Solved Exercises on Repeated Addition and Multiplication Sentence in Grade 2

Master repeated addition and multiplication sentence: connecting addition to multiplication, writing number sentences, and foundational multiplication skills through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Converting addition to multiplication
Exercise 1
Write the multiplication sentence for: 2 + 2 + 2 + 2
Definition:

Multiplication Sentence: A mathematical statement showing how many groups of equal size there are (e.g., 4 × 2 = 8).

Conversion Method:
  1. Count how many numbers are being added
  2. Identify what number is being repeated
  3. Write as multiplication: (number of groups) × (items per group)
  4. Calculate the product
Repeated Addition
→
Multiplication
2
2
2
2
Addition
2 + 2 + 2 + 2
Count Groups
4 groups of 2
Multiplication
4 × 2 = 8
Step 1: Count the additions

You see the number 2 four times

Step 2: Identify the repeated number

The number being repeated is 2

Step 3: Write multiplication sentence

4 groups of 2 = 4 × 2

Step 4: Calculate the product

4 × 2 = 8

↓
2 + 2 + 2 + 2 = 4 × 2 = 8
Final answer:

The multiplication sentence is: 4 × 2 = 8

Applied rules:

• Conversion principle: Repeated addition equals multiplication

• Group identification: Count how many times a number repeats

• Number sentence format: groups × items per group = total

Conversion Tip: Count how many times the number appears!
Learning Tip: Multiplication is a shortcut for repeated addition.
2 Writing both sentences
Exercise 2
Write both the repeated addition and multiplication sentences for 3 groups of 5.
Definition:

Number Sentences: Mathematical statements that show relationships between numbers using symbols (+, ×, =).

Groups
Items per Group
Total
3
5
15
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Groups
3 groups
Per Group
5 each
Total
15
Step 1: Understand the situation

You have 3 groups, each with 5 items

Step 2: Write repeated addition

5 + 5 + 5 (adding 5 three times)

Step 3: Write multiplication sentence

3 × 5 = 15

Step 4: Verify they're equal

5 + 5 + 5 = 15 and 3 × 5 = 15 ✓

↔
Addition: 5 + 5 + 5 = 15
Multiplication: 3 × 5 = 15
Final answer:

Repeated addition: 5 + 5 + 5 = 15

Multiplication: 3 × 5 = 15

Applied rules:

• Equivalence: Both sentences equal the same total

• Structure: groups × items per group = total

• Connection: Multiplication is condensed repeated addition

Writing Tip: Always write both sentences to see the connection!
Understanding Tip: Multiplication is just a faster way to add.
3 From picture to sentence
Exercise 3
You see 4 rows of 3 stars each. Write the repeated addition and multiplication sentences.
Definition:

Visual to Symbolic: Converting pictures or arrangements into mathematical sentences.

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Rows
Stars per Row
Total Stars
Picture
4 rows of 3
Addition
3 + 3 + 3 + 3
Multiplication
4 × 3 = 12
Step 1: Count the rows

You see 4 rows of stars

Step 2: Count stars per row

Each row has 3 stars

Step 3: Write repeated addition

3 + 3 + 3 + 3 = 12

Step 4: Write multiplication

4 × 3 = 12

↓
3 + 3 + 3 + 3 = 12
4 × 3 = 12
Final answer:

Repeated addition: 3 + 3 + 3 + 3 = 12

Multiplication: 4 × 3 = 12

Applied rules:

• Visual interpretation: Convert pictures to numbers

• Pattern recognition: Equal rows create repeated addition

• Symbolic representation: Pictures → numbers → sentences

Picture Tip: Count rows first, then items in each row!
Connection Tip: Pictures help visualize the math concepts.
Conversion Rules & Connections
a + a + ... + a (n times) = n × a
Addition to Multiplication Formula
Addition Form
a + a + a
Repeated addition
Multiplication Form
3 × a
Condensed form
Equivalence
a + a + a = 3 × a
Same result
2 + 2 + 2
=
3 × 2
Key definitions:

Number Sentence: A mathematical statement using numbers and symbols

Repeated Addition: Adding the same number multiple times

Multiplication Sentence: Showing groups × items per group = total

Conversion benefit: Multiplication is faster than repeated addition
Mathematical connection: Both forms equal the same total
Conversion Process:
  1. Identify repetition: Find the number being added repeatedly
  2. Count occurrences: Determine how many times it appears
  3. Write multiplication: (count) × (repeated number)
  4. Verify equality: Both sentences should equal the same total
Solution: Exercises 4 to 5
4 Solving word problems
Exercise 4
Emma has 5 bags of candy. Each bag has 4 pieces. Write both number sentences.
Definition:

Word Problem Translation: Converting story problems into mathematical sentences.

