How to Turn Word Problems into Algebraic Expressions

Transforming word problems into algebraic expressions might seem tough for many students, especially in Grade 9. But if you break it down into simple steps, it can become a lot easier. Let's go through these steps together.

Step 1: Understand the Problem

First, read the word problem carefully. Make sure you know exactly what it’s asking you. Look for important words and ideas. Here's an example:

If a store sells apples for $2 each and you want to buy$x$ apples, how much will it cost?

In this example, the words "sells," “each,” and “cost” help us understand the problem better.

Step 2: Identify the Variables

Next, figure out the letters (variables) that will stand for unknown numbers in the problem. A variable is just a letter that represents a number. For example, if we say $x$ is the number of apples, that helps us describe the problem.

Using our example again:

• Let $x$ = the number of apples bought.

Step 3: Translate Words into Math Operations

Now, we need to change the action words in the problem into math operations. Here are some common keywords:

• "Plus" or "increased by" means addition ($+$).
• "Minus" or "decreased by" means subtraction ($-$).
• "Times" or "product of" means multiplication ($\times$).
• "Divided by" or "per" means division ($\div$).

In our apple example, since each apple costs $2, we can say:

• Cost = $2 \cdot x$ (which is the same as $2x$).

Step 4: Create the Expression or Equation

Now, take what you've figured out and put it together into a math expression or equation. If the problem asks for the total cost, you can write it down using the expressions we established earlier.

So for this problem:

• The total cost of apples = $2x$.

If there’s also a fixed cost, like a $5 delivery fee, you would add that:

• Total cost = $2x + 5$.

Step 5: Complete the Problem

Finally, combine everything to write down a complete mathematical expression or equation.

For example: "If I buy $x$ apples at $2 each, plus a$5 delivery fee, what is my total cost?" can be written as:

$$\text{Total Cost} = 2x + 5.$$

Step 6: Solve the Equation (if needed)

If the word problem asks you to solve an equation (to find $x$), set it equal to another value. For example, if the total cost is $15, you would write:

$$2x + 5 = 15.$$

Now you can solve for $x$.

Conclusion

By following these steps—understanding the problem, identifying variables, translating words into operations, creating expressions, and solving when needed—you can turn word problems into algebraic expressions. With practice, it will get easier, and you'll become more confident in solving linear equations. With these tips, you're on your way to mastering algebra in Grade 9!