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

Let's solve each of the 20 algebraic simplification problems listed in the "Simplifying – Time Challenge" worksheet. We'll go through each one step by step, simplifying expressions using algebraic rules (like combining like terms, multiplying coefficients, and simplifying fractions).

---

Rules Used:

- Multiplication of variables: $ a \times b = ab $
- Coefficients are multiplied together.
- Division: Cancel common factors.
- Order of operations: parentheses first, then multiplication/division.

---

Solutions:

#### 1. $ 5 \times a $
- Simply written as: $ 5a $

#### 2. $ d \times 4 $
- $ 4d $

#### 3. $ a \times b $
- $ ab $

#### 4. $ a \div 6 $
- $ \frac{a}{6} $

#### 5. $ 7x \div 4y $
- $ \frac{7x}{4y} $ → cannot simplify further

#### 6. $ 2y \times 4 $
- $ 8y $

#### 7. $ 5 \times 3d $
- $ 15d $

#### 8. $ 4g \times 2 $
- $ 8g $

#### 9. $ 2n \times 10m $
- $ 20mn $

#### 10. $ 5k \times 2w $
- $ 10kw $

#### 11. $ 5a \times 2b \times 4c $
- Multiply coefficients: $ 5 \times 2 \times 4 = 40 $
- Variables: $ a \times b \times c = abc $
- So: $ 40abc $

#### 12. $ (x + 1) \div 6y $
- $ \frac{x+1}{6y} $ → can't simplify further

#### 13. $ 6d \div 6t $
- $ \frac{6d}{6t} = \frac{d}{t} $

#### 14. $ 5ab \div 2b $
- $ \frac{5ab}{2b} = \frac{5a}{2} $ (cancel $ b $)

#### 15. $ 6y \times 2y $
- $ 12y^2 $

#### 16. $ 3a \times 2ab $
- $ 6a^2b $

#### 17. $ (4 \times 2d) \div 8 $
- First: $ 4 \times 2d = 8d $
- Then: $ 8d \div 8 = d $

#### 18. $ 15rt \div 10r $
- $ \frac{15rt}{10r} = \frac{3t}{2} $ (cancel $ r $, simplify $ 15/10 = 3/2 $)

#### 19. $ 6g \times 2h \times g $
- Coefficients: $ 6 \times 2 = 12 $
- Variables: $ g \times h \times g = g^2h $
- So: $ 12g^2h $

#### 20. $ 3m \times 2n \times 4z $
- Coefficients: $ 3 \times 2 \times 4 = 24 $
- Variables: $ m \times n \times z = mnz $
- So: $ 24mnz $

---

✔ Final Answers:

| No. | Expression | Simplified Form |
|-----|-----------------------------|--------------------------|
| 1 | $ 5 \times a $ | $ 5a $ |
| 2 | $ d \times 4 $ | $ 4d $ |
| 3 | $ a \times b $ | $ ab $ |
| 4 | $ a \div 6 $ | $ \frac{a}{6} $ |
| 5 | $ 7x \div 4y $ | $ \frac{7x}{4y} $ |
| 6 | $ 2y \times 4 $ | $ 8y $ |
| 7 | $ 5 \times 3d $ | $ 15d $ |
| 8 | $ 4g \times 2 $ | $ 8g $ |
| 9 | $ 2n \times 10m $ | $ 20mn $ |
|10 | $ 5k \times 2w $ | $ 10kw $ |
|11 | $ 5a \times 2b \times 4c $| $ 40abc $ |
|12 | $ (x + 1) \div 6y $ | $ \frac{x+1}{6y} $ |
|13 | $ 6d \div 6t $ | $ \frac{d}{t} $ |
|14 | $ 5ab \div 2b $ | $ \frac{5a}{2} $ |
|15 | $ 6y \times 2y $ | $ 12y^2 $ |
|16 | $ 3a \times 2ab $ | $ 6a^2b $ |
|17 | $ (4 \times 2d) \div 8 $ | $ d $ |
|18 | $ 15rt \div 10r $ | $ \frac{3t}{2} $ |
|19 | $ 6g \times 2h \times g $ | $ 12g^2h $ |
|20 | $ 3m \times 2n \times 4z $| $ 24mnz $ |

---

📌 Notes:

- The worksheet has two identical columns — likely for practice or timing.
- Number of questions: 20
- Accuracy: You can fill this in after checking your answers.

---

Let me know if you'd like this formatted as a printable answer sheet!