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Y.1 Addition and subtraction word problems - up to two digits

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What are mixed operations word problems?

Mixed operations word problems are math problems that ask you to use both addition and subtraction to solve. They usually include two steps and numbers written in words or digits.

Example:

Maria had 24 apples. She gave 5 to her friend, then she bought 7 more. How many apples does she have now?

Note

Always read carefully. Look for the actions in the problem (like “gave away” for subtraction or “bought” for addition).

How to identify mixed operations word problems

These problems often include more than one action. You might see both adding and subtracting in the same story problem.

Steps to identify:
  • Look for the first action: does it ask you to add or subtract?
  • Find the second action: does it ask you to do the opposite operation?
  • Notice that one number is a two-digit number and the other is a one-digit number.
Note

Underline the important numbers and circle the key words (like “more,” “left,” “gave,” or “together”).

Strategies for solving

You can use different strategies to solve two-step mixed problems. The goal is to keep track of both steps and make sure your answer makes sense.

Common Strategies:
  • Counting back: Start from the bigger number and count back for subtraction. Example: 36 − 4 → count back 4 to get 32.
  • Place value: Break apart numbers by tens and ones to add or subtract. Example: 27 + 6 → 20 + 7 + 6 = 33.
  • Break apart the smaller number: Use subtraction in parts. Example: 45 − 8 → 45 − 5 = 40, then 40 − 3 = 37.
Note

Choose the strategy that helps you solve the problem most clearly and check your work after each step.

Examples of solving mixed operations

Let’s look at some full examples and solve them step by step.

Examples:
  • Ben had 42 marbles. He gave 6 to his friend. Then he found 5 more. How many marbles does Ben have now?
    Step 1: 42 − 6 = 36 (he gave some away).
    Step 2: 36 + 5 = 41 (he found more).
    Answer: 41 marbles.
  • Lily read 25 pages of her book. The next day she read 8 more pages but then forgot 3 pages and had to reread them. How many pages did she read in all?
    Step 1: 25 + 8 = 33 (she read more).
    Step 2: 33 + 3 = 36 (she reread some pages).
    Answer: 36 pages.
Note

Always solve one step at a time. Write each step down to stay organized.

Checking your answers

After solving, make sure your answer makes sense in the story problem. You can check by using the opposite operation or rereading the problem.

Checking Example:

Tom had 34 pencils. He used 7, then bought 2 more. How many pencils now?
Solve: 34 − 7 = 27, then 27 + 2 = 29.
Check: If Tom has 29 now, 29 − 2 = 27, and 27 + 7 = 34. ✔ Correct!

Note

Checking helps you catch mistakes. If the answer does not make sense, go back and try again.

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