Solve Multi-Step Word Problems

Complete guide with exercises on solving multi-step word problems: step-by-step solutions and detailed explanations.

Word Problem Problems 1 to 3
1 Shopping Word Problem
Problem 1
Sarah bought 4 packs of pencils. Each pack contains 12 pencils. She gave 15 pencils to her friends. How many pencils does she have left?
Definition:

Multi-step word problem: A problem requiring multiple operations to solve (multiplication, then subtraction)

Solution method:
  1. Identify what needs to be found (pencils left)
  2. Determine the operations needed (find total pencils, then subtract)
  3. Calculate total pencils: 4 packs × 12 pencils per pack
  4. Subtract pencils given away: Total - 15
  5. State the answer in context
Step 1
4 × 12
Step 2
- 15
Result
33
Step 1: Calculate total pencils

4 packs × 12 pencils per pack = 48 pencils

Step 2: Subtract pencils given away

48 - 15 = 33 pencils

Step 3: Interpret result

Sarah has 33 pencils left

Sarah has 33 pencils left
Final answer:

Sarah has 33 pencils left.

Applied rules:

• Order of operations: Multiplication before subtraction

• Context: Answer must relate back to the problem situation

• Verification: Check: 33 + 15 = 48, 48 ÷ 12 = 4 ✓

2 School Word Problem
Problem 2
A school has 6 classrooms. Each classroom has 24 students. If 15 students are absent today, how many students are present?
Definition:

Multi-step word problem: A problem involving multiple operations (multiplication, then subtraction)

Total students
6 × 24
Absent
- 15
Present
129
Step 1: Calculate total students

6 classrooms × 24 students per classroom = 144 students

Step 2: Subtract absent students

144 - 15 = 129 students

Step 3: Interpret result

129 students are present

129 students are present
Final answer:

There are 129 students present.

Applied rules:

• Multiplication: Find total by multiplying groups by items per group

• Subtraction: Find remaining by subtracting what's taken away

• Verification: Check: 129 + 15 = 144, 144 ÷ 24 = 6 ✓

3 Pet Store Word Problem
Problem 3
A pet store has 8 fish tanks. Each tank has 15 fish. The store owner moves 4 fish from each tank to a new tank. How many fish remain in the original tanks?
Definition:

Multi-step word problem: A problem involving multiple operations across groups

Total fish
8 × 15
Moved fish
8 × 4
Remaining
88
Step 1: Calculate total fish initially

8 tanks × 15 fish per tank = 120 fish

Step 2: Calculate fish moved

8 tanks × 4 fish per tank = 32 fish moved

Step 3: Calculate remaining fish

120 - 32 = 88 fish

Step 4: Interpret result

88 fish remain in the original tanks

88 fish remain in original tanks
Final answer:

There are 88 fish remaining in the original tanks.

Applied rules:

• Group operations: Apply operations to each group separately

• Subtraction: Subtract moved fish from total

• Verification: Check: 88 + 32 = 120, 120 ÷ 8 = 15 ✓

Multi-Step Word Problem Strategies
Problem Solving Steps 🧠
Step 1: Read Carefully
Understand what the problem is asking and identify key information.
Step 2: Plan Your Approach
Decide what operations to perform and in what order.
Step 3: Solve Step-by-Step
Work through each step carefully, keeping track of your work.
Step 4: Check Your Answer
Verify your answer makes sense in the context of the problem.
Operation Clues 📊
Addition Clues
"total," "altogether," "sum," "in all," "combined"
Subtraction Clues
"left," "remaining," "difference," "less than," "take away"
Multiplication Clues
"each," "per," "times," "product," "groups of"
Division Clues
"shared equally," "per," "quotient," "divided by," "split"
Visual Problem Solving 📐
1
Read
→
2
Plan
→
3
Solve
→
4
Check
4 × 12
Multiply
→
48 - 15
Subtract
→
33
Answer
Advanced Word Problem Problems 4 to 6
4 Farm Word Problem
Problem 4
A farmer harvested 180 apples. He packed 5 boxes with 12 apples each. Then he divided the remaining apples equally among 6 baskets. How many apples were in each basket?
Definition:

Multi-step word problem: A problem requiring multiple operations including division

Solution method:
  1. Calculate apples packed in boxes: 5 × 12
  2. Calculate remaining apples: 180 - (5 × 12)
  3. Divide remaining apples among baskets: Remaining ÷ 6
  4. State the answer in context
Total
180
Boxes
- 60
Baskets
÷ 6
Result
20
Step 1: Calculate apples in boxes

5 boxes × 12 apples each = 60 apples

Step 2: Calculate remaining apples

180 - 60 = 120 apples remaining

Step 3: Divide among baskets

120 ÷ 6 baskets = 20 apples per basket

Step 4: Interpret result

Each basket has 20 apples

Each basket has 20 apples
Final answer:

Each basket has 20 apples.

Applied rules:

• Order of operations: Perform multiplication before subtraction

• Division: Distribute remaining items equally

• Verification: Check: (5 × 12) + (6 × 20) = 60 + 120 = 180 ✓

5 Library Word Problem
Problem 5
A library has 9 shelves. Each shelf holds 20 books. The librarian removes 8 books from each shelf to repair them. How many books are left on all the shelves combined?
Definition:

Multi-step word problem: A problem involving operations across multiple identical groups

Total books
9 × 20
Removed
- (9 × 8)
Result
108
Step 1: Calculate total books initially

9 shelves × 20 books per shelf = 180 books

Step 2: Calculate books removed

9 shelves × 8 books per shelf = 72 books removed

Step 3: Calculate remaining books

180 - 72 = 108 books

Step 4: Interpret result

108 books are left on all shelves

108 books left on all shelves
Final answer:

There are 108 books left on all the shelves combined.

