Year 7 Maths: Solve One-Step Equations with Decimals

Introduction to One-Step Equations

Today, we are going to learn about solving one-step equations that have decimals. This means we will find the missing number in an equation that involves decimals.

What is an Equation?

An equation is like a balance scale. What you do to one side, you must do to the other side to keep it balanced.

For example:

$$x + 2.5 = 5.5$$

In this equation, we need to find the value of (x).

Key Rules for Solving Equations

1. Keep it Balanced: Whatever operation you do to one side, you must do to the other side.
2. Inverse Operations: Use the opposite operation to isolate the variable.
   • If there is addition, use subtraction.
   • If there is subtraction, use addition.
   • If there is multiplication, use division.
   • If there is division, use multiplication.

Steps to Solve One-Step Equations with Decimals

1. Identify the Operation: Look at what is being done to the variable (addition, subtraction, multiplication, or division).
2. Use the Inverse Operation: Apply the opposite operation to both sides of the equation.
3. Simplify: Calculate the new value to find the variable’s value.

Examples

Example 1: Addition with Decimals

Solve the equation:

$$x + 3.2 = 7.2$$

Step 1: Identify the operation: (+) 3.2.

Step 2: Use the inverse operation: (-) 3.2.

Step 3: Subtract 3.2 from both sides:

$$x + 3.2 – 3.2 = 7.2 – 3.2$$

This simplifies to:

$$x = 4.0$$

Example 2: Subtraction with Decimals

Solve the equation:

$$y – 1.5 = 2.5$$

Step 1: Identify the operation: (-) 1.5.

Step 2: Use the inverse operation: (+) 1.5.

Step 3: Add 1.5 to both sides:

$$y – 1.5 + 1.5 = 2.5 + 1.5$$

This simplifies to:

$$y = 4.0$$

Tips and Tricks

• Write Work Neatly: Keep your work organised. This will help you avoid mistakes.
• Check Your Answer: After finding the value of the variable, put it back into the original equation to see if both sides are equal.

Questions

Easy Level Questions

1. $$x + 0.5 = 2.0$$
2. $$y – 0.3 = 1.2$$
3. $$z + 1.1 = 3.1$$
4. $$a – 2.5 = 0.5$$
5. $$b + 1.0 = 1.7$$
6. $$c – 0.2 = 0.8$$
7. $$d + 0.4 = 2.4$$
8. $$e – 0.9 = 0.1$$
9. $$f + 0.6 = 2.6$$
10. $$g – 0.1 = 1.9$$
11. $$h + 0.3 = 1.3$$
12. $$i – 0.5 = 0.5$$
13. $$j + 2.2 = 3.2$$
14. $$k – 1.1 = 0.9$$
15. $$l + 0.8 = 1.8$$
16. $$m – 0.4 = 1.6$$
17. $$n + 0.7 = 2.7$$
18. $$o – 0.6 = 0.4$$
19. $$p + 1.4 = 2.4$$
20. $$q – 1.0 = 0.0$$

Medium Level Questions

1. $$x + 2.5 = 5.3$$
2. $$y – 3.6 = 1.4$$
3. $$z + 1.7 = 4.9$$
4. $$a – 2.2 = 1.3$$
5. $$b + 0.8 = 2.9$$
6. $$c – 4.5 = 2.5$$
7. $$d + 3.1 = 6.1$$
8. $$e – 1.9 = 1.1$$
9. $$f + 2.4 = 5.0$$
10. $$g – 0.3 = 1.2$$
11. $$h + 1.5 = 3.5$$
12. $$i – 0.8 = 1.2$$
13. $$j + 1.1 = 3.1$$
14. $$k – 3.3 = 1.7$$
15. $$l + 2.6 = 4.6$$
16. $$m – 1.5 = 0.5$$
17. $$n + 0.9 = 1.9$$
18. $$o – 2.0 = 0.0$$
19. $$p + 3.3 = 6.3$$
20. $$q – 1.4 = 0.6$$

Hard Level Questions

1. $$x + 4.7 = 9.5$$
2. $$y – 2.6 = 3.4$$
3. $$z + 5.2 = 8.9$$
4. $$a – 3.7 = 1.2$$
5. $$b + 6.8 = 10.8$$
6. $$c – 2.9 = 2.1$$
7. $$d + 4.4 = 7.9$$
8. $$e – 5.5 = 0.5$$
9. $$f + 3.1 = 11.1$$
10. $$g – 4.1 = 1.9$$
11. $$h + 7.6 = 9.6$$
12. $$i – 2.3 = 5.2$$
13. $$j + 5.5 = 12.5$$
14. $$k – 6.0 = 1.0$$
15. $$l + 2.2 = 10.2$$
16. $$m – 3.8 = 0.2$$
17. $$n + 4.5 = 15.5$$
18. $$o – 2.7 = 3.3$$
19. $$p + 6.1 = 9.1$$
20. $$q – 4.4 = 2.6$$

Answers

Easy Level Answers

1. $$x = 1.5$$
2. $$y = 1.5$$
3. $$z = 2.0$$
4. $$a = 3.0$$
5. $$b = 0.7$$
6. $$c = 1.0$$
7. $$d = 2.0$$
8. $$e = 1.0$$
9. $$f = 2.0$$
10. $$g = 2.0$$
11. $$h = 1.0$$
12. $$i = 1.0$$
13. $$j = 1.0$$
14. $$k = 2.0$$
15. $$l = 1.0$$
16. $$m = 2.0$$
17. $$n = 2.0$$
18. $$o = 1.0$$
19. $$p = 1.0$$
20. $$q = 1.0$$

Medium Level Answers

1. $$x = 2.8$$
2. $$y = 5.0$$
3. $$z = 3.2$$
4. $$a = 3.5$$
5. $$b = 2.1$$
6. $$c = 7.4$$
7. $$d = 3.0$$
8. $$e = 3.0$$
9. $$f = 2.6$$
10. $$g = 1.5$$
11. $$h = 2.0$$
12. $$i = 2.0$$
13. $$j = 2.0$$
14. $$k = 5.0$$
15. $$l = 2.0$$
16. $$m = 1.0$$
17. $$n = 1.0$$
18. $$o = 2.0$$
19. $$p = 3.0$$
20. $$q = 1.4$$

Hard Level Answers

1. $$x = 4.8$$
2. $$y = 6.0$$
3. $$z = 3.7$$
4. $$a = 4.9$$
5. $$b = 4.0$$
6. $$c = 5.0$$
7. $$d = 3.5$$
8. $$e = 6.0$$
9. $$f = 8.0$$
10. $$g = 6.0$$
11. $$h = 2.0$$
12. $$i = 7.5$$
13. $$j = 7.0$$
14. $$k = 7.0$$
15. $$l = 8.0$$
16. $$m = 4.0$$
17. $$n = 11.0$$
18. $$o = 6.0$$
19. $$p = 3.0$$
20. $$q = 7.0$$

Now that you’ve learned how to solve one-step equations with decimals, practice the questions provided and check your answers. Remember, practice makes perfect! Good luck!