Solved Exercises on Multi-Step Problems in Grade 4

Master multi-step problem solving: mathematical reasoning and sequential operations through these 5 detailed exercises with step-by-step solutions.

Solution: Exercises 1 to 3
1 Shopping Multi-Step Problem
Exercise 1
Sarah bought 3 notebooks for $2.50 each and 2 pens for $1.75 each. She paid with a $20 bill. How much change did she receive?
Definition:

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

Solution method:
  1. Identify what you need to find (change received)
  2. Calculate the cost of notebooks
  3. Calculate the cost of pens
  4. Add the costs together
  5. Subtract total cost from amount paid
Notebooks
3 × $2.50
Pens
2 × $1.75
Change
$20 - total
Step 1: Calculate cost of notebooks

3 notebooks × $2.50 each = $7.50

Step 2: Calculate cost of pens

2 pens × $1.75 each = $3.50

Step 3: Calculate total cost

$7.50 + $3.50 = $11.00

Step 4: Calculate change

$20.00 - $11.00 = $9.00

Change = $9.00
Final answer:

Sarah received $9.00 in change

Applied rules:

• Order of operations: Multiplication before addition

• Sequential solving: Solve one step at a time

• Money calculations: Align decimal points when adding/subtracting

2 Class Trip Multi-Step Problem
Exercise 2
A class of 24 students went on a field trip. Each student paid $8 for the entrance fee. The teacher also paid $15 for her entrance. The school paid $60 for the bus. What was the total cost of the field trip?
Definition:

Multi-step problem: Requires calculating different components and combining them

Students
24 × $8
Teacher
$15
Bus
$60
Step 1: Calculate students' entrance fees

24 students × $8 each = $192

Step 2: Add teacher's entrance fee

$192 + $15 = $207

Step 3: Add bus cost

$207 + $60 = $267

Total = $267
Final answer:

The total cost of the field trip was $267

Applied rules:

• Component breakdown: Separate different costs

• Addition sequence: Add components one by one

• Total calculation: Combine all expenses

3 Fruit Store Multi-Step Problem
Exercise 3
A fruit store started the day with 120 apples. During the morning, they sold 35 apples. Then they received a delivery of 5 boxes with 18 apples each. How many apples did they have at the end of the day?
Definition:

Multi-step problem: Involves tracking changes to an initial amount

Start
120 apples
Sold
-35 apples
Delivery
+5 × 18
Step 1: Calculate apples after sales

120 - 35 = 85 apples

Step 2: Calculate delivery amount

5 boxes × 18 apples each = 90 apples

Step 3: Calculate final amount

85 + 90 = 175 apples

Final = 175 apples
Final answer:

The store had 175 apples at the end of the day

Applied rules:

• Sequential operations: Perform operations in chronological order

• Multiplication first: Calculate the delivery amount before adding

• Tracking changes: Update the amount after each event

Multi-Step Problem Solving Rules and Methods
Total = Initial + Changes
Problem Structure
Read
Understand problem
What is asked?
Plan
Steps to solve
What operations?
Solve
Do the math
Calculate each step
Check
Verify answer
Does it make sense?
Key definitions:

Multi-step problem: A problem requiring multiple operations to reach the solution

Problem solving: Systematic approach to finding solutions to mathematical problems

Mathematical reasoning: Logical thinking used to solve problems

Operations: Addition, subtraction, multiplication, and division

Sequential thinking: Following steps in the correct order

Multi-Step Problem Solving Method:
  1. Read carefully: Identify what is being asked
  2. Identify information: Note all given numbers and facts
  3. Plan the solution: Determine the order of operations needed
  4. Solve step by step: Perform calculations in sequence
  5. Check your work: Verify the answer makes sense
Tip 1: Underline key information in the problem to keep track of important numbers.
Tip 2: Write down each step clearly so you don't lose track of your progress.
Tip 3: Ask yourself "Does this answer make sense?" after each step.
Tip 4: If you get stuck, try drawing a picture or making a list of the information.
Common errors: Performing operations in wrong order, skipping steps, miscalculating, forgetting to include all information.
Memorization tip: "R-P-S-C" - Read, Plan, Solve, Check - the 4 steps of problem solving!
Multi-Step Problem Principles:

• Always perform operations in the correct order (multiplication/division before addition/subtraction)

• Complete each step before moving to the next

• Keep track of units (dollars, apples, etc.) throughout the problem

• Verify that your final answer addresses the original question

• Check that your answer is reasonable in the context of the problem

Solution: Exercises 4 to 5
4 Running Multi-Step Problem
Exercise 4
Tom ran 2.5 miles on Monday, 3.2 miles on Tuesday, and 1.8 miles on Wednesday. He wants to run a total of 15 miles during the week. If he runs the same distance on Thursday and Friday, how many miles should he run each day?
Definition:

Multi-step problem: Requires calculating what remains after known quantities

Week Goal
15 miles
Ran Mon-Wed
2.5 + 3.2 + 1.8
Thu + Fri
? miles each
Step 1: Calculate miles run Mon-Wed

2.5 + 3.2 + 1.8 = 7.5 miles

Step 2: Calculate remaining miles needed

15.0 - 7.5 = 7.5 miles remaining

Step 3: Calculate miles per day for Thu-Fri

7.5 miles ÷ 2 days = 3.75 miles each day

3.75 miles each day
Final answer:

Tom should run 3.75 miles on Thursday and 3.75 miles on Friday

Applied rules:

