Introduction to Variable Expressions

Hello Year 7! Today, we are going to learn about evaluating variable expressions with decimals. This means we will look at expressions that have letters (which we call variables) and numbers with decimal points.

What is a Variable?

A variable is a letter that stands for a number we don’t know yet. For example, in the expression $$3x + 2.5$$, the letter $$x$$ is the variable.

What is an Expression?

An expression is a combination of numbers, variables, and operations (like +, -, ×, and ÷) that we can calculate.

Evaluating Variable Expressions

To evaluate a variable expression, we need to:

  1. Substitute: Replace the variable with a specific number.
  2. Calculate: Follow the order of operations (also known as BIDMAS/BODMAS).

Order of Operations

BIDMAS/BODMAS stands for:

  • Brackets
  • Indices (or Orders, like powers)
  • Division and Multiplication (from left to right)
  • Addition and Subtraction (from left to right)

Example

Let’s evaluate the expression $$2x + 3.5$$ when $$x = 4$$.

  1. Substitute: Replace $$x$$ with $$4$$.$$2(4) + 3.5$$
  2. Calculate:
    • First, do the multiplication: $$2 \times 4 = 8$$.
    • Then, add: $$8 + 3.5 = 11.5$$.

So, when $$x = 4$$, the expression $$2x + 3.5$$ equals $$11.5$$.

Key Rules and Tips

  • Always replace the variable with the correct number first.
  • Carefully follow the order of operations to avoid mistakes.
  • Double-check your calculations, especially when dealing with decimals.

Practice Questions

Easy Level Questions

  1. Evaluate $$2x + 1.5$$ when $$x = 1$$.
  2. Evaluate $$3y – 0.5$$ when $$y = 2$$.
  3. Evaluate $$4a + 2.2$$ when $$a = 3$$.
  4. Evaluate $$5b – 1.1$$ when $$b = 2$$.
  5. Evaluate $$6c + 0.5$$ when $$c = 0$$.
  6. Evaluate $$1.5d + 3$$ when $$d = 4$$.
  7. Evaluate $$2.5e – 2$$ when $$e = 2$$.
  8. Evaluate $$3f + 4.5$$ when $$f = 1$$.
  9. Evaluate $$4g + 1.2$$ when $$g = 0$$.
  10. Evaluate $$5h – 0.75$$ when $$h = 1$$.
  11. Evaluate $$3.5j + 2$$ when $$j = 3$$.
  12. Evaluate $$2k + 0.9$$ when $$k = 5$$.
  13. Evaluate $$4.5m – 3$$ when $$m = 2$$.
  14. Evaluate $$0.5n + 5$$ when $$n = 4$$.
  15. Evaluate $$7p + 0.5$$ when $$p = 1$$.
  16. Evaluate $$2.2q – 0.2$$ when $$q = 2$$.
  17. Evaluate $$3.1r + 4$$ when $$r = 2$$.
  18. Evaluate $$5s – 1$$ when $$s = 2$$.
  19. Evaluate $$2.8t + 3$$ when $$t = 1$$.
  20. Evaluate $$0.5u – 1.5$$ when $$u = 4$$.

Medium Level Questions

  1. Evaluate $$4x + 1.5$$ when $$x = 2.5$$.
  2. Evaluate $$3y – 0.2$$ when $$y = 1.7$$.
  3. Evaluate $$2.5a + 3.8$$ when $$a = 1.5$$.
  4. Evaluate $$7b – 1.9$$ when $$b = 3$$.
  5. Evaluate $$6c + 2.4$$ when $$c = 0.5$$.
  6. Evaluate $$1.2d + 4.5$$ when $$d = 5.5$$.
  7. Evaluate $$0.8e – 0.5$$ when $$e = 3.3$$.
  8. Evaluate $$5.5f + 2$$ when $$f = 2$$.
  9. Evaluate $$4.1g + 3.3$$ when $$g = 1.5$$.
  10. Evaluate $$3.6h – 2.1$$ when $$h = 1.2$$.
  11. Evaluate $$5.2j + 1.4$$ when $$j = 0.8$$.
  12. Evaluate $$2.9k – 0.9$$ when $$k = 2.5$$.
  13. Evaluate $$1.5m + 3.3$$ when $$m = 4.4$$.
  14. Evaluate $$2.2n – 1$$ when $$n = 3.6$$.
  15. Evaluate $$4.4p + 2$$ when $$p = 1.9$$.
  16. Evaluate $$0.7q + 1.1$$ when $$q = 2.4$$.
  17. Evaluate $$3.3r – 0.8$$ when $$r = 1.5$$.
  18. Evaluate $$2.6s + 4.2$$ when $$s = 1.3$$.
  19. Evaluate $$1.9t – 1.1$$ when $$t = 2.1$$.
  20. Evaluate $$0.5u + 3.5$$ when $$u = 4.2$$.

