Solving Word Problems With Decimals

🔑 Key Concepts

  • Many real-world decimal problems require more than one operation.
  • Read carefully and identify the cost, quantity, tax, amount paid, and question being asked.
  • Multiply when several items have the same price.
  • Add all purchases and tax to find the total amount spent.
  • Subtract the total cost from the amount paid to find the change.
  • Line up decimal points when adding or subtracting money amounts.
  • Estimate before calculating to check whether the final answer is reasonable.

✏️ Worked Example — Finding the Total Cost and Change

🧠 Math Vocabulary and Key Words

  • Per or each: indicates an amount for one item and often signals multiplication.
  • Subtotal: the combined cost before tax or other additional charges are included.
  • Total: the complete amount after all costs are combined.
  • Change: the amount returned after subtracting the total cost from the amount paid.
  • Tax: an additional amount added to the cost of a purchase.
  • Product: the answer to a multiplication problem.
  • Difference: the answer to a subtraction problem.

💡 Main Idea

Multi-step decimal word problems require students to determine which operations to use and the order in which to use them. In a shopping problem, multiply to find the cost of repeated items, add all purchases and tax to find the total cost, and subtract the total from the amount paid to determine the change.

📚 What You Should Already Know

Before solving multi-step decimal problems, students should know how to multiply, add, and subtract decimals. Students should also understand decimal place value, line up decimal points when adding or subtracting, and interpret common money terms such as each, tax, total, and change.

🚀 What Comes Next

After mastering multi-step decimal word problems, students can apply these skills to budgeting, unit prices, percent discounts, sales tax, tips, and other financial situations. These concepts also support later work with proportions, expressions, equations, and algebraic problem solving.

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