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X.2 Addition, subtraction, multiplication, and division word problems

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Solving word problems

A word problem is a math question written as a short story or situation. To solve it, you must decide which operation (addition, subtraction, multiplication, or division) to use and find the answer.

Example:
  • Maya has 12 stickers. She buys a pack with 8 more. How many stickers does she have now?
  • This is an addition problem: 12 + 8 = 20 stickers.
Note

The first step is always to read the problem carefully. Look for keywords and numbers, and decide what the question is asking you to find.

Key words and phrases

Certain words can help you determine which mathematical operation to use. These are clues within the story.

Common word clues:
  • Addition: in all, altogether, total, combined, sum, more
  • Subtraction: how many more, how many left, difference, fewer, remain
  • Multiplication: each, times, product, total of equal groups, twice
  • Division: share equally, each, per, split, divided into equal groups
Note

Words are helpful clues, but you must always think about the whole situation. For example, "how many more" usually means to subtract, but you must check which numbers you are comparing.

Steps for solving any word problem

Follow a clear plan to organize your thinking and find the correct solution.

The four-step plan:
  1. Understand: Read the problem. What is happening? What are you asked to find?
  2. Plan: Choose the operation. Will you add, subtract, multiply, or divide? Write a number sentence or draw a picture.
  3. Solve: Do the math carefully. Find the answer.
  4. Check: Look back. Does your answer make sense? Can you explain how you got it?
Note

Drawing a simple picture or diagram is often the best way to understand what is happening in the problem, especially for multiplication and division.

Identifying different problem types

Word problems can describe different real-world situations. Recognizing the situation helps you choose the right operation.

Sample situations:
  • Combine (Addition): "There are 7 blue marbles and 9 red marbles. How many marbles are there total?"
  • Compare (Subtraction): "Jason has 15 comic books. Alex has 6. How many more comic books does Jason have?"
  • Equal Groups (Multiplication): "There are 4 bags. Each bag has 5 apples. How many apples are there in all?"
  • Share (Division): "Ms. Chen has 18 cookies to share equally among her 3 children. How many cookies does each child get?"
Note

In division problems, pay close attention to what the "whole" amount is and how many equal groups it is being split into.

Checking your work for reasonableness

An answer is reasonable if it makes sense based on the information in the problem. Estimating can help you check.

Example:
  • Problem: "A box holds 6 juice boxes. How many juice boxes are in 4 boxes?"
  • Solve: 6 x 4 = 24
  • Check for Reasonableness: 6 is close to 5, and 5 x 4 = 20. 24 is close to 20, so the answer of 24 is reasonable. An answer like 240 would not make sense.
Note

Always ask yourself: "Is this answer too big or too small for the story?" If you subtracted and got a larger number, or multiplied and got a smaller number, re-check your plan.