Deriving and Evaluating Expressions with One Variable
Expressions with one variable combine numbers with a letter, like 20 + 5x. Here 20 is the starting amount and 5x adds 5 for each x. To evaluate it, replace the letter with a number: when x = 8, 20 + 5 × 8 = 60.
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Understanding Variables
- A variable is a letter that stands for a number that can change.
- For example, x can represent the number of months passed.
Understanding Expressions
- An expression is formed by combining numbers and variables.
- It shows how a value changes and has no equals sign.
Forming Expressions
- Example 1: 20 + 5x means start with 20 and add 5 for each x.
- Example 2: 50 − 3y means start with 50 and subtract 3 for each y.
Evaluating Expressions
- To evaluate an expression, you replace the variable with a number.
- You then calculate to find the value of the expression.
Practice Questions
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Julia has £20 in savings. Each month, she saves an additional £5. How much will she have saved after 5 months?
Correct! 🎉 +10 pointsNot quite right
The expression is . After 5 months, Julia will have £).
A library has 200 books. Every week, 10 new books are added. How many books will the library have after 3 weeks?
Correct! 🎉 +10 pointsNot quite right
The expression is . After 3 weeks, the library will have books.
You start with £100, and you spend £8 each day. How much money will you have left after 12 days?
Correct! 🎉 +20 pointsNot quite right
The expression is . After 12 days, you'll have £) left.
A factory starts with 1000 units of a product. They produce 125 units every day. After how many days will they have a total of 2000 units?
Correct! 🎉 +20 pointsNot quite right
The equation is . Solving for x, we get days.
A gardener plants 15 flowers each day. They start with 50 flowers already planted. How many flowers will they have after 7 days?
Correct! 🎉 +20 pointsNot quite right
The expression is . After 7 days, the gardener will have flowers in total.
A photographer charges £50 for a session. They charge an additional £30 for each extra photo. How much will the photographer charge after 12 photos?
Correct! 🎉 +30 pointsNot quite right
The expression is . After 12 photos, , so the photographer will charge £).
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Students Also Ask
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It is called a variable because its value can vary. The same letter can stand for many different numbers, so it is not fixed. For example, x might represent 8 months in one calculation and 12 months in another, changing the result each time.
5x means 5 times x. When a number is written directly in front of a letter, it tells you to multiply that number by the variable. So if x equals 8, then 5x means 5 times 8, which works out as 40.
Replace the variable with the number you are given, then work out the calculation. For example, in 20 + 5x with x equal to 8, you get 20 + 5 times 8. Work out 5 times 8 first to make 40, then add 20 to reach 60.
A simple example is 20 + 5x, which works out Julia's savings. Here 20 is her starting amount and 5 is the monthly saving. The letter x is the variable for the number of months. Replacing x with a number gives her total for that many months.
A variable expression saves you from rewriting a calculation every time one number changes. You write it once using a letter, then replace that letter with any value. This makes everyday maths, such as working out savings or spending, much quicker and clearer.