Applied rules:

• Group operations: Apply operations to each group separately

• Subtraction: Subtract total removed from total initial

• Verification: Check: 108 + 72 = 180, 180 ÷ 9 = 20 ✓

6 Bakery Word Problem
Problem 6
A bakery made 150 cookies. They put 5 cookies in each bag. Then they arranged the bags into boxes, with 6 bags in each box. How many boxes did they fill completely?
Definition:

Multi-step word problem: A problem requiring division in multiple steps

Cookies to bags
150 ÷ 5
Bags to boxes
÷ 6
Result
5
Step 1: Calculate number of bags

150 cookies ÷ 5 cookies per bag = 30 bags

Step 2: Calculate number of boxes

30 bags ÷ 6 bags per box = 5 boxes

Step 3: Interpret result

They filled 5 boxes completely

5 boxes filled completely
Final answer:

They filled 5 boxes completely.

Applied rules:

• Sequential division: Divide step by step through the process

• Context: Answer must relate back to the problem situation

• Verification: Check: 5 × 6 × 5 = 150 ✓

Detailed Summary & Study Guide
Solving Multi-Step Word Problems - Complete Summary
Definition of Multi-Step Word Problems:
Multi-step word problems are mathematical problems presented in narrative form that require more than one operation to solve. They often involve real-world situations and require students to identify relevant information, determine the sequence of operations needed, and apply mathematical concepts to find the solution.
Key Characteristics:
Multi-step word problems typically involve multiple operations like addition, subtraction, multiplication, and division. They require students to break down complex problems into smaller, manageable steps and apply mathematical reasoning in a sequential manner.
Core Problem-Solving Rules:

1. Read Carefully: Understand what the problem is asking and identify all given information

2. Plan Your Approach: Determine the sequence of operations needed to solve the problem

3. Solve Step-by-Step: Work through each operation carefully, keeping track of intermediate results

4. Check Your Answer: Verify that your answer makes sense in the context of the problem

Operation Keywords:

Addition: "total," "altogether," "sum," "in all," "combined," "more than"

Subtraction: "left," "remaining," "difference," "less than," "take away," "decreased by"

Multiplication: "each," "per," "times," "product," "groups of," "multiplied by"

Division: "shared equally," "per," "quotient," "divided by," "split," "average"

Simple Multi-Step Example:

Problem: "Sarah has 3 bags with 10 apples each. She gives 15 apples to her friend. How many apples does she have left?"

Solution: (3 × 10) - 15 = 30 - 15 = 15 apples

Complex Multi-Step Example:

Problem: "A store has 200 books. They sell 4 boxes of 12 books each, then divide the remaining books into 8 equal groups. How many books are in each group?"

Solution: (200 - (4 × 12)) ÷ 8 = (200 - 48) ÷ 8 = 152 ÷ 8 = 19 books per group

Key Tips for Success:

1. Circle Key Numbers: Highlight important numbers in the problem

2. Underline Action Words: Identify words like "total," "remaining," "each," "per" to determine operations

3. Sketch Diagrams: Draw pictures to visualize the problem when possible

4. Work Neatly: Keep your calculations organized to avoid errors

5. Estimate First: Make a rough estimate to check if your answer is reasonable

Common Mistakes to Avoid:

1. Rushing Through: Not reading the problem carefully enough

2. Wrong Order: Performing operations in the wrong sequence

3. Misinterpreting Words: Confusing "times more" with "times as many"

4. Calculation Errors: Making arithmetic mistakes in multi-step processes

5. No Verification: Not checking if the answer makes sense

Problem-Solving Strategy:

1. Read the Problem Twice: First for general understanding, second to identify details

2. Identify What You Need to Find: Clearly understand the question

3. Plan the Steps: Write down the operations needed in order

4. Solve Systematically: Complete each step before moving to the next

5. Review Your Answer: Check against the original problem

Verification Techniques:

Work Backwards: Use your answer to recreate the original conditions

Estimate Check: Compare your answer to your initial estimate

Alternative Method: Try solving using a different approach

Reasonableness Test: Ask if the answer makes sense in the real world

Questions & Answers

Question: How do I know what order to do the operations in a multi-step word problem?

Answer: Follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In word problems, think about what makes logical sense.

For example, if you need to find how many items are in each group, you usually multiply first to find the total, then divide. Read the problem carefully to understand the sequence of events.

Always work through the problem step by step, and check if your answer makes sense.

Question: What strategies can I teach my child to tackle multi-step word problems?

Answer: Here are effective strategies for multi-step word problems:

  • Read the problem twice - once for understanding, once to identify numbers and operations
  • Circle key numbers and underline action words
  • Draw a diagram or model to visualize the problem
  • Write down the steps before solving
  • Check the answer by working backwards

Encourage your child to take their time and not rush through the problem-solving process.

Question: What if I get stuck on a step in a multi-step word problem?

Answer: If you get stuck, try these approaches:

1. Reread the problem to make sure you understood it correctly

2. Look for simpler parts of the problem you can solve first

3. Draw a picture or make a table to organize information

4. Try working backwards from what you know

5. Make an educated guess and check if it works

Remember, it's okay to take breaks and come back to challenging problems with fresh eyes.