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H.2 Perform operations with whole numbers: word problems

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Understanding Word Problems with Whole Numbers

Word problems are mathematical exercises presented in everyday language that require you to identify the correct operation and solve using numbers.

Examples:
  • Maria has 15 stickers. She buys 8 more. How many stickers does she have now?
  • A box holds 24 crayons. If 6 students share them equally, how many crayons does each student get?
Note

Word problems tell a story with numbers. Your job is to figure out what the problem is asking and which mathematical operation will help you find the answer.

Identifying Operations in Word Problems

Each word problem contains clues that help you determine whether to add, subtract, multiply, or divide.

Operation Clues:
  • Addition: combined, total, sum, altogether, in all
  • Subtraction: difference, fewer, left, remain, how many more
  • Multiplication: times, product, each, per, equal groups
  • Division: share, equally, each, per, split, quotient
Note

Look for these key words and phrases to help you decide which operation to use. Sometimes problems require multiple steps with different operations.

Solving Addition and Subtraction Problems

Addition combines quantities, while subtraction finds the difference between quantities or takes away from a total.

Examples:
  • Addition: "The school library has 2,345 books. They receive 568 new books. How many books are in the library now?" (2,345 + 568 = 2,913)
  • Subtraction: "James needs to read 350 pages. He has read 187 pages. How many pages does he have left to read?" (350 - 187 = 163)
Note

When subtracting, make sure you align numbers properly by place value. Always check your work by adding your answer to the smaller number to see if you get the larger number.

Solving Multiplication and Division Problems

Multiplication finds the total when you have equal groups, while division splits a total into equal parts or finds how many are in each group.

Examples:
  • Multiplication: "There are 15 classrooms. Each classroom has 24 students. How many students are there in all?" (15 × 24 = 360)
  • Division: "The school has 625 students. If there are 25 students on each bus, how many buses are needed?" (625 ÷ 25 = 25)
Note

In division word problems, pay attention to whether there might be a remainder. Sometimes remainders mean you need to round up your answer.

Multi-Step Word Problems

Multi-step problems require you to perform more than one operation to find the final answer.

Example:
  • "Sarah bought 3 packs of markers with 8 markers in each pack. She gave 5 markers to her friend. How many markers does Sarah have left?"
  • Step 1: 3 × 8 = 24 markers total
  • Step 2: 24 - 5 = 19 markers left
Note

Read multi-step problems carefully. Identify what you need to find first before you can solve for the final answer. Underlining or circling important information can help.

Problem-Solving Strategy

Using a consistent strategy helps you solve word problems accurately.

Steps to Success:
  1. Read the problem carefully
  2. Identify what you know and what you need to find
  3. Choose the correct operation(s)
  4. Solve the problem step by step
  5. Check your answer to see if it makes sense
Note

Always ask yourself: "Does my answer make sense in the context of the problem?" If you have 150 students but only 3 classrooms, you might want to check your work!