Solving Multi-Step Problems with Multiplication

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

Solutions: Multi-Step Problems
1 Cookie Party Problem
Exercise 1
Emma is organizing a party. She has 3 boxes of cookies. Each box has 8 cookies. She gives 5 cookies to her teacher and keeps the rest. How many cookies does Emma keep?
Definition:

Multi-step problem: A problem requiring more than one operation to find the solution. This problem needs multiplication (to find total cookies) and subtraction (to find remaining cookies).

Step-by-step method:
  1. Read the problem carefully and identify what is asked
  2. Find the total amount first (multiplication)
  3. Subtract what is given away (subtraction)
  4. Write the final answer in a complete sentence
Step 1
3 × 8 = 24
Step 2
24 - 5 = 19
Step 1: Find total cookies

Emma has 3 boxes with 8 cookies each

3 boxes × 8 cookies per box = 24 cookies total

Step 2: Subtract given cookies

She gives 5 cookies to her teacher

24 - 5 = 19 cookies remaining

Step 3: Verify answer

If Emma keeps 19 and gave 5: 19 + 5 = 24 ✓

Emma keeps 19 cookies
Final answer:

Emma keeps 19 cookies for the party

Applied rules:

• Multiplication: Finding total in equal groups (3 groups of 8)

• Subtraction: Taking away part of the whole

• Order matters: First multiply, then subtract

2 Book Reading Problem
Exercise 2
Lucas reads 4 pages every day for 6 days. Then he reads 7 more pages on Sunday. How many pages did Lucas read in total?
Definition:

Multi-step problem with mixed operations: Requires multiplication (pages per day × days) and addition (extra pages).

Step 1
4 × 6 = 24
Step 2
24 + 7 = 31
Step 1: Pages for 6 days

Lucas reads 4 pages each day for 6 days

4 pages/day × 6 days = 24 pages

Step 2: Add extra pages

He reads 7 more pages on Sunday

24 + 7 = 31 pages total

Step 3: Verification

Regular reading (24) + extra reading (7) = 31 ✓

Lucas read 31 pages in total
Final answer:

Lucas read 31 pages in total over the week

Applied rules:

• Multiplication: Repeated addition (6 groups of 4)

• Addition: Combining different amounts

• Problem structure: Regular + extra

3 Garden Planting Problem
Exercise 3
A gardener plants 5 rows of tomatoes with 6 plants in each row. Then he plants 3 rows of cucumbers with 4 plants in each row. How many plants did he plant altogether?
Definition:

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

Step 1
5 × 6 = 30
Step 2
3 × 4 = 12
Step 3
30 + 12 = 42
Step 1: Count tomato plants

5 rows of tomatoes with 6 plants in each row

5 × 6 = 30 tomato plants

Step 2: Count cucumber plants

3 rows of cucumbers with 4 plants in each row

3 × 4 = 12 cucumber plants

Step 3: Find total plants

Add tomatoes and cucumbers together

30 + 12 = 42 plants total

Step 4: Verification

We can write this as: (5 × 6) + (3 × 4) = 30 + 12 = 42 ✓

The gardener planted 42 plants altogether
Final answer:

The gardener planted 42 plants altogether (30 tomatoes + 12 cucumbers)

Applied rules:

• Repeated multiplication: Two separate multiplication problems

• Addition: Combining two totals

• Grouping: Organizing information by plant 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?
Detailed Summary: Multi-Step Problem Solving
? = (Groups × Items) ± Extra
Multi-Step Pattern
Key Definitions:

Multi-step problem: A math problem that requires more than one operation to solve. It might involve addition, subtraction, multiplication, or division in sequence.

Operations: Mathematical actions like adding (+), subtracting (-), multiplying (×), or dividing (÷).

Keywords: Words in the problem that tell you which operation to use (e.g., "each" means multiply).

Core Rules:

• Read the entire problem first - Don't rush to calculate

• Identify the question - What are you trying to find?

• Circle important numbers - These are your values

• Underline key words - They indicate operations

• Solve step by step - Don't try to do everything at once

Step-by-Step Method:
  1. Read: Read the problem completely to understand the situation
  2. Identify: Find what the question is asking for
  3. Plan: Decide which operations to use and in what order
  4. Solve: Work through each step carefully
  5. Check: Verify your answer makes sense
Tip 1: Look for these keywords: "each", "per", "times", "product", "total", "altogether", "in all", "more than", "less than".
Tip 2: Draw pictures or make lists to visualize the problem.
Tip 3: Write down each step so you don't lose track.
Tip 4: Always check if your final answer is reasonable.
Common mistakes: Adding instead of multiplying, forgetting steps, miscalculating, not reading the question carefully.
Success strategies: Take your time, organize information, check work, use drawings when helpful.
More Examples

Simple example: 3 bags with 4 apples each → 3 × 4 = 12 apples

Medium example: 2 boxes of 6 crayons, use 3 → (2 × 6) - 3 = 9 remaining

Advanced example: 4 shelves with 5 books each, add 7 more → (4 × 5) + 7 = 27 total

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 book problem: First we found how many pages Lucas read in 6 days (4 × 6 = 24), then added the extra pages (24 + 7 = 31).

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 more complex problems?

Answer: When we multiply three numbers, we're finding the total of multiple groups of groups! For example:

  • 3 boxes of cookies
  • Each box has 4 packages
  • Each package has 5 cookies

So we have: 3 × 4 × 5 = 60 cookies total

We can multiply in any order: 3 × 4 × 5 = 12 × 5 = 60 OR 3 × 20 = 60

Think of it as: (boxes × packages per box) × cookies per package = total cookies