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Y.2 Multiplication and division two-step word problems

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Understanding two-step word problems

A two-step word problem is a math problem that requires you to perform two different operations (like multiplication and division) to find the final answer. You must solve the first step before you can solve the second.

Example:
  • Problem: Bobby has 4 boxes. Each box holds 6 markers. He wants to give an equal number of these markers to 3 tables of students. How many markers will each table get?
  • Step 1 (Multiplication): Find the total markers. 4 boxes × 6 markers = 24 markers total.
  • Step 2 (Division): Share them equally. 24 markers ÷ 3 tables = 8 markers per table.
Note

The words "each" and "equal" often give you clues about which operations to use. "Each" can point to multiplication, and "equal shares" or "divided among" can point to division.

Identifying the operations

To solve a two-step problem, you must read carefully to identify the two hidden math questions. Look for key phrases that tell you whether to multiply or divide.

Clue words:
  • Multiplication Clues: "each," "in each group," "per," "total," "altogether," "times."
  • Division Clues: "share equally," "divided by," "split among," "how many each," "equal groups."
Practice problem:

There are 9 classrooms. Each class needs 5 new notebooks. The notebooks come in packs of 3. How many packs need to be bought?

  • Step 1 (×): 9 classes × 5 notebooks = 45 notebooks needed.
  • Step 2 (÷): 45 notebooks ÷ 3 per pack = 15 packs.
Note

Always write down the answer to your first step clearly. This becomes the starting number for your second step. Label your numbers with words like "total markers" to keep track.

Checking your work

Checking your answer helps ensure you solved the problem correctly and used the right operations in the right order.

How to check:
  • Work backwards: Start with your final answer and perform the opposite operations.
  • Use estimation: See if your answer is reasonable.
  • Re-read the problem: Make sure you answered the question that was asked.
Example check:

Problem: A baker makes 8 trays of muffins. Each tray has 12 muffins. She puts them into boxes of 4 muffins each. How many boxes does she fill?

  • Solution: (8 × 12) ÷ 4 = 96 ÷ 4 = 24 boxes.
  • Check by working backwards: If she has 24 boxes with 4 muffins each, that's 24 × 4 = 96 muffins. Did she start with 96 muffins? Yes, because 8 trays × 12 muffins = 96. The answer is correct.
Note

If your final answer is a number of objects (like boxes or bags), it should usually be a whole number. If you get a remainder, think: "Do I need to round up, or does the problem ask for what's left over?"

Solving problems with different step orders

Not all problems follow the same pattern. Sometimes you divide first, then multiply. The order depends entirely on the story the problem tells.

Examples of different orders:
  • Multiply then Divide: "Jane bought 7 bags with 10 apples each. She divided all the apples equally among 5 pies. How many apples were in each pie?"
    Solution: (7 × 10) ÷ 5 = 70 ÷ 5 = 14 apples per pie.
  • Divide then Multiply: "A farmer has 48 eggs. He puts them into cartons that hold 12 eggs. He sells 3 cartons. How many eggs did he sell?"
    Solution: First, find cartons: 48 ÷ 12 = 4 cartons. Then, find eggs sold: 3 cartons × 12 eggs = 36 eggs sold. (Notice the second step uses the number 12 from the problem, not the 4 you just found).
Note

The most important rule is: Read the entire problem first. Find the final question, then figure out what you need to know first to answer it. Underlining the question can help you stay focused.