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糖果
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Bags
Candy per Bag
Total Candy
Story
5 bags of 4
Addition
4 + 4 + 4 + 4 + 4
Multiplication
5 × 4 = 20
Step 1: Identify the groups

Emma has 5 bags

Step 2: Identify items per group

Each bag has 4 pieces

Step 3: Write repeated addition

4 + 4 + 4 + 4 + 4 = 20

Step 4: Write multiplication

5 × 4 = 20

↓
4 + 4 + 4 + 4 + 4 = 20
5 × 4 = 20
Final answer:

Repeated addition: 4 + 4 + 4 + 4 + 4 = 20

Multiplication: 5 × 4 = 20

Applied rules:

• Story interpretation: Identify groups and items per group

• Real-world connection: Math applies to everyday situations

• Sentence translation: Words → numbers → equations

Word Problem Tip: Look for words like "each," "per," or "groups of"!
Translation Tip: Draw pictures to visualize the problem.
5 Reverse conversion
Exercise 5
Given the multiplication sentence 6 × 3 = 18, write the repeated addition sentence.
Definition:

Reverse Conversion: Starting with multiplication and writing the expanded addition form.

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Groups
Items per Group
Total
Given
6 × 3 = 18
Interpret
6 groups of 3
Convert
3 + 3 + 3 + 3 + 3 + 3
Step 1: Analyze the multiplication

6 × 3 means 6 groups of 3

Step 2: Identify what's repeated

The number 3 is repeated 6 times

Step 3: Write repeated addition

3 + 3 + 3 + 3 + 3 + 3 = 18

Step 4: Verify the result

3 + 3 + 3 + 3 + 3 + 3 = 18 ✓

↑
6 × 3 = 18
3 + 3 + 3 + 3 + 3 + 3 = 18
Final answer:

Repeated addition: 3 + 3 + 3 + 3 + 3 + 3 = 18

Applied rules:

• Reverse operation: Multiplication can be expanded to addition

• Structure analysis: First number = times to repeat

• Verification: Both forms must equal the same total

Reverse Tip: The first number tells you how many times to repeat!
Verification Tip: Always check that both sentences equal the same number.
Detailed Summary: Repeated Addition and Multiplication Sentence
a + a + ... + a (n times) = n × a
Fundamental Connection Formula
Key definitions:

Repeated Addition: Adding the same number multiple times (e.g., 4 + 4 + 4 = 12)

Multiplication Sentence: A statement showing groups × items per group = total (e.g., 3 × 4 = 12)

Number Sentence: A mathematical statement using numbers and symbols

Conversion: Changing between addition and multiplication forms

Conversion Methods:
  1. Addition to Multiplication: Count repetitions and write as groups × repeated number
  2. Multiplication to Addition: Repeat the second number as many times as the first number indicates
  3. Visual to Symbolic: Count groups and items, then convert to number sentences
  4. Word Problem to Equation: Identify groups and items per group from the story
  5. Verification: Ensure both forms equal the same total
Tip 1: In multiplication, the first number tells you how many times to repeat the second number.
Tip 2: Both repeated addition and multiplication always equal the same total.
Tip 3: Multiplication is just a shorter way to write repeated addition.
Tip 4: Draw pictures to help visualize the groups when converting.
Tip 5: Always check your work by calculating both forms to ensure they're equal.
Common errors: Mixing up which number represents groups vs. items, forgetting to count all repetitions.
Practice advice: Start with small numbers, use visual aids, practice both directions.
Essential conversion facts:

• n × m = m + m + ... + m (n times)

• Repeated addition is the foundation for multiplication

• Multiplication is a shortcut for repeated addition

• Both forms always equal the same total

• The first number in multiplication = number of repetitions in addition

• The second number in multiplication = the number being repeated in addition

Conversion Process
1
Identify Repetition
2
Count Occurrences
3
Write Multiplication
4
Verify Total

Questions & Answers

Question: Why do we need to learn both repeated addition and multiplication? Isn't multiplication enough?

Answer: Great question! Learning both is very important:

  • Understanding: Repeated addition shows WHY multiplication works
  • Foundation: Addition comes before multiplication in math development
  • Flexibility: Sometimes addition is easier for small numbers
  • Problem-solving: Some problems are easier to solve with one form or the other

Think of repeated addition as training wheels that help you understand multiplication!

Question: How can I help my child practice converting between addition and multiplication?

Answer: Here are effective practice strategies:

  • Use manipulatives: Counters, blocks, or toys to show equal groups
  • Draw pictures: Circles, dots, or shapes arranged in equal groups
  • Practice both directions: Addition to multiplication AND multiplication to addition
  • Start small: Begin with 2's and 3's before moving to larger numbers
  • Make it visual: Arrays and grids help see the connection clearly

Consistent practice with visual aids strengthens the connection between both forms!

Question: How do I know which number goes first in multiplication? Like why is it 3 × 4 and not 4 × 3?

Answer: Both 3 × 4 and 4 × 3 equal 12, but they mean different things:

  • 3 × 4: 3 groups of 4 items each (3 + 3 + 3 + 3)
  • 4 × 3: 4 groups of 3 items each (4 + 4 + 4)

When the problem says "3 groups of 4," write it as 3 × 4. The first number tells you HOW MANY groups, and the second number tells you HOW MANY in each group.