Expressions and Equations - IELTS Academic Writing IELTS Study Notes
Overview
Have you ever tried to figure out how many cookies you can eat if you have a certain number and your friend takes some? Or how much money you'll have if you save a little bit each week? That's exactly what expressions and equations help us do! They are like secret codes that help us describe situations and solve puzzles using numbers and letters. In IELTS Academic Writing, especially when you're describing charts and graphs, you'll often need to talk about relationships between numbers, and understanding these basics will make your writing much clearer and more accurate. Think of it as learning the language of math to better explain what's happening in the world around you, whether it's population growth, sales figures, or temperature changes. It's not just about math class; it's about making sense of information!
What Is This? (The Simple Version)
Imagine you're at a candy store. You want to buy some lollipops. You don't know how many yet, so you just say 'a certain number of lollipops'. In math, we use a variable (a letter like 'x' or 'y') to stand for that unknown number. So, 'x lollipops'.
An expression is like a phrase in English, but with numbers and letters. It doesn't tell you the whole story, just a part of it. For example, if each lollipop costs $1, and you buy 'x' lollipops, the cost would be '1 * x' or simply 'x'. If you also buy a chocolate bar for $2, your total cost expression would be x + 2. It's just a way to show a calculation you could do.
An equation is like a complete sentence. It says that two expressions are equal to each other. It always has an equals sign (=) in the middle. So, if you know your total cost for 'x' lollipops and a $2 chocolate bar was $7, you'd write the equation: x + 2 = 7. Now, this is a puzzle we can solve to find out how many lollipops you bought!
Real-World Example
Let's say you're tracking how many books you read each month. Last month, you read 5 books. This month, you're aiming to read 'x' more books than last month. So, the expression for the number of books you read this month would be 5 + x.
Now, imagine your friend tells you, "Hey, I heard you read 12 books this month!" You can turn that into an equation to figure out how many more books ('x') you read compared to last month:
Step 1: Identify the knowns.
- Books last month: 5
- Total books this month (from your friend): 12
Step 2: Set up the expression.
- Books this month = 5 (from last month) + x (more books)
- So, the expression is: 5 + x
Step 3: Form the equation.
- Since your friend said you read 12 books this month, we can say our expression equals 12.
- 5 + x = 12
Step 4: Solve the equation.
- To find 'x', we need to get 'x' by itself. We can take 5 away from both sides of the equation.
- 5 + x - 5 = 12 - 5
- x = 7
So, you read 7 more books this month than last month! See how equations help us solve real-life puzzles?
How It Works (Step by Step)
Solving an equation is like balancing a seesaw. Whatever you do to one side, you must do to the other to keep it balanced. 1. **Understand the Goal:** Your main goal is to get the **variable** (the letter like 'x') all by itself on one side of the equals sign. 2. **Identify Operations:** Look at wh...
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Key Concepts
- Variable: A letter (like x or y) that stands for an unknown number in a math problem.
- Expression: A mathematical phrase that combines numbers, variables, and operations (like +, -, *, /) but does not have an equals sign.
- Equation: A mathematical sentence that shows two expressions are equal to each other, always containing an equals sign (=).
- Equals Sign (=): The symbol that means 'is the same as' or 'has the same value as', used to connect two equal expressions in an equation.
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Exam Tips
- →When describing data trends in Task 1, use clear language to explain relationships, e.g., 'The number of participants (P) doubled each year, which can be represented as P = 2 * (previous year's P)'.
- →If comparing two figures, think in terms of 'is equal to', 'is greater than', 'is less than', which are the verbal equivalents of equations and inequalities.
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