Hard Level Questions

  1. Evaluate $$2.5x + 4.75$$ when $$x = 3.6$$.
  2. Evaluate $$3.8y – 1.25$$ when $$y = 2.5$$.
  3. Evaluate $$1.6a + 5.5$$ when $$a = 4.75$$.
  4. Evaluate $$2.2b – 0.75$$ when $$b = 3.4$$.
  5. Evaluate $$6.5c + 2.8$$ when $$c = 0.2$$.
  6. Evaluate $$4.1d – 1.9$$ when $$d = 2.5$$.
  7. Evaluate $$3.3e + 4.4$$ when $$e = 1.2$$.
  8. Evaluate $$1.9f – 2.1$$ when $$f = 3.5$$.
  9. Evaluate $$5.5g + 3.3$$ when $$g = 1.4$$.
  10. Evaluate $$2.8h – 0.6$$ when $$h = 4.5$$.
  11. Evaluate $$3.7j + 1.5$$ when $$j = 0.9$$.
  12. Evaluate $$4.6k – 0.2$$ when $$k = 2.2$$.
  13. Evaluate $$1.1m + 5.9$$ when $$m = 3.8$$.
  14. Evaluate $$0.9n – 1.4$$ when $$n = 2.6$$.
  15. Evaluate $$5.3p + 2.7$$ when $$p = 1.8$$.
  16. Evaluate $$2.7q – 1.5$$ when $$q = 3.2$$.
  17. Evaluate $$3.1r + 4.9$$ when $$r = 2.4$$.
  18. Evaluate $$0.4s – 3.8$$ when $$s = 10.5$$.
  19. Evaluate $$1.8t + 0.6$$ when $$t = 3.1$$.
  20. Evaluate $$2.3u – 0.4$$ when $$u = 5.5$$.

Answers and Explanations

Easy Level Answers

  1. $$2(1) + 1.5 = 3.5$$.Substitute $$1$$ for $$x$$, multiply, then add.The answer is $$3.5$$.
  2. $$3(2) – 0.5 = 5.5$$.Replace $$y$$ with $$2$$, multiply, then subtract.The answer is $$5.5$$.
  3. $$4(3) + 2.2 = 14.2$$.Substitute $$3$$ for $$a$$, multiply, then add.The answer is $$14.2$$.
  4. $$5(2) – 1.1 = 8.9$$.Replace $$b$$ with $$2$$, multiply, then subtract.The answer is $$8.9$$.
  5. $$6(0) + 0.5 = 0.5$$.Substitute $$0$$ for $$c$$, multiply, then add.The answer is $$0.5$$.
  6. $$1.5(4) + 3 = 9$$.Replace $$d$$ with $$4$$, multiply, then add.The answer is $$9$$.
  7. $$2.5(2) – 2 = 3$$.Substitute $$2$$ for $$e$$, multiply, then subtract.The answer is $$3$$.
  8. $$3(1) + 4.5 = 7.5$$.Replace $$f$$ with $$1$$, multiply, then add.The answer is $$7.5$$.
  9. $$4(0) + 1.2 = 1.2$$.Substitute $$0$$ for $$g$$, multiply, then add.The answer is $$1.2$$.
  10. $$5(1) – 0.75 = 4.25$$.Replace $$h$$ with $$1$$, multiply, then subtract.The answer is $$4.25$$.
  11. $$3.5(3) + 2 = 12.5$$.Substitute $$3$$ for $$j$$, multiply, then add.The answer is $$12.5$$.
  12. $$2(5) + 0.9 = 10.9$$.Replace $$k$$ with $$5$$, multiply, then add.The answer is $$10.9$$.
  13. $$4.5(2) – 3 = 6$$.Substitute $$2$$ for $$m$$, multiply, then subtract.The answer is $$6$$.
  14. $$0.5(4) + 5 = 7$$.Replace $$n$$ with $$4$$, multiply, then add.The answer is $$7$$.
  15. $$7(1) + 0.5 = 7.5$$.Substitute $$1$$ for $$p$$, multiply, then add.The answer is $$7.5$$.
  16. $$2.2(2) – 0.2 = 4.2$$.Replace $$q$$ with $$2$$, multiply, then subtract.The answer is $$4.2$$.
  17. $$3.1(2) + 4 = 10.2$$.Substitute $$2$$ for $$r$$, multiply, then add.The answer is $$10.2$$.
  18. $$5(2) – 1 = 9$$.Replace $$s$$ with $$2$$, multiply, then subtract.The answer is $$9$$.
  19. $$2.8(1) + 3 = 5.8$$.Substitute $$1$$ for $$t$$, multiply, then add.The answer is $$5.8$$.
  20. $$0.5(4) – 1.5 = -1.5$$.Substitute $$4$$ for $$u$$, multiply, then subtract.The answer is $$-1.5$$.

