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J.3 Multi-step word problems: with remainders

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What are multi-step word problems?

Multi-step word problems are math problems that require more than one operation to find the answer. You may need to add, subtract, multiply, or divide — sometimes more than once — to solve the problem correctly.

Example:
  • Sam bought 3 boxes of pencils. Each box holds 12 pencils. He gave 7 pencils to his friend. How many pencils does Sam have left?
  • Step 1: 3 × 12 = 36 pencils in total
  • Step 2: 36 − 7 = 29 pencils left
Note

Always read the entire problem carefully. Look for clue words that tell you which operations to use and in what order.

How do we solve multi-step problems with remainders?

When you divide and there is something left over, that extra amount is called a remainder. In real-life problems, you must decide what the remainder means and how to use it to answer the question correctly.

Example:
  • A bus can hold 40 students. There are 125 students going on a field trip. How many buses are needed?
  • Step 1: 125 ÷ 40 = 3 R5
  • Step 2: The remainder means 5 students still need seats, so a fourth bus is required.
Note

When a remainder appears, think about the situation. Sometimes you round up, sometimes you ignore it, and sometimes it becomes part of another step in the problem.

Types of operations used in multi-step problems

Multi-step problems often combine two or more of the four operations: addition, subtraction, multiplication, and division. Knowing how and when to use each operation helps you plan your steps and check your work.

Example Scenarios:
  • Addition and Multiplication: Each of 5 classrooms has 18 students. If 7 new students enroll, how many total students are there? (5 × 18) + 7 = 97
  • Subtraction and Division: A library has 250 books and gives away 10 old books. If the remaining books are placed evenly on 8 shelves, how many books are on each shelf? (250 − 10) ÷ 8 = 30
  • Multiplication and Subtraction: A bakery sells 9 trays of muffins with 24 muffins each. If 65 muffins are sold, how many are left? (9 × 24) − 65 = 151
Note

Plan your steps before solving. Write down what each step represents so you understand how the numbers relate to the story.

Checking your work

After solving a multi-step word problem, always review your solution. Make sure your answer makes sense in the context of the question. You can check by using the inverse operation or estimating.

Example:
  • If you solved 125 ÷ 40 = 3 R5, check it by multiplying: 3 × 40 = 120, and 120 + 5 = 125.
  • Your division is correct, and the remainder matches the situation described.
Note

Always explain your reasoning in words or in writing. Showing your thinking helps others understand how you reached your answer and proves that your solution is logical.