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Solve multi-step addition and subtraction problems

The learner interprets multi-step situations involving addition and subtraction of whole numbers through 1,000,000, identifying the quantities, relationships, and unknowns and determining which operation and sequence represent each step. Equations, bar models, and place-value reasoning support composing, decomposing, comparing, and checking intermediate and final results for reasonableness; the steps are chosen from the context rather than applied mechanically from left to right. This scope excludes decimal and fraction operations, negative numbers, and more generalized algebraic treatment.

Detailed Explanation: Solve multi-step addition and subtraction problems

Read the problem carefully and decide what happens first, next, and last. Do not automatically calculate from left to right. Ask:

  • What amount do we start with?
  • Is each change an increase or a decrease?
  • What does the question ask us to find?

Example

A library has 246,800246{,}800 books. It buys 18,45018{,}450 more books, removes 12,67512{,}675 damaged books, and receives a donation of 9,3009{,}300 books. How many books does the library have now?

1. Find the starting amount and the first change.

The library starts with 246,800246{,}800 books and buys more, so add:

246,800+18,450=265,250246{,}800+18{,}450=265{,}250

After buying the books, the library has 265,250265{,}250 books.

2. Use the next event.

The library removes damaged books, so subtract:

265,250−12,675=252,575265{,}250-12{,}675=252{,}575

Now the library has 252,575252{,}575 books.

3. Use the final event.

The library receives more books, so add:

252,575+9,300=261,875252{,}575+9{,}300=261{,}875

The library has 261,875261{,}875 books now.

The whole situation can be shown with one equation:

246,800+18,450−12,675+9,300=261,875246{,}800+18{,}450-12{,}675+9{,}300=261{,}875

Check that the answer is reasonable: starting with about 247,000247{,}000, adding about 18,00018{,}000, subtracting about 13,00013{,}000, and adding about 9,0009{,}000 gives about 261,000261{,}000. This is close to 261,875261{,}875, so the answer makes sense.

Learn by doing: Solve multi-step addition and subtraction problems

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    Subtraction - Missing Value, 3 Digit, 3 Numbers

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