Multiplying and dividing algebraic expressions worksheet | Live ... - Free Printable

Let’s solve each problem step by step. We’re simplifying algebraic expressions — that means writing them in the shortest, clearest way possible.

We’ll go one by one:

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1. 5 × a
→ Just write as 5a

2. d × 4
→ Write number first: 4d

3. a × b
→ Just ab

4. a ÷ 6
→ Write as fraction: a/6

5. 7x ÷ 4y
→ Write as fraction: 7x / 4y

6. 2y × 4
→ Multiply numbers: 2×4 = 8 → 8y

7. 5 × 3d
→ 5×3 = 15 → 15d

8. 4g × 2
→ 4×2 = 8 → 8g

9. 2n × 10m
→ 2×10 = 20, and n×m = nm → 20nm

10. 5k × 2w
→ 5×2 = 10, k×w = kw → 10kw

11. 5a × 2b × 4c
→ Multiply numbers: 5×2×4 = 40
→ Variables: a×b×c = abc
→ 40abc

12. (x + 1) ÷ 6y
→ Write as fraction: (x + 1) / 6y

13. 6d ÷ 6t
→ 6÷6 = 1, so left with d/t → d/t

14. 5ab ÷ 2b
→ Cancel ‘b’ top and bottom → 5a / 2 → 5a/2

15. 6y × 2y
→ 6×2 = 12, y×y = y² → 12y²

16. 3a × 2ab
→ 3×2 = 6, a×a = a², and b stays → 6a²b

17. (4 × 2d) ÷ 8
→ First: 4×2d = 8d
→ Then 8d ÷ 8 = d → d

18. 15rt ÷ 10r
→ 15÷10 = 3/2, r cancels out → 3t/2

19. 6g × 2h × g
→ Numbers: 6×2 = 12
→ Variables: g×g = g², and h → 12g²h

20. 3m × 2n × 4z
→ Numbers: 3×2×4 = 24
→ Variables: m×n×z = mnz → 24mnz

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Final Answer:
1. 5a
2. 4d
3. ab
4. a/6
5. 7x/4y
6. 8y
7. 15d
8. 8g
9. 20nm
10. 10kw
11. 40abc
12. (x + 1)/6y
13. d/t
14. 5a/2
15. 12y²
16. 6a²b
17. d
18. 3t/2
19. 12g²h
20. 24mnz