Solved Exercises on Multi-step Multiplication Problems in Grade 3

Master multi-step multiplication problems: word problems, mixed operations, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Shopping Problem
Exercise 1
Sarah buys 3 packs of markers. Each pack has 8 markers. She gives 5 markers to her friend. How many markers does Sarah have left?
Definition:

Multi-step Multiplication Problem: A word problem that requires multiple operations to solve, including multiplication followed by addition, subtraction, or division.

Multi-step Problem Solving Method:
  1. Read the problem carefully: Identify what is being asked
  2. Find the information: Identify numbers and operations needed
  3. Plan the steps: Determine the order of operations
  4. Solve step by step: Perform calculations in order
  5. Check your answer: Verify it makes sense in context
Sarah buys 3 packs of markers. Each pack has 8 markers. She gives 5 markers to her friend. How many markers does Sarah have left?
Information: 3 packs, 8 markers per pack, gives away 5 markers
Question: How many markers left after giving some away?
1
Find total markers: 3 packs × 8 markers per pack = 24 markers
2
Subtract markers given away: 24 - 5 = 19 markers
Step 1:
3 × 8 = 24
Step 2:
24 - 5 = 19
3
packs
→ ×8
24
total
→ -5
19
left
Step 1
3 × 8 = 24
Step 2
24 - 5 = 19
Answer
19 markers
Step 1: Calculate total markers bought

Sarah bought 3 packs with 8 markers each: 3 × 8 = 24 markers

Step 2: Subtract markers given away

She gave 5 markers to her friend: 24 - 5 = 19 markers remaining

Step 3: Verify the answer

Does 19 make sense? Yes, because 24 - 5 = 19

✓
3 × 8 = 24, then 24 - 5 = 19
3 × 8 - 5 = 19 markers
Final answer:

Sarah has 19 markers left after giving 5 to her friend.

Applied rules:

• Order of Operations: Multiplication before subtraction

• Multi-step Problem: Requires more than one operation to solve

• Contextual Answer: Includes appropriate units (markers)

2 Classroom Problem
Exercise 2
There are 4 tables in a classroom. Each table has 6 students. If 3 more students join the class, how many students are there in total?
Definition:

Multi-step Problem with Addition: A problem requiring multiplication followed by addition to find the total number of items or people.

There are 4 tables in a classroom. Each table has 6 students. If 3 more students join the class, how many students are there in total?
Information: 4 tables, 6 students per table, 3 more join
Question: Total students after new students join?
1
Find current students: 4 tables × 6 students per table = 24 students
2
Add new students: 24 + 3 = 27 students
Step 1:
4 × 6 = 24
Step 2:
24 + 3 = 27
4
tables
→ ×6
24
current
→ +3
27
total
Step 1
4 × 6 = 24
Step 2
24 + 3 = 27
Answer
27 students
Step 1: Calculate current students

4 tables with 6 students each: 4 × 6 = 24 students

Step 2: Add new students

3 more students join: 24 + 3 = 27 students total

Step 3: Verify the answer

Does 27 make sense? Yes, because 24 + 3 = 27

✓
4 × 6 = 24, then 24 + 3 = 27
4 × 6 + 3 = 27 students
Final answer:

There are 27 students in total after 3 more join the class.

Applied rules:

• Order of Operations: Multiplication before addition

• Multi-step Problem: Requires multiplication and addition

• Real-world Context: Applies math to classroom scenario

3 Fruit Problem
Exercise 3
A farmer has 5 baskets. Each basket contains 9 apples. He sells 20 apples. How many apples does he have left?
Definition:

Multi-step Problem with Subtraction: A problem requiring multiplication followed by subtraction to find the remaining quantity.

A farmer has 5 baskets. Each basket contains 9 apples. He sells 20 apples. How many apples does he have left?
Information: 5 baskets, 9 apples per basket, sells 20 apples
Question: Apples remaining after selling?
1
Find total apples: 5 baskets × 9 apples per basket = 45 apples
2
Subtract sold apples: 45 - 20 = 25 apples
Step 1:
5 × 9 = 45
Step 2:
45 - 20 = 25
5
baskets
→ ×9
45
total
→ -20
25
left
Step 1
5 × 9 = 45
Step 2
45 - 20 = 25
Answer
25 apples
Step 1: Calculate total apples

5 baskets with 9 apples each: 5 × 9 = 45 apples

Step 2: Subtract sold apples

Farmer sells 20 apples: 45 - 20 = 25 apples remaining

Step 3: Verify the answer

Does 25 make sense? Yes, because 45 - 20 = 25

✓
5 × 9 = 45, then 45 - 20 = 25
5 × 9 - 20 = 25 apples
Final answer:

The farmer has 25 apples left after selling 20 apples.

