What Are Variable Expressions?

Today, we’re going to talk about something exciting in Maths called variable expressions. Sounds a bit tricky, right? But don’t worry, I’ll help you understand it step by step!

What Is a Variable?

First, let’s start with the word variable. A variable is a letter that stands for a number we don’t know yet. For example, in the expression x + 5, the letter x is the variable. It can be any number!

What Is an Expression?

An expression is a combination of numbers, variables, and operations (like adding, subtracting, multiplying, or dividing). So, x + 5 is an expression that tells us to add 5 to whatever number x stands for.

Evaluating Variable Expressions

Evaluating means finding out what the expression equals. To do this, we need to know what the variable stands for.

How to Evaluate a Variable Expression:

  1. Identify the Value of the Variable: What number does the variable represent?
  2. Substitute the Value: Replace the variable with the number you found.
  3. Perform the Operations: Do the math to find the answer.

Example 1

Evaluate the expression:

x + 3 when x = 4

Step 1: Identify the value of the variable: x = 4

Step 2: Substitute the value: 4 + 3

Step 3: Perform the operation: 4 + 3 = 7

So, when x = 4, x + 3 = 7.

Example 2

Evaluate the expression:

2y – 5 when y = 3

Step 1: Identify the value of the variable: y = 3

Step 2: Substitute the value: 2(3) – 5

Step 3: Perform the operation: 6 – 5 = 1

So, when y = 3, 2y – 5 = 1.

Key Rules to Remember

  • Always replace the variable with the correct number.
  • Follow the order of operations (if there are multiple operations).
  • Be careful with negative numbers and subtraction!

Tips and Tricks

  • Use a calculator if you’re unsure about your calculations.
  • Write down each step to avoid mistakes.
  • Double-check your answer by plugging the number back into the expression.

Questions to Practice

Easy Level (20 Questions)

  1. Evaluate: a + 2 when a = 1
  2. Evaluate: b – 1 when b = 5
  3. Evaluate: c + 4 when c = 2
  4. Evaluate: d + 3 when d = 7
  5. Evaluate: e – 2 when e = 6
  6. Evaluate: f + 5 when f = 0
  7. Evaluate: g – 3 when g = 8
  8. Evaluate: h + 1 when h = 4
  9. Evaluate: i + 6 when i = 3
  10. Evaluate: j – 4 when j = 9
  11. Evaluate: k + 2 when k = 5
  12. Evaluate: l – 1 when l = 10
  13. Evaluate: m + 7 when m = 2
  14. Evaluate: n – 5 when n = 12
  15. Evaluate: o + 3 when o = 1
  16. Evaluate: p – 4 when p = 14
  17. Evaluate: q + 0 when q = 6
  18. Evaluate: r – 2 when r = 5
  19. Evaluate: s + 9 when s = 1
  20. Evaluate: t – 5 when t = 15

Medium Level (20 Questions)

  1. Evaluate: 3x + 2 when x = 2
  2. Evaluate: 4y – 3 when y = 5
  3. Evaluate: 2z + 6 when z = 4
  4. Evaluate: 5a – 2 when a = 3
  5. Evaluate: 6b + 1 when b = 3
  6. Evaluate: 7c – 4 when c = 2
  7. Evaluate: 8d + 3 when d = 1
  8. Evaluate: 9e – 5 when e = 2
  9. Evaluate: 2f + 5 when f = 0
  10. Evaluate: 3g – 7 when g = 4
  11. Evaluate: 4h + 2 when h = 3
  12. Evaluate: 5i – 1 when i = 2
  13. Evaluate: 10j + 10 when j = 2
  14. Evaluate: 6k – 2 when k = 5
  15. Evaluate: 12l + 4 when l = 1
  16. Evaluate: 14m – 6 when m = 1
  17. Evaluate: 8n + 2 when n = 2
  18. Evaluate: 11o – 3 when o = 1
  19. Evaluate: 2p + 1 when p = 6
  20. Evaluate: 3q – 4 when q = 10

Hard Level (20 Questions)

  1. Evaluate: 2x + 3y when x = 1 and y = 2
  2. Evaluate: 3a – 4b + 2 when a = 5 and b = 1
  3. Evaluate: 4c + 5d – 6 when c = 2 and d = 3
  4. Evaluate: 7e – 3f + 1 when e = 6 and f = 1
  5. Evaluate: 2g + 3h + 4 when g = 3 and h = 2
  6. Evaluate: 5i – 2j + 3 when i = 4 and j = 2
  7. Evaluate: 3k + 2l – 1 when k = 5 and l = 4
  8. Evaluate: 6m + 7n – 5 when m = 2 and n = 1
  9. Evaluate: 8o – 4p + 2 when o = 5 and p = 3
  10. Evaluate: 10q + 2r – 8 when q = 4 and r = 3
  11. Evaluate: 3s + 2t – 2u when s = 2, t = 3, and u = 1
  12. Evaluate: 5v – 3w + 10 when v = 4 and w = 2
  13. Evaluate: 9x + 5y – 4z when x = 2, y = 1, and z = 3
  14. Evaluate: 2a + 4b – 3c when a = 5, b = 2, and c = 1
  15. Evaluate: 7d + 8e – 5f when d = 3, e = 2, and f = 6
  16. Evaluate: 6g – 2h + 3i when g = 1, h = 2, and i = 4
  17. Evaluate: 5j + 4k – 3l when j = 2, k = 5, and l = 1
  18. Evaluate: 3m + 2n – 4o when m = 4, n = 1, and o = 2
  19. Evaluate: 12p + 5q – 10r when p = 1, q = 3, and r = 1
  20. Evaluate: 8s + 3t – 2u + 1 when s = 1, t = 2, and u = 1

Answers and Explanations

Easy Level Answers

  1. 3
  2. 4
  3. 6
  4. 10
  5. 4
  6. 5
  7. 5
  8. 5
  9. 9
  10. 5
  11. 7
  12. 9
  13. 9
  14. 7
  15. 4
  16. 10
  17. 6
  18. 3
  19. 10
  20. 10

Medium Level Answers

  1. 8
  2. 17
  3. 14
  4. 13
  5. 19
  6. 38
  7. 11
  8. 13
  9. 5
  10. 5
  11. 14
  12. 5
  13. 30
  14. 28
  15. 16
  16. 8
  17. 18
  18. 20
  19. 13
  20. 26

Hard Level Answers

  1. 9
  2. 7
  3. 22
  4. 33
  5. 15
  6. 17
  7. 27
  8. 17
  9. 30
  10. 38
  11. 11
  12. 27
  13. 34
  14. 25
  15. 36
  16. 16
  17. 21
  18. 14
  19. 37
  20. 16

I hope this helps you understand how to evaluate variable expressions better. Keep practicing, and you’ll get even better at it! Happy learning!