Solved Exercises on Multi-step Word Problems in 4th Grade

Master multi-step word problems: problem analysis, step-by-step solutions, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Shopping problem
Exercise 1
Sarah bought 3 notebooks for $2 each and 2 pens for $1.50 each. She paid with a $20 bill. How much change did she receive?
Definition:

Multi-step word problem: A problem requiring multiple operations (addition, subtraction, multiplication, division) performed in a specific order to find the solution.

Problem-solving method:
  1. Read carefully: Identify what is given and what is asked
  2. Plan: Determine the sequence of operations needed
  3. Solve step by step: Perform calculations in order
  4. Check: Verify the answer makes sense
Step 1
Cost of notebooks
Step 2
Cost of pens
Step 3
Total cost
Step 4
Change received
Step 1: Calculate cost of notebooks

3 notebooks × $2 each = $6

Step 2: Calculate cost of pens

2 pens × $1.50 each = $3

Step 3: Calculate total cost

$6 + $3 = $9

Step 4: Calculate change

$20 - $9 = $11

Sarah received $11 in change
Final answer:

Sarah received $11 in change

Applied rules:

• Order of operations: Multiplication before addition

• Problem decomposition: Break complex problems into simpler parts

• Money calculation: Handle decimals carefully

2 Fruit problem
Exercise 2
A farmer harvested 120 apples on Monday and 150 apples on Tuesday. He sold 85 apples on Wednesday and then picked 90 more apples on Thursday. How many apples does he have now?
Definition:

Sequential operations: Problems where quantities change over time through additions and subtractions.

Monday
120 apples
Tuesday
+150 apples
Wednesday
-85 apples
Thursday
+90 apples
Total
? apples
Step 1: Calculate apples after Monday

Start: 0 apples + 120 apples = 120 apples

Step 2: Add Tuesday's harvest

120 apples + 150 apples = 270 apples

Step 3: Subtract Wednesday's sales

270 apples - 85 apples = 185 apples

Step 4: Add Thursday's harvest

185 apples + 90 apples = 275 apples

The farmer has 275 apples now
Final answer:

The farmer has 275 apples now

Applied rules:

• Sequential processing: Handle changes in chronological order

• Addition and subtraction: Keep track of increases and decreases

• Running total: Update quantity after each operation

3 Group problem
Exercise 3
There are 4 classrooms with 25 students each. If 15 students are absent today, how many students are present in school?
Definition:

Group multiplication: Problems involving equal groups that require multiplication followed by addition or subtraction.

Total students
4 × 25
Absent students
15
Present students
? students
Step 1: Calculate total number of students

4 classrooms × 25 students each = 100 students

Step 2: Subtract absent students

100 students - 15 absent students = 85 students present

Step 3: Verify the answer

85 present + 15 absent = 100 total students ✓

There are 85 students present in school
Final answer:

There are 85 students present in school

Applied rules:

• Equal groups: Use multiplication for identical quantities

• Total minus part: Find remaining quantity by subtraction

• Verification: Check that parts add up to whole

Rules and methods, laws,...
Total = (Groups × Items per group) - Subtracted items
Multi-step Formula
Problem Type 1
A + B - C = ?
Sequential Operations
Problem Type 2
(A × B) + (C × D) = ?
Multiple Groups
Problem Type 3
(A × B) - C = ?
Groups Minus Part
Key definitions:

Multi-step problem: Requires more than one mathematical operation to solve

Word problem: Mathematical problem presented in narrative form

Problem decomposition: Breaking complex problems into smaller, manageable parts

Complete methodology:
  1. Analyze: Identify given information and what is being asked
  2. Plan: Decide which operations to perform and in what order
  3. Solve: Execute each step carefully
  4. Check: Verify the answer is reasonable and accurate
Tip 1: Underline important numbers and keywords in the problem.
Tip 2: Draw pictures or make tables to visualize the problem.
Tip 3: Always check if your answer makes sense in the context of the problem.
Tip 4: Write down each step clearly to avoid mistakes.
Common errors: Performing operations in wrong order, misreading numbers, forgetting units.
Key strategies: Read twice, plan before calculating, show work clearly, verify answer.
Formulas and patterns to remember:

• Total = Sum of all parts

• Remaining = Total - Used/Removed

• Equal groups = Number of groups × Items per group

• Average = Total ÷ Number of items

Solution: Exercises 4 to 5
4 Garden problem
Exercise 4
Mrs. Johnson planted 6 rows of carrots with 12 plants in each row. After a week, 8 plants died. She then planted 15 more plants. How many carrot plants does she have now?
Definition:

Dynamic quantity problem: Problems where the initial amount changes due to additions and subtractions.

Initial plants
6 × 12
After losses
-8 plants
After additions
+15 plants
Step 1: Calculate initial number of plants

6 rows × 12 plants per row = 72 plants

Step 2: Subtract dead plants

72 plants - 8 dead plants = 64 plants

Step 3: Add new plants

64 plants + 15 new plants = 79 plants

Step 4: Verify the result

Start: 72, lost: 8, gained: 15 → 72 - 8 + 15 = 79 ✓

Mrs. Johnson has 79 carrot plants now
Final answer:

Mrs. Johnson has 79 carrot plants now

Applied rules:

• Equal groups: Use multiplication for arrays (rows × columns)

• Sequential changes: Apply operations in chronological order

• Verification: Double-check calculations with alternative method

5 Library problem
Exercise 5
The school library had 450 books. On Monday, 25 books were borrowed and 12 books were returned. On Tuesday, 18 more books were borrowed and 7 books were returned. How many books are in the library now?
Definition:

Multi-day tracking: Problems involving changes over multiple time periods requiring careful bookkeeping.

