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

The task involves simplifying algebraic expressions. Below, I will solve each problem step by step and provide the simplified form for each expression.

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Left Column: Simplifying Expressions

#### 1. \( 5 \times a \)
- Simplification: \( 5a \)

#### 2. \( d \times 4 \)
- Simplification: \( 4d \)

#### 3. \( a \times b \)
- Simplification: \( ab \)

#### 4. \( a \div 6 \)
- Simplification: \( \frac{a}{6} \)

#### 5. \( 7x \div 4y \)
- Simplification: \( \frac{7x}{4y} \)

#### 6. \( 2y \times 4 \)
- Simplification: \( 8y \)

#### 7. \( 5 \times 3d \)
- Simplification: \( 15d \)

#### 8. \( 4g \times 2 \)
- Simplification: \( 8g \)

#### 9. \( 2n \times 10m \)
- Simplification: \( 20nm \)

#### 10. \( 5k \times 2w \)
- Simplification: \( 10kw \)

#### 11. \( 5a \times 2b \times 4c \)
- Simplification: \( 5 \times 2 \times 4 \times a \times b \times c = 40abc \)

#### 12. \( (x + 1) \div 6y \)
- Simplification: \( \frac{x + 1}{6y} \)

#### 13. \( 6d \div 6t \)
- Simplification: \( \frac{6d}{6t} = \frac{d}{t} \)

#### 14. \( 5ab \div 2b \)
- Simplification: \( \frac{5ab}{2b} = \frac{5a}{2} \) (since \( b \neq 0 \))

#### 15. \( 6y \times 2y \)
- Simplification: \( 6 \times 2 \times y \times y = 12y^2 \)

#### 16. \( 3a \times 2ab \)
- Simplification: \( 3 \times 2 \times a \times a \times b = 6a^2b \)

#### 17. \( (4 \times 2d) \div 8 \)
- Simplification: \( \frac{4 \times 2d}{8} = \frac{8d}{8} = d \)

#### 18. \( 15rt \div 10r \)
- Simplification: \( \frac{15rt}{10r} = \frac{15t}{10} = \frac{3t}{2} \) (since \( r \neq 0 \))

#### 19. \( 6g \times 2h \times g \)
- Simplification: \( 6 \times 2 \times g \times g \times h = 12g^2h \)

#### 20. \( 3m \times 2n \times 4z \)
- Simplification: \( 3 \times 2 \times 4 \times m \times n \times z = 24mnz \)

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Right Column: Simplifying Expressions

The right column is identical to the left column, so the solutions are the same as above.

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Final Answer

The simplified forms of all expressions are:

1. \( 5a \)
2. \( 4d \)
3. \( ab \)
4. \( \frac{a}{6} \)
5. \( \frac{7x}{4y} \)
6. \( 8y \)
7. \( 15d \)
8. \( 8g \)
9. \( 20nm \)
10. \( 10kw \)
11. \( 40abc \)
12. \( \frac{x + 1}{6y} \)
13. \( \frac{d}{t} \)
14. \( \frac{5a}{2} \)
15. \( 12y^2 \)
16. \( 6a^2b \)
17. \( d \)
18. \( \frac{3t}{2} \)
19. \( 12g^2h \)
20. \( 24mnz \)

Thus, the final answer is:

\[
\boxed{
\begin{array}{ll}
1. & 5a \\
2. & 4d \\
3. & ab \\
4. & \frac{a}{6} \\
5. & \frac{7x}{4y} \\
6. & 8y \\
7. & 15d \\
8. & 8g \\
9. & 20nm \\
10. & 10kw \\
11. & 40abc \\
12. & \frac{x + 1}{6y} \\
13. & \frac{d}{t} \\
14. & \frac{5a}{2} \\
15. & 12y^2 \\
16. & 6a^2b \\
17. & d \\
18. & \frac{3t}{2} \\
19. & 12g^2h \\
20. & 24mnz \\
\end{array}
}
\]