Medium Level Answers

  1. $$4(2.5) + 1.5 = 11.5$$.Substitute $$2.5$$ for $$x$$, multiply, then add.The answer is $$11.5$$.
  2. $$3(1.7) – 0.2 = 5.9$$.Replace $$y$$ with $$1.7$$, multiply, then subtract.The answer is $$5.9$$.
  3. $$2.5(1.5) + 3.8 = 6.3$$.Substitute $$1.5$$ for $$a$$, multiply, then add.The answer is $$6.3$$.
  4. $$7(3) – 1.9 = 20.1$$.Replace $$b$$ with $$3$$, multiply, then subtract.The answer is $$20.1$$.
  5. $$6(0.5) + 2.4 = 5.4$$.Substitute $$0.5$$ for $$c$$, multiply, then add.The answer is $$5.4$$.
  6. $$1.2(5.5) + 4.5 = 11.1$$.Replace $$d$$ with $$5.5$$, multiply, then add.The answer is $$11.1$$.
  7. $$0.8(3.3) – 0.5 = 2.14$$.Substitute $$3.3$$ for $$e$$, multiply, then subtract.The answer is $$2.14$$.
  8. $$5.5(2) + 2 = 13$$.Replace $$f$$ with $$2$$, multiply, then add.The answer is $$13$$.
  9. $$4.1(1.5) + 3.3 = 10.35$$.Substitute $$1.5$$ for $$g$$, multiply, then add.The answer is $$10.35$$.
  10. $$3.6(1.2) – 2.1 = 0.3$$.Replace $$h$$ with $$1.2$$, multiply, then subtract.The answer is $$0.3$$.
  11. $$5.2(0.8) + 1.4 = 5.18$$.Substitute $$0.8$$ for $$j$$, multiply, then add.The answer is $$5.18$$.
  12. $$2.9(2.5) – 0.9 = 6.35$$.Replace $$k$$ with $$2.5$$, multiply, then subtract.The answer is $$6.35$$.
  13. $$1.5(4.4) + 3.3 = 10.5$$.Substitute $$4.4$$ for $$m$$, multiply, then add.The answer is $$10.5$$.
  14. $$2.2(3.6) – 1 = 7.92$$.Replace $$n$$ with $$3.6$$, multiply, then subtract.The answer is $$7.92$$.
  15. $$4.4(1.9) + 2 = 10.36$$.Substitute $$1.9$$ for $$p$$, multiply, then add.The answer is $$10.36$$.
  16. $$0.7(2.4) + 1.1 = 2.78$$.Replace $$q$$ with $$2.4$$, multiply, then add.The answer is $$2.78$$.
  17. $$3.3(1.5) – 0.8 = 4.75$$.Substitute $$1.5$$ for $$r$$, multiply, then subtract.The answer is $$4.75$$.
  18. $$2.6(1.3) + 4.2 = 7.58$$.Replace $$s$$ with $$1.3$$, multiply, then add.The answer is $$7.58$$.
  19. $$1.9(2.1) – 1.1 = 2.89$$.Substitute $$2.1$$ for $$t$$, multiply, then subtract.The answer is $$2.89$$.
  20. $$0.5(4.2) + 3.5 = 5.6$$.Replace $$u$$ with $$4.2$$, multiply, then add.The answer is $$5.6$$.

Hard Level Answers

  1. $$2.5(3.6) + 4.75 = 11.75$$.Substitute $$3.6$$ for $$x$$, multiply, then add.The answer is $$11.75$$.
  2. $$3.8(2.5) – 1.25 = 8.75$$.Replace $$y$$ with $$2.5$$, multiply, then subtract.The answer is $$8.75$$.
  3. $$1.6(4.75) + 5.5 = 15.1$$.Substitute $$4.75$$ for $$a$$, multiply, then add.The answer is $$15.1$$.
  4. $$2.2(3.4) – 0.75 = 7.45$$.Replace $$b$$ with $$3.4$$, multiply, then subtract.The answer is $$7.45$$.
  5. $$6.5(0.2) + 2.8 = 3.8$$.Substitute $$0.2$$ for $$c$$, multiply, then add.The answer is $$3.8$$