication results (like counting by 5s: 5, 10, 15, 20...).

Core Rules & Laws

Zero Property: Any number multiplied by 0 equals 0 (a×0=0).

Identity Property: Any number multiplied by 1 equals itself (a×1=a).

Commutative Property: The order of factors doesn't change the product (a×b=b×a).

Associative Property: The grouping of factors doesn't change the product ((a×b)×c=a×(b×c)).

Distributive Property: a×(b+c) = (a×b) + (a×c).

Methods & Procedures

Repeated Addition Method: Convert multiplication to addition (3×4 = 4+4+4 = 12).

Counting by Multiples: Skip count by the second factor (for 4×3, count by 3s: 3, 6, 9, 12).

Visual Arrays: Arrange items in rows and columns to see multiplication patterns.

Pattern Recognition: Notice patterns in multiplication tables (even numbers in 2s table, etc.).

Using Known Facts: Build on familiar facts to solve unknown ones (if 5×4=20, then 6×4=20+4=24).

Examples (Simple → Advanced)

Simple: 2×3 = 3+3 = 6

Intermediate: 4×5 = 5+5+5+5 = 20

Advanced: 7×8 = 8+8+8+8+8+8+8 = 56

Word Problem: 6 friends have 4 stickers each → 6×4 = 24 stickers total

Pattern Problem: If 7×3=21, then 7×4=21+7=28

Tips & Tricks

Memorize Patterns: 2's are doubles, 5's end in 0 or 5, 10's add a zero.

Use Known Facts: If you know 2×4=8, then 4×2=8 too (commutative property).

Check Your Work: Reverse the operation (if 3×4=12, then 12÷4=3).

Visualize: Draw circles or dots to represent groups.

Build Up: Use known facts to figure out harder ones (7×6 = 5×6 + 2×6 = 30+12 = 42).

Key Notes for Memorization

Rhymes: "5, 10, 15, 20 - multiples of 5 are easy!"

Patterns: In the 9s table, digits add up to 9 (9×2=18, 1+8=9).

Building Blocks: Start with 2s, then 5s, then 10s, then others.

Practice Daily: Just 5-10 minutes daily builds strong memory.

Flashcards: Use physical or digital flashcards for regular practice.

Steps to Solve Multiplication Problems

Follow these steps to solve multiplication problems effectively:

Step 1
Read the problem carefully
Step 2
Identify the numbers involved
Step 3
Decide if multiplication is needed
Step 4
Set up the multiplication
Step 5
Calculate the answer
Step 6
Check your answer

Practice Problems: Multiplication to Solve

Try these practice problems to improve your multiplication skills:

Q1
3 × 7 = ?
Q2
5 × 4 = ?
Q3
6 × 8 = ?
Q4
9 × 2 = ?
Q5
7 × 5 = ?
Q6
4 × 6 = ?

Questions & Answers

Question: I'm confused about multiplication. Why is 3×4 the same as 4×3? They look different to me.

Answer: Great question! This is called the commutative property of multiplication. Let me explain with an example:

• 3×4 means 3 groups of 4 items each: 🍎🍎🍎🍎 + 🍎🍎🍎🍎 + 🍎🍎🍎🍎 = 12 apples

• 4×3 means 4 groups of 3 items each: 🍎🍎🍎 + 🍎🍎🍎 + 🍎🍎🍎 + 🍎🍎🍎 = 12 apples

Both ways, you end up with 12 apples total! Even though the groups look different (3 big groups vs 4 smaller groups), the total amount stays the same.

Think of it like a rectangle: 3 rows of 4 dots makes the same rectangle as 4 rows of 3 dots.

Question: I keep forgetting my multiplication facts. Is there an easy way to remember them?

Answer: Yes, here are some helpful strategies for remembering multiplication facts:

  • Start with patterns: Multiplying by 1 always gives the same number (5×1=5)
  • Count by 2s: 2, 4, 6, 8, 10... This helps with the 2 times table
  • Count by 5s: 5, 10, 15, 20, 25... These are easier to remember
  • Draw pictures: Draw groups of items to visualize the multiplication
  • Practice with songs: Many children learn through music and rhythm

Remember, it's okay to use repeated addition when you're just learning: 3×4 = 3+3+3+3 = 12.

Practice a little bit every day, and soon these facts will become automatic!

Question: My child understands multiplication as repeated addition, but struggles with word problems. How can I help?

Answer: This is very common! Here's a systematic approach to help with word problems:

  1. Read carefully: Have your child read the problem twice
  2. Find key words: Look for words like "each", "groups", "total", "altogether"
  3. Identify numbers: Circle or underline important numbers
  4. Draw a picture: Sketch the situation described
  5. Write the equation: Convert the word problem to a number sentence
  6. Solve: Use multiplication to find the answer
  7. Check: Make sure the answer makes sense in the story

Practice with simple, relatable scenarios first (like sharing cookies or arranging toys) before moving to more complex problems.