• Subtraction to find remainder: Total - completed = remaining

• Division for equal sharing: Remaining amount ÷ number of parts

• Decimal arithmetic: Careful alignment when adding/subtracting decimals

5 Box Packing Multi-Step Problem
Exercise 5
A factory produces 240 toys each day. They pack the toys in boxes, with each box holding 8 toys. If they operate 5 days a week, how many boxes do they need for one week of production? If each box costs $3, what is the total weekly cost for boxes?
Definition:

Multi-step problem: Involves multiple calculations with dependent results

Daily production
240 toys
Toys per box
8 toys
Box cost
$3 each
Step 1: Calculate weekly toy production

240 toys/day × 5 days = 1,200 toys

Step 2: Calculate number of boxes needed

1,200 toys ÷ 8 toys per box = 150 boxes

Step 3: Calculate total box cost

150 boxes × $3 per box = $450

150 boxes, $450 cost
Final answer:

The factory needs 150 boxes for one week of production

The total weekly cost for boxes is $450

Applied rules:

• Sequential dependency: Second calculation depends on first result

• Division for grouping: Total items ÷ items per group = number of groups

• Multiplication for cost: Number of units × cost per unit = total cost

Multi-Step Problem Solving Laws and Methods
Final = Initial + Operations
Solution Formula
Key definitions:

Mathematical reasoning: Logical thinking used to solve problems systematically

Problem decomposition: Breaking complex problems into simpler steps

Operational hierarchy: Order in which operations are performed

Complete Multi-Step Problem Solving Methodology:
  1. Comprehension: Read the problem completely and identify what is being asked
  2. Information extraction: List all given numbers and relevant information
  3. Operation planning: Determine the sequence of operations needed
  4. Step execution: Perform each calculation carefully
  5. Verification: Check that each step leads logically to the next
  6. Validation: Ensure the final answer makes sense in context
Tip 1: Make a plan before starting calculations - write down what you need to find first.
Tip 2: Check your work after each step to catch errors early.
Tip 3: Draw diagrams or make lists to visualize the problem when needed.
Tip 4: Always include units in your calculations to stay organized.
Common errors: Performing operations out of order, miscalculations in intermediate steps, losing track of units, not addressing all parts of the question.
Memory aids: "R-P-S-C" - Read, Plan, Solve, Check - always follow these steps!
Essential Multi-Step Problem Principles:

• Always read the entire problem before beginning calculations

• Identify the question being asked before solving

• Perform operations in the correct order (PEMDAS/BODMAS)

• Keep track of units throughout the solution

• Verify that your answer addresses the original question

Questions & Answers

Question: I have trouble knowing what operations to use in multi-step problems. How do I figure out whether to add, subtract, multiply, or divide?

Answer: Look for clue words that indicate operations:

  • Addition (+): "total," "altogether," "sum," "in all," "combined," "more than"
  • Subtraction (-): "difference," "less than," "remaining," "left," "decreased by," "how many more"
  • Multiplication (×): "each," "per," "product," "times," "groups of," "total cost"
  • Division (÷): "shared equally," "per," "quotient," "divided by," "how many in each group"

Also think about the situation:
- If you're putting things together → Addition
- If you're finding what's left → Subtraction
- If you have equal groups → Multiplication
- If you're sharing or grouping → Division

Always read the entire problem to understand the context!

Question: How do I know what order to do the steps in a multi-step problem? Sometimes I get confused about which calculation to do first.

Answer: Follow this general order and think about the logical sequence:

  1. Read the problem completely to understand what's happening
  2. Identify the question - what do you need to find?
  3. Look for dependencies - what information do you need first?
  4. Perform operations in order of the story (chronologically)
  5. Follow mathematical order when needed (multiplication before addition)

Example: If you buy 3 items at $5 each and pay with $20:
- First calculate: 3 × $5 = $15 (cost of items)
- Then calculate: $20 - $15 = $5 (change)

You need the total cost BEFORE you can calculate the change!

Question: I sometimes make mistakes in the middle of a multi-step problem and then everything after that is wrong. How can I prevent this?

Answer: Use these strategies to catch errors early:

  • Check each step before moving to the next one
  • Estimate the answer first to know if your result is reasonable
  • Circle or box your intermediate answers so you can review them
  • Work backwards occasionally to verify your calculations

Example: If you calculate that 3 notebooks at $2.50 each cost $75.00, stop! That's too much - $2.50 × 3 should be around $7.50.

Always ask yourself: "Does this answer make sense?" after each calculation!

Question: How do I make sure I've answered the actual question being asked? Sometimes I solve part of the problem but forget the final step.

Answer: Use this systematic approach to ensure completeness:

Before solving:
- Read the question twice
- Underline what you need to find
- Write down the unit you need (dollars, miles, etc.)

During solving:
- Keep the question in mind as you work
- Write down each step clearly
- Check if you have all the information needed

After solving:
- Reread the original question
- Make sure your answer addresses exactly what was asked
- Verify the unit and format of your answer

Example: If asked "How much change did she receive?" make sure your answer is specifically the change amount, not the total spent!

Question: What should I do when a multi-step problem seems overwhelming? It feels like there's too much information to keep track of.

Answer: Break the problem into smaller, manageable parts:

  1. Read slowly and identify the main question
  2. Highlight or circle important numbers and information
  3. Write down what happens first, second, third, etc.
  4. Solve one piece at a time instead of trying to do everything at once
  5. Connect the pieces to get the final answer

Think of it like following a recipe - you do one step at a time until you reach the final dish!

Example: Instead of trying to solve everything about the field trip at once, calculate:
1. Students' fees
2. Teacher's fee
3. Bus cost
4. Total cost

Take it one bite at a time!