Applied rules:

• Order of Operations: Multiplication before subtraction

• Multi-step Problem: Requires multiplication and subtraction

• Real-world Context: Applies math to farming scenario

Multi-step Problem Solving Strategies
(a × b) + c = ?
Multi-step Formula
Step 1
Identify
Read problem carefully
Step 2
Plan
Determine operations needed
Step 3
Solve
Perform operations in order
Step 4
Check
Verify your answer
Key definitions:

Multi-step Problem: A problem requiring more than one operation to solve

Order of Operations: Perform multiplication before addition/subtraction

Context: The real-world situation described in the problem

Units: The measurement or type of item being counted

Problem-Solving Steps:
  1. Read and Understand: Carefully read the problem to understand what's happening
  2. Identify Information: Find the numbers and operations needed
  3. Plan Solution: Decide what operations to perform and in what order
  4. Solve Step-by-Step: Calculate each step carefully
  5. Check Answer: Make sure the answer makes sense in the context
Key Pattern: Multi-step problems always require multiple operations.
Order Matters: Always do multiplication before addition/subtraction.
Tip 1: Circle or highlight important numbers in the problem.
Tip 2: Write down each step as you solve the problem.
Tip 3: Always check if your answer makes sense in the real-world context.
Solution: Exercises 4 to 5
4 Library Problem
Exercise 4
A library has 6 shelves. Each shelf holds 12 books. If the librarian adds 8 more books to each shelf, how many books are there in total?
Definition:

Complex Multi-step Problem: A problem requiring multiplication followed by another multiplication and addition to find the final total.

A library has 6 shelves. Each shelf holds 12 books. If the librarian adds 8 more books to each shelf, how many books are there in total?
Information: 6 shelves, 12 books per shelf, adds 8 more per shelf
Question: Total books after adding more to each shelf?
1
Find initial books: 6 shelves × 12 books per shelf = 72 books
2
Find added books: 6 shelves × 8 books per shelf = 48 books
3
Add totals: 72 + 48 = 120 books
Step 1:
6 × 12 = 72
Step 2:
6 × 8 = 48
Step 3:
72 + 48 = 120
6
shelves
→ ×12
72
initial
+ (6×8)
48
added
→ =
120
total
Step 1
6 × 12 = 72
Step 2
6 × 8 = 48
Step 3
72 + 48 = 120
Step 1: Calculate initial books

6 shelves with 12 books each: 6 × 12 = 72 books initially

Step 2: Calculate added books

6 shelves with 8 more books each: 6 × 8 = 48 books added

Step 3: Find total books

Total: 72 + 48 = 120 books

Step 4: Verify the answer

Does 120 make sense? Yes, because 72 + 48 = 120

✓
6 × 12 = 72, 6 × 8 = 48, 72 + 48 = 120
6 × 12 + 6 × 8 = 120 books
Final answer:

There are 120 books in total after adding 8 more books to each of the 6 shelves.

Applied rules:

• Order of Operations: Perform all multiplications before addition

• Multi-step Problem: Requires multiple multiplication and addition steps

• Real-world Context: Applies math to library management scenario

5 Game Tournament
Exercise 5
In a tournament, there are 4 teams. Each team has 7 players. During the game, 3 players from each team leave early. How many players remain in the tournament?
Definition:

Multi-step Problem with Multiple Operations: A problem requiring multiplication followed by multiplication and subtraction to find the remaining quantity.

