Solved Exercises on Multiplication Pre-Test in Grade 3

Master multiplication basics: repeated addition, arrays, and word problems through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic multiplication
Exercise 1
Solve:
\(4 \times 3 = ?\)
Definition:

Multiplication: Repeated addition of the same number

Multiplication method:
  1. Understand multiplication as repeated addition
  2. Add the first number as many times as the second number indicates
  3. Count the total to get the product
Expression
\(4 \times 3\)
Repeated Addition
\(4 + 4 + 4\)
Result
\(12\)
4
4
4
3 groups of 4
Step 1: Understand the problem

\(4 \times 3\) means 4 added 3 times

Step 2: Convert to repeated addition

\(4 \times 3 = 4 + 4 + 4\)

Step 3: Calculate the sum

\(4 + 4 + 4 = 12\)

\(4 \times 3 = 12\)
Final answer:

\(4 \times 3 = 12\)

Applied rules:

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

• Commutative property: \(4 \times 3 = 3 \times 4\)

• Grouping concept: Understanding equal groups

2 Array representation
Exercise 2
Show \(3 \times 5\) using an array
Definition:

Array: Rectangular arrangement of objects in rows and columns

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Expression
\(3 \times 5\)
Rows × Columns
\(3 \times 5\)
Total Count
\(15\)
Step 1: Identify the factors

\(3 \times 5\) means 3 rows and 5 columns

Step 2: Draw the array

Create 3 rows with 5 items in each row

Step 3: Count the total

Count all items: \(3 \times 5 = 15\)

\(3 \times 5 = 15\)
Final answer:

\(3 \times 5 = 15\)

Applied rules:

• Array model: Visual representation of multiplication

• Rows × Columns: Total items in rectangular array

• Visual grouping: Helps understand multiplication concept

3 Word problem
Exercise 3
Sarah has 4 bags of apples. Each bag has 6 apples. How many apples does Sarah have in total?
Definition:

Word problem: Real-life situation requiring mathematical solution

Given
4 bags × 6 apples
Operation
\(4 \times 6\)
Result
\(24\)
Step 1: Identify the key information

Sarah has 4 bags, each containing 6 apples

Step 2: Determine the operation

We need to find the total number of apples: 4 groups of 6

Step 3: Set up the multiplication

Total = Number of bags × Apples per bag = \(4 \times 6\)

Step 4: Calculate the result

\(4 \times 6 = 24\)

Step 5: State the answer

Sarah has 24 apples in total

Sarah has 24 apples in total
Final answer:

Sarah has 24 apples in total

Applied rules:

• Problem-solving: Identify key information and operation needed

• Equal groups: Multiplication represents equal-sized groups

• Real-world application: Connect math to everyday situations

Multiplication Chart (Up to 10×10)
Multiplication Table
×
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 equal groups together quickly

Factors: Numbers being multiplied together

Product: Result of a multiplication problem

Multiplication strategies:
  1. Repeated addition: \(4 \times 3 = 4 + 4 + 4\)
  2. Arrays: Organizing items in rows and columns
  3. Number lines: Skip counting
  4. Groups: Equal sets of objects
Tip 1: Practice with small numbers first, then increase gradually.
Tip 2: Use arrays or grouping to visualize multiplication.
Tip 3: Remember that multiplication is commutative: \(4 \times 3 = 3 \times 4\).
Tip 4: Use the multiplication table to find patterns and shortcuts.
Important property: Any number multiplied by 0 equals 0.
Important property: Any number multiplied by 1 equals itself.
Multiplication Concepts and Properties
\(a \times b = c\)
Basic Multiplication
Commutative Property
\(a \times b = b \times a\)
Order doesn't matter
Associative Property
\(a \times (b \times c) = (a \times b) \times c\)
Grouping doesn't matter
Identity Property
\(a \times 1 = a\)
Multiplying by 1
Zero Property
\(a \times 0 = 0\)
Multiplying by 0
Patterns in Multiplication
Pattern
Example
Rule
Why
Visual
×2
2×4=8
Double
Add to itself
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×5
5×6=30
Ends in 0 or 5
Skip count by 5s
5,10,15,20,25,30
×10
10×7=70
Add zero
Place value shift
7→70
×9
9×8=72
Digits sum to 9
7+2=9
72
×4
4×3=12
Double twice
2×(2×3)=12
(2×3)×2
Multiplication Practice and Tips
\(3 \times 4 = 12\)
Three Groups of Four
Key concepts:

Equal groups: Multiplication shows equal-sized groups

Arrays: Visual representation in rows and columns

Repeated addition: Another way to think about multiplication

Problem-solving steps:
  1. Read the problem: Understand what is being asked
  2. Find key information: Identify numbers and relationships
  3. Choose operation: Decide if multiplication is needed
  4. Solve: Calculate the multiplication
  5. Check: Make sure the answer makes sense
Tip 1: Practice skip counting (2, 4, 6, 8...) to learn multiplication facts.
Tip 2: Draw pictures or use objects to represent multiplication problems.
Tip 3: Notice patterns in the multiplication table to help with memorization.
Tip 4: Use known facts to figure out unknown ones (e.g., 6×7 = 5×7 + 7).
Common error: Confusing multiplication with addition. Remember: multiplication is repeated addition.
Practice tip: Start with smaller numbers and work up. Master 0-5 before moving to 6-10.
Important multiplication facts to remember:

• Any number × 0 = 0

• Any number × 1 = that number

• Multiplication is commutative: 3×4 = 4×3

• Multiplication by 10 adds a zero to the end

• Multiplication by 5 ends in 0 or 5

Questions & Answers

Question: I don't understand why 3×4 is the same as 4×3. They look different to me!

Answer: Great question! This is called the commutative property of multiplication. Let's visualize it:

  • 3×4 means 3 groups of 4: ●●●● + ●●●● + ●●●● = 12 total
  • 4×3 means 4 groups of 3: ●●● + ●●● + ●●● + ●●● = 12 total

Both give us 12! We can also think of it as an array:

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This array shows 3 rows of 4 (3×4) OR 4 columns of 3 (4×3). Either way, we count 12 dots!

Question: My child is struggling with multiplication word problems. How can I help them identify when to multiply?

Answer: Here are key strategies to help identify multiplication in word problems:

  • Look for keywords: "each," "per," "every," "groups of," "sets of," "total," "altogether" (when referring to equal groups)
  • Identify equal groups: Does the problem describe the same amount in multiple groups?
  • Think about the situation: Are we finding a total amount made up of identical parts?

For example: "There are 4 bags with 6 apples each" → This describes 4 equal groups of 6, so we multiply 4×6.

Practice having your child draw pictures or make arrays to represent the problem before solving.

Question: Why do we need to learn multiplication? Can't I just keep adding numbers?

Answer: That's a smart question! Actually, multiplication IS repeated addition, but it's a faster way to add equal groups.

Compare these approaches:

  • Adding: 6+6+6+6+6+6+6+6+6+6 = ? (That's 10 additions!)
  • Multiplying: 10×6 = 60 (Just one calculation!)

As you grow up, you'll use multiplication for many things:

  • Calculating area of rooms
  • Shopping (finding totals)
  • Cooking (adjusting recipes)
  • Understanding time and money

Multiplication saves time and helps us solve bigger problems more efficiently!