Class 6 Algebra Worksheet
Part 1: Identify the Variable and Coefficient
Write the variable and coefficient for each expression.
- 5x
- 7y
- 12a
- 9b
- 3m
- 8n
- 15p
- 6q
- 11r
- 4s
Part 2: Simplify Algebraic Expressions
Simplify the following expressions:
- 3x + 5x = ______
- 7y + 2y = ______
- 6a + 4a = ______
- 9b + 3b = ______
- 5m + 7m = ______
- 8n + 12n = ______
- 14p + 6p = ______
- 10q + 5q = ______
- 11r + 9r = ______
- 6s + 14s = ______
Part 3: Evaluate Algebraic Expressions
If x = 3, y = 4, z = 2, evaluate:
- 5x + 2 = ______
- 3y + 7 = ______
- 4z + 6 = ______
- 2x + 3y = ______
- 6y + 5z = ______
- 7x – 2 = ______
- 5y – 3 = ______
- 9z + 4 = ______
- 3x + 2y + z = ______
- 2x + 3y – z = ______
Part 4: Solve the Simple Equations
Solve for the variable:
- x + 5 = 12
- y – 7 = 9
- 3x = 15
- 2y = 14
- x/4 = 3
- 5y = 35
- z + 8 = 17
- 6x – 4 = 14
- 7y + 3 = 24
- 8z – 5 = 19
Part 5: Word Problems
- A number increased by 7 gives 15. Find the number.
- Three times a number is 18. Find the number.
- A number divided by 4 gives 5. Find the number.
- The sum of a number and 9 is 20. Find the number.
- Two times a number minus 6 equals 10. Find the number.
- A number added to 12 equals 25. Find the number.
- Five more than a number equals 20. Find the number.
- Four times a number plus 3 equals 19. Find the number.
- Seven less than a number is 10. Find the number.
- Six times a number minus 4 equals 32. Find the number.
Part 6: Challenge (Optional)
- Simplify: 3x + 5 + 7x + 2 = ______
- Evaluate: 4x + 3y – 2z, if x = 2, y = 3, z = 1
- Solve: 2(x + 3) = 14
- Solve: 5(y – 2) = 20
- Simplify: 6a + 3b – 2a + 5b = ______
- Evaluate: 3p + 2q – r, if p=1, q=2, r=3
- Solve: x/5 + 3 = 7
- Simplify: 7m + 4n – 3m + 2n = ______
- Solve: 2x + 3 = 11
- Word problem: Twice a number increased by 6 equals 18. Find the number.
Class 6 Algebra Worksheet – Answer Key
Part 1: Identify the Variable and Coefficient
| Expression | Variable | Coefficient |
|---|---|---|
| 5x | x | 5 |
| 7y | y | 7 |
| 12a | a | 12 |
| 9b | b | 9 |
| 3m | m | 3 |
| 8n | n | 8 |
| 15p | p | 15 |
| 6q | q | 6 |
| 11r | r | 11 |
| 4s | s | 4 |
Part 2: Simplify Algebraic Expressions
- 3x + 5x = 8x
- 7y + 2y = 9y
- 6a + 4a = 10a
- 9b + 3b = 12b
- 5m + 7m = 12m
- 8n + 12n = 20n
- 14p + 6p = 20p
- 10q + 5q = 15q
- 11r + 9r = 20r
- 6s + 14s = 20s
Part 3: Evaluate Algebraic Expressions
Given: x=3, y=4, z=2
- 5x + 2 = 5×3 + 2 = 17
- 3y + 7 = 3×4 + 7 = 19
- 4z + 6 = 4×2 + 6 = 14
- 2x + 3y = 2×3 + 3×4 = 6 + 12 = 18
- 6y + 5z = 6×4 + 5×2 = 24 + 10 = 34
- 7x – 2 = 7×3 – 2 = 21 – 2 = 19
- 5y – 3 = 5×4 – 3 = 20 – 3 = 17
- 9z + 4 = 9×2 + 4 = 18 + 4 = 22
- 3x + 2y + z = 3×3 + 2×4 + 2 = 9 + 8 + 2 = 19
- 2x + 3y – z = 2×3 + 3×4 – 2 = 6 + 12 – 2 = 16
Part 4: Solve Simple Equations
- x + 5 = 12 → x = 12 – 5 = 7
- y – 7 = 9 → y = 9 + 7 = 16
- 3x = 15 → x = 15 ÷ 3 = 5
- 2y = 14 → y = 14 ÷ 2 = 7
- x/4 = 3 → x = 3 × 4 = 12
- 5y = 35 → y = 35 ÷ 5 = 7
- z + 8 = 17 → z = 17 – 8 = 9
- 6x – 4 = 14 → 6x = 14 + 4 = 18 → x = 3
- 7y + 3 = 24 → 7y = 21 → y = 3
- 8z – 5 = 19 → 8z = 24 → z = 3
Part 5: Word Problems
- Number + 7 = 15 → Number = 8
- 3 × Number = 18 → Number = 6
- Number ÷ 4 = 5 → Number = 20
- Number + 9 = 20 → Number = 11
- 2 × Number – 6 = 10 → 2 × Number = 16 → Number = 8
- Number + 12 = 25 → Number = 13
- Number + 5 = 20 → Number = 15
- 4 × Number + 3 = 19 → 4 × Number = 16 → Number = 4
- Number – 7 = 10 → Number = 17
- 6 × Number – 4 = 32 → 6 × Number = 36 → Number = 6
Part 6: Challenge (Optional)
- 3x + 5 + 7x + 2 = 10x + 7
- 4x + 3y – 2z, x=2, y=3, z=1 → 4×2 + 3×3 – 2×1 = 8 + 9 – 2 = 15
- 2(x + 3) = 14 → x + 3 = 7 → x = 4
- 5(y – 2) = 20 → y – 2 = 4 → y = 6
- 6a + 3b – 2a + 5b = 4a + 8b
- 3p + 2q – r, p=1, q=2, r=3 → 3×1 + 2×2 – 3 = 3 + 4 – 3 = 4
- x/5 + 3 = 7 → x/5 = 4 → x = 20
- 7m + 4n – 3m + 2n = 4m + 6n
- 2x + 3 = 11 → 2x = 8 → x = 4
- Twice a number + 6 = 18 → 2 × Number = 12 → Number = 6