Two-Step Word Problems with Addition, Subtraction, and Multiplication

Master two-step word problems: addition, subtraction, and multiplication through these 5 detailed exercises with visual explanations and step-by-step solutions.

Solution: Exercises 1 to 3
1 Two-step problem with addition and multiplication
Exercise 1
Sarah has 12 stickers. Her friend gives her 8 more stickers. Then Sarah puts all her stickers into albums, putting 5 stickers on each page. How many pages does she fill?
Definition:

Two-step word problem: A problem that requires two mathematical operations to solve.

Problem-solving method:
  1. Read the problem carefully and identify what is being asked
  2. Identify the operations needed (addition, subtraction, multiplication)
  3. Solve step by step, one operation at a time
  4. Check your answer makes sense in the context
Step 1
12 + 8
Step 2
20 ÷ 5
Step 1: Find total stickers

Sarah starts with 12 stickers and gets 8 more: 12 + 8 = 20 stickers

Step 2: Find number of pages

She puts 5 stickers on each page, so 20 ÷ 5 = 4 pages

Step 3: Verify the answer

4 pages × 5 stickers per page = 20 stickers ✓

Sarah fills 4 pages
Final answer:

Sarah fills 4 pages with her stickers.

Applied rules:

• Addition: Combine quantities to find totals

• Division: Split total into equal groups

• Order of operations: Solve problems step by step

2 Two-step problem with multiplication and subtraction
Exercise 2
A farmer has 7 baskets. Each basket contains 6 apples. The farmer sells 15 apples. How many apples does the farmer have left?
Definition:

Multiplication: Repeated addition to find total groups

Step 1
7 × 6
Step 2
42 - 15
Step 1: Find total apples

7 baskets with 6 apples each: 7 × 6 = 42 apples

Step 2: Subtract sold apples

Farmer had 42 apples, sold 15: 42 - 15 = 27 apples left

Step 3: Verify the answer

27 remaining + 15 sold = 42 total ✓

The farmer has 27 apples left
Final answer:

The farmer has 27 apples left.

Applied rules:

• Multiplication: Find total when groups are equal

• Subtraction: Find what remains after taking away

• Problem structure: Total - Amount taken = Amount remaining

3 Two-step problem with addition and subtraction
Exercise 3
Emma had 45 marbles. She found 18 more marbles in her room. Then she gave 23 marbles to her brother. How many marbles does Emma have now?
Definition:

Addition: Combining quantities to make a larger total

Step 1
45 + 18
Step 2
63 - 23
Step 1: Find marbles after finding more

Emma started with 45 marbles and found 18 more: 45 + 18 = 63 marbles

Step 2: Subtract marbles given away

Emma had 63 marbles and gave 23 to her brother: 63 - 23 = 40 marbles

Step 3: Verify the answer

Start with 45, add 18, subtract 23: 45 + 18 - 23 = 40 ✓

Emma has 40 marbles now
Final answer:

Emma has 40 marbles now.

Applied rules:

• Addition: Finding new total after gaining items

• Subtraction: Finding remaining amount after giving away

• Sequential operations: Work from left to right

Key Rules, Methods, and Strategies
Addition + Subtraction = Two-step Problem
Problem Structure
Addition Rule
Total = Start + Added
Combine quantities
Subtraction Rule
Remaining = Total - Taken
Find what's left
Multiplication Rule
Total = Groups × Items per group
Equal groups
Key definitions:

Two-step problem: A problem requiring two different mathematical operations to solve.

Operations: Addition (+), subtraction (-), multiplication (×), division (÷).

Word clues: "more than", "less than", "each", "total", "left", "altogether".

Complete methodology:
  1. Read carefully: Understand what the problem is asking
  2. Identify operations: Look for key words that indicate operations
  3. Plan steps: Decide which operation to do first
  4. Solve sequentially: Complete one step before moving to the next
  5. Check answer: Make sure it makes sense in the story
Tip 1: Look for clue words: "more" (add), "less" (subtract), "each" (multiply).
Tip 2: Draw pictures or use manipulatives to visualize the problem.
Tip 3: Always solve the first step completely before starting the second.
Tip 4: Estimate your answer first to check reasonableness.
Common errors: Solving steps out of order, misreading clue words, calculation mistakes.
Success strategies: Circle key numbers, underline clue words, work systematically.
Key formulas to remember:

• Addition: Total = Part₁ + Part₂

• Subtraction: Remaining = Original - Taken Away

• Multiplication: Total = Number of Groups × Items per Group

• Two-step pattern: (First Operation) → (Second Operation)

Visual Problem-Solving: Operations Flow
Problem-Solving Flowchart
Visual representation of two-step problem-solving process:

Analysis: The flowchart shows how two-step problems progress through operations.

  • Start with initial quantity → Apply first operation → Use result → Apply second operation → Final answer
  • Always follow the sequence described in the word problem
  • Check that each step makes logical sense

Questions & Answers

Question: I get confused about which operation to do first in two-step problems. How do I know whether to add or multiply first?

Answer: Great question! The order follows the story in the word problem:

  • Read the problem carefully and identify the sequence of events
  • Follow the order the story tells you, not just left to right in the equation
  • Look for clue words: "each", "groups of", "rows of" usually mean multiplication
  • "More", "added", "combined" usually mean addition

Example: "Sarah has 5 boxes with 4 toys each. She finds 6 more toys." First multiply (5 × 4) because of "each", then add (20 + 6) because of "finds more".

The key is to understand the situation, not just look at numbers!

Question: My child often adds when they should subtract in word problems. How can I help them identify the correct operation?

Answer: This is a very common issue! Try these strategies:

  • Act out the problem: Use physical objects to represent the situation
  • Look for action words: "Give away", "lose", "eat", "sell" mean subtraction
  • Ask: "Are we getting more or less?" More = addition, Less = subtraction
  • Draw a picture: Visual representation helps clarify the situation

Example: "Tom had 15 cookies. He ate 4." The action is eating (taking away), so subtract: 15 - 4 = 11.

Practice with many examples and encourage your child to explain their thinking aloud.

Question: Sometimes I don't know what the problem is asking me to find. How do I figure it out?

Answer: This happens to many students! Here's how to identify what to find:

  • Look for question words: "How many?", "How much?", "What is the total?", "How many left?"
  • Circle or underline the question: Focus on the specific question being asked
  • Read the whole problem twice: First for understanding, second to identify what's needed
  • Ask yourself: "What information do I need to find?"

Example: "There are 6 bags with 8 apples each. 15 apples are eaten. How many apples are left?" The question asks for "apples left", so you need to find the remaining amount after some were eaten.

Always reread the question part to make sure you're answering exactly what's asked!