In a tournament, there are 4 teams. Each team has 7 players. During the game, 3 players from each team leave early. How many players remain in the tournament?
Information: 4 teams, 7 players per team, 3 leave per team
Question: Players remaining in tournament?
1
Find total players: 4 teams × 7 players per team = 28 players
2
Find players who left: 4 teams × 3 players per team = 12 players
3
Subtract to find remaining: 28 - 12 = 16 players
Step 1:
4 × 7 = 28
Step 2:
4 × 3 = 12
Step 3:
28 - 12 = 16
4
teams
→ ×7
28
total
- (4×3)
12
left
→ =
16
remain
Step 1
4 × 7 = 28
Step 2
4 × 3 = 12
Step 3
28 - 12 = 16
Step 1: Calculate total players

4 teams with 7 players each: 4 × 7 = 28 players total

Step 2: Calculate players who left

4 teams with 3 players leaving each: 4 × 3 = 12 players left

Step 3: Find remaining players

Remaining: 28 - 12 = 16 players

Step 4: Verify the answer

Does 16 make sense? Yes, because 28 - 12 = 16

✓
4 × 7 = 28, 4 × 3 = 12, 28 - 12 = 16
4 × 7 - 4 × 3 = 16 players
Final answer:

There are 16 players remaining in the tournament after 3 players from each team leave early.

Applied rules:

• Order of Operations: Perform all multiplications before subtraction

• Multi-step Problem: Requires multiple multiplication and subtraction steps

• Real-world Context: Applies math to tournament scenario

Advanced Multi-step Problem Concepts
a × b + c × d = ?
Advanced Multi-step Formula
Key definitions:

Multi-step Problem: A mathematical problem requiring multiple operations to solve

Order of Operations: The sequence in which operations should be performed (multiplication before addition/subtraction)

Contextual Problem: A word problem set in a real-world scenario

Problem Decomposition: Breaking complex problems into simpler steps

Advanced Problem-Solving Strategies:
  1. Identify Key Information: Extract relevant numbers and operations from the text
  2. Recognize Operation Sequence: Determine the order in which operations need to be performed
  3. Plan the Solution Path: Create a logical sequence of steps to solve the problem
  4. Execute Calculations: Perform each step carefully and accurately
  5. Verify Results: Check that the final answer makes sense in the problem context
Tip 1: Always perform multiplication before addition or subtraction in multi-step problems.
Tip 2: Draw diagrams or models to visualize the problem situation.
Tip 3: Write down each step separately to avoid calculation errors.
Tip 4: Check your answer by estimating if it seems reasonable.
Common Mistakes: Performing operations in the wrong order, missing steps, calculation errors.
Success Strategies: Reading carefully, planning steps, checking work, using visual aids.
Advanced rules:

• Order of Operations: Always multiply before adding or subtracting

• Step-by-Step Approach: Break complex problems into simpler parts

• Context Preservation: Keep track of units and meaning throughout the solution

• Verification: Always check if the answer makes sense in the problem context

Problem Type
Structure
Example
Multiply then Add
(a × b) + c
4 × 6 + 3 = 27
Multiply then Subtract
(a × b) - c
5 × 9 - 20 = 25
Multiply then Multiply then Add
(a × b) + (c × d)
6×12 + 6×8 = 120

Questions & Answers

Question: How do I know which operation to do first in multi-step problems?

Answer: In multi-step multiplication problems, always follow this order:

  • First: Do all multiplication operations
  • Then: Do addition or subtraction operations

For example, in the problem "3 packs with 8 items each, then add 5 more":

  • First: 3 × 8 = 24 (do the multiplication)
  • Then: 24 + 5 = 29 (do the addition)

Remember: multiplication comes before addition or subtraction!

Question: How can I help my child organize their thinking when solving multi-step problems?

Answer: Here are some organizational strategies:

  • Write down each step: Have your child write one calculation per line
  • Use boxes or circles: Encourage highlighting important numbers
  • Draw diagrams: Visual representations help organize thoughts
  • Number the steps: Step 1, Step 2, Step 3, etc.
  • Check as they go: Verify each step before moving to the next
  • Read the question twice: Ensure they answer what's being asked

The key is to slow down and be methodical!

Question: What if a multi-step problem has more than 3 steps? How do I keep track?

Answer: For problems with more steps, use these techniques:

  • Label each step clearly: Step 1, Step 2, Step 3, etc.
  • Keep intermediate results: Write down answers from earlier steps
  • Use scratch paper: Work out each step separately
  • Check your progress: Make sure each step logically leads to the next
  • Look for patterns: Sometimes steps repeat or follow a pattern

For example, if you have a problem with 5 steps, solve it like this:

  • Step 1: 4 × 6 = 24
  • Step 2: 24 + 8 = 32
  • Step 3: 32 - 10 = 22
  • Step 4: 22 × 2 = 44
  • Step 5: 44 + 6 = 50

Keep each step organized and neat!