Start
450 books
Mon Change
-25 + 12
Tue Change
-18 + 7
Final
? books
Step 1: Start with initial number of books

Library starts with 450 books

Step 2: Process Monday's transactions

Borrowed: 25 books (subtract), Returned: 12 books (add)

450 - 25 + 12 = 437 books after Monday

Step 3: Process Tuesday's transactions

Borrowed: 18 books (subtract), Returned: 7 books (add)

437 - 18 + 7 = 426 books after Tuesday

Step 4: Alternative calculation method

Total borrowed: 25 + 18 = 43 books

Total returned: 12 + 7 = 19 books

Net change: 450 - 43 + 19 = 426 books

There are 426 books in the library now
Final answer:

There are 426 books in the library now

Applied rules:

• Day-by-day tracking: Process each day's events separately

• Net change calculation: Compare totals of increases vs decreases

• Alternative verification: Use different calculation methods to confirm

Comprehensive Guide to Multi-step Word Problems
Problem Analysis → Planning → Execution → Verification
Problem-Solving Cycle
Key definitions:

Multi-step word problem: A mathematical problem presented in narrative form that requires multiple operations to solve.

Problem decomposition: The process of breaking a complex problem into smaller, manageable steps.

Operational sequence: The order in which mathematical operations must be performed to reach the correct solution.

Complete methodology:
  1. Read and analyze: Carefully read the problem multiple times to understand what is given and what is being asked
  2. Identify key information: Circle numbers, underline important words, note units of measurement
  3. Plan the solution: Determine which operations are needed and in what order
  4. Solve step by step: Execute each operation carefully, showing all work
  5. Check and verify: Ensure the answer makes sense and is mathematically correct
Tip 1: Look for clue words that indicate operations: "total," "sum," "altogether" for addition; "difference," "less," "fewer" for subtraction; "each," "per," "product" for multiplication; "shared equally" for division.
Tip 2: Draw diagrams or make lists to visualize the problem. For example, draw boxes for equal groups or make a timeline for sequential events.
Tip 3: Always check if your answer is reasonable. If the problem asks for the number of people and you get 15.7, reconsider your solution.
Tip 4: Use estimation to check if your answer is in the right ballpark. If you estimate 50 and get 500, there might be an error.
Tip 5: Write your final answer in a complete sentence that addresses the question asked.
Common errors: Performing operations in wrong order, misreading numbers, forgetting to include all steps, not checking if the answer makes sense in context.
Success strategies: Read the problem twice, identify what's being asked, plan before calculating, show all work, verify the answer.
Essential patterns to recognize:

• Sequential problems: Events happen over time (A happens, then B happens, then C)

• Group problems: Multiple equal groups that require multiplication

• Comparison problems: Comparing quantities or finding differences

• Part-whole problems: Finding missing parts when the whole is known

• Mixed operations: Problems requiring addition, subtraction, multiplication, or division in sequence

Questions & Answers

Question: I often get confused about which operation to use first in multi-step problems. How do I know whether to add, subtract, multiply, or divide first?

Answer: Great question! Here's a systematic approach:

  • Look for clue words: "Each," "per," "times," "product" usually mean multiplication; "total," "sum," "altogether" suggest addition; "difference," "less," "remaining" indicate subtraction; "shared equally," "divided among" point to division.
  • Think about the situation: Are you putting things together? That's addition. Taking away? Subtraction. Making equal groups? Multiplication. Sharing? Division.
  • Follow the story: Read the problem like a story and determine what happens first, second, third.
  • Use the "What if?" test: Does your answer make sense? If you're finding how many are left after some are taken away, your answer should be smaller than the starting amount.

Example: "There are 4 boxes with 6 toys each. 8 toys break. How many are left?"

First: 4 boxes × 6 toys = 24 toys (multiplication for equal groups)

Then: 24 - 8 = 16 toys (subtraction because toys are taken away)

Question: My child struggles with showing their work in multi-step problems. How can I help them organize their thinking better?

Answer: Organization is key to success in multi-step problems. Try these strategies:

  • Use a step-by-step format: Have your child write "Step 1:", "Step 2:", etc., and clearly label each calculation.
  • Create a problem map: Draw circles or boxes showing the sequence of operations needed.
  • Circle important numbers: Have them circle or highlight key numbers and underline what the question is asking.
  • Write sentences: Instead of just numbers, encourage them to write what each calculation represents ("Step 1: Find total number of apples...").
  • Use color coding: Different colors for different operations or steps.

Example organization:

Problem: "Tom has 3 bags with 8 marbles each. He gives 5 marbles to his friend."

Step 1: Find total marbles: 3 × 8 = 24 marbles

Step 2: Find remaining marbles: 24 - 5 = 19 marbles

Answer: Tom has 19 marbles left.

Question: Sometimes I get the right numbers but in the wrong order. How can I make sure I'm solving the problem correctly?

Answer: This is a very common issue! Here's how to ensure you're following the correct sequence:

  • Read the problem twice: First for general understanding, second to identify the sequence of events.
  • Identify the question: What exactly are you trying to find? This is your end goal.
  • Work backwards: Think about what information you need to find the answer, then determine how to get that information.
  • Use the timeline approach: List events in the order they happen chronologically.
  • Check reasonableness: After each step, ask "Does this make sense?"

Example: "A store had 100 pencils. They sold 25 in the morning, received 40 more in the afternoon, and sold 15 in the evening. How many are left?"

Timeline: Start (100) → Sold (100-25=75) → Received (75+40=115) → Sold (115-15=100)

Notice how we follow the story in chronological order!