When you’re trying to solve word problems in math, figuring out when to add or subtract is really important, especially in algebra. Addition and subtraction often pop up in these problems, and knowing when to use each one helps you write the right algebraic expressions. Let’s look at how to tell which operation to use through some simple tips and examples!

Understanding the Context

1. Keywords and Phrases: Some words or phrases can help you decide if you should add or subtract. Here are some common clues:

   • Addition Keywords:
     • "total"
     • "combined"
     • "together"
     • "more than"
     • "increased by"
   • Subtraction Keywords:
     • "difference"
     • "less"
     • "decreased by"
     • "fewer"
     • "left over"

   Example:

   • For addition: "A bakery sold 30 cakes in the morning and 50 in the afternoon. How many cakes were sold in total?"

     • The phrase "in total" tells us to add: $30 + 50 = 80$

   • For subtraction: "There were 100 apples, and Mark took away 25. How many apples are left?"

     • The word "left" means we will subtract: $100 - 25 = 75$

2. The Situation: Pay attention to what the problem is asking. Are we putting things together, or are we figuring out what’s left?

   Example:

   • If the problem talks about two friends collecting stickers and asks how many they have together, you would add.
   • If it mentions someone spending money and asks how much is left, that would need subtraction.

Identifying Structures

• Other times, the problem might not have clear keywords but still suggests adding or subtracting based on its setup:

  • Whole vs. Part: If it talks about a whole amount versus parts of that whole, you’ll probably use subtraction. For example, "A classroom can hold 30 students, and there are currently 22 students. How many more students can join?" Here, we find the available spots: $30 - 22 = 8$

• Sequential Events: If the problem shares a series of events, it may use both operations.

  Example: "Maria had $200. She earned$50, then spent $30. How much does she have now?"

  • First, add what she earned: $200 + 50 = 250$
  • Then, subtract what she spent: $250 - 30 = 220$

Constructing Algebraic Expressions

Once you know how to tell when to add or subtract, let’s look at how to create algebraic expressions from word problems.

1. Identify Variables: Give a variable a name for unknown amounts.

   • For example, if you don’t know how many more fruits Sam needs, you could use $x$ for that.

2. Set Up the Expression:

   • With your variables and numbers ready, write out the expression using addition or subtraction based on the clues or the situation.

   Example: "Anna has $x$ dollars. She finds $50 more." The expression looks like this: $x + 50$

   • If Anna then spends $30, it would be: $x + 50 - 30$

Practice Makes Perfect

The best way to get good at knowing when to add or subtract in word problems is to practice. Try out different problems while looking for those keywords and understanding the context. With time, you’ll get better at figuring out which operation to use and making algebraic expressions easier!

By keeping these tips in mind, you’ll feel more confident when tackling word problems. Happy learning!