Solving Multi-Step Word Problems with Multiplication

Master multi-step word problems involving multiplication through 3 detailed exercises with step-by-step solutions.

Solutions: Multi-Step Word Problems
1 Farm Animals Problem
Exercise 1
Sarah has 4 chickens. Each chicken lays 3 eggs every day. She collects eggs for 5 days. How many eggs does Sarah collect in total?
Definition:

Multi-step word problem: A problem requiring multiple operations to find the solution. In this case, multiplication followed by another multiplication.

Step-by-step method:
  1. Read the problem carefully and identify key information
  2. Find what is being asked (total number of eggs)
  3. Identify the steps needed (chickens × eggs per day × days)
  4. Perform calculations step by step
  5. Check your answer makes sense
Step 1
4 × 3 = 12
Step 2
12 × 5 = 60
Step 1: Eggs per day

Sarah has 4 chickens, each laying 3 eggs daily

4 chickens × 3 eggs = 12 eggs per day

Step 2: Total eggs over 5 days

If she collects 12 eggs per day for 5 days

12 eggs/day × 5 days = 60 eggs total

Step 3: Alternative approach

We could also multiply all together: 4 × 3 × 5 = 60

Sarah collects 60 eggs in total
Final answer:

Sarah collects 60 eggs in total over 5 days

Applied rules:

• Multiplication: Repeated addition (4 groups of 3)

• Order of operations: We can multiply in any order

• Problem-solving: Break complex problems into smaller steps

2 Stickers Problem
Exercise 2
Tom bought 6 packs of stickers. Each pack has 8 stickers. He gave 15 stickers to his friends. How many stickers does Tom have left?
Definition:

Multi-step problem with mixed operations: Requires both multiplication and subtraction to solve.

Step 1
6 × 8 = 48
Step 2
48 - 15 = 33
Step 1: Total stickers bought

Tom bought 6 packs, each with 8 stickers

6 × 8 = 48 stickers total

Step 2: Stickers remaining

He gave away 15 stickers, so we subtract

48 - 15 = 33 stickers left

Step 3: Verification

If Tom has 33 stickers left and gave away 15: 33 + 15 = 48 ✓

Tom has 33 stickers left
Final answer:

Tom has 33 stickers left after giving 15 to his friends

Applied rules:

• Multiplication: Finding total amount (groups × items per group)

• Subtraction: Taking away part of the whole

• Order matters: First multiply, then subtract

3 Garden Planting Problem
Exercise 3
A farmer plants 7 rows of carrots with 6 carrots in each row. Then he plants 4 rows of beans with 5 beans in each row. How many vegetables did the farmer plant altogether?
Definition:

Multi-step problem with addition: Requires two multiplications and one addition to find the total.

Step 1
7 × 6 = 42
Step 2
4 × 5 = 20
Step 3
42 + 20 = 62
Step 1: Count carrot plants

7 rows of carrots with 6 in each row

7 × 6 = 42 carrots

Step 2: Count bean plants

4 rows of beans with 5 in each row

4 × 5 = 20 beans

Step 3: Find total vegetables

Add carrots and beans together

42 + 20 = 62 vegetables total

Step 4: Verification

We can write this as: (7 × 6) + (4 × 5) = 42 + 20 = 62 ✓

The farmer planted 62 vegetables altogether
Final answer:

The farmer planted 62 vegetables altogether (42 carrots + 20 beans)

Applied rules:

• Repeated multiplication: Two separate multiplication problems

• Addition: Combining two totals

• Grouping: Organizing information by vegetable type

Multiplication Concepts & Methods
Groups × Items per Group = Total
Basic Multiplication Formula
Multiplication
3 × 4 = 12
Same as 3 + 3 + 3 + 3 = 12
Arrays
Rows × Columns
Visual representation
Word Clues
each, per, total, altogether
Indicators for multiplication
Key definitions:

Multiplication: Repeated addition (adding equal groups)

Multi-step problem: A problem requiring more than one operation

Array: Objects arranged in rows and columns

Problem-solving steps:
  1. Read carefully: Understand what the problem asks
  2. Find key words: Look for multiplication clues (each, per, total)
  3. Plan steps: Decide what operations to perform
  4. Solve step by step: Perform calculations in order
  5. Check answer: Does it make sense in context?
Multiplication Strategies & Tips
5 × 7 = 7 × 5
Commutative Property
Tip 1: Draw pictures or arrays to visualize multiplication problems.
Tip 2: Look for keywords like "each", "per", "total", "altogether", "in all".
Tip 3: Break large problems into smaller steps.
Tip 4: Always check if your answer makes sense in the story.
Common errors: Forgetting to perform all steps, misreading the question, calculation mistakes.
Success strategies: Read twice, draw diagrams, write steps clearly, check work.
Important properties:

• Commutative: a × b = b × a

• Associative: (a × b) × c = a × (b × c)

• Identity: a × 1 = a

• Zero: a × 0 = 0

Multi-Step Problem Solving

🔢
Step 1: Read Carefully
Read the entire problem slowly. Identify what you're looking for.
Step 2: Find Key Information
Circle numbers and underline important words (each, per, total).
Step 3: Plan Operations
Decide which operations to use and in what order.
Step 4: Solve & Check
Perform calculations and verify your answer makes sense.
Problem-Solving Workflow
1
READ
2
PLAN
3
SOLVE
4
CHECK
Multiplication Array Example
🟨🟨🟨 (3 columns)
🟨🟨🟨
🟨🟨🟨 (3 rows)
3 × 3 = 9 total squares
Practice Makes Perfect!

Questions & Answers

Question: I get confused when a word problem has both multiplication and addition. How do I know which to do first?

Answer: Great question! When solving multi-step problems, think about the story:

  • First, do what makes sense in the story. For example, if you need to find how many items are in each group first, do the multiplication.
  • Then, if you need to combine those results, do the addition.

In our garden problem: First we found how many carrots (7 × 6 = 42) and beans (4 × 5 = 20), then added them together (42 + 20 = 62).

Always read the problem carefully to understand what's happening in the story!

Question: My child struggles with knowing whether to multiply or add in word problems. Any suggestions?

Answer: Try these helpful strategies:

  • Look for clue words: "Each," "per," "every," "times" often mean multiply. "Total," "altogether," "sum," "more" often mean add.
  • Draw pictures: Visualize the problem with groups or arrays.
  • Act it out: Use physical objects to represent the problem.

For example, if the problem says "4 boxes with 5 apples each," you're looking at 4 groups of 5, which is multiplication (4 × 5).

Practice with simple problems first, then gradually increase difficulty.

Question: Why do we sometimes multiply three numbers together like in the egg problem (4 × 3 × 5)?

Answer: When we multiply three numbers, we're finding the total of multiple groups of groups! Let's break down the egg problem:

  • 4 chickens (groups of chickens)
  • Each chicken lays 3 eggs per day (eggs per chicken)
  • For 5 days (days of collection)

So we have: 4 chickens × 3 eggs/chicken × 5 days = 60 eggs total

We can multiply in any order: 4 × 3 × 5 = 12 × 5 = 60 OR 4 × 15 = 60

Think of it as: (chickens × eggs per chicken) × days = (eggs per day) × days = total eggs