Expressions, Formulae, and Equations Drag and Drop worksheet ... - Free Printable

To solve this problem, we need to classify the given expressions, formulae, and equations into their respective groups. Let's break it down step by step:

Definitions:

1. Expressions: A mathematical phrase that combines numbers, variables, and operators but does not contain an equals sign.
2. Formulae: A rule or equation that expresses a relationship between quantities, often used in science or mathematics.
3. Equations: A statement that asserts the equality of two expressions, typically containing an equals sign.

Step-by-Step Classification:

#### Expressions:
- These are mathematical phrases without an equals sign.
- Examples: \( 3x^2 + 2x + 5 \), \( 4p + 9 \), \( ax^2 + bx + c \), \( 3y + 10 \), \( 1.8x + 2.9y \).

#### Formulae:
- These are specific types of equations that describe relationships between variables, often used in scientific contexts.
- Examples: \( W = fd \) (work = force × distance), \( B = 24x^2 - 4 \), \( V = \pi r^2 h \) (volume of a cylinder), \( F = ma \) (force = mass × acceleration).

#### Equations:
- These are statements that assert the equality of two expressions.
- Examples: \( 48 = 3x + 3 \), \( 10 = 3x + 4 \), \( 21 = 3x + 9 \), \( 89 = 9Y + 8 \), \( 20 = 0.5x + 5 \), \( a^2 + b^2 = c^2 \).

Classification Results:

#### Expressions:
- \( 3x^2 + 2x + 5 \)
- \( 4p + 9 \)
- \( ax^2 + bx + c \)
- \( 3y + 10 \)
- \( 1.8x + 2.9y \)

#### Formulae:
- \( W = fd \)
- \( B = 24x^2 - 4 \)
- \( V = \pi r^2 h \)
- \( F = ma \)

#### Equations:
- \( 48 = 3x + 3 \)
- \( 10 = 3x + 4 \)
- \( 21 = 3x + 9 \)
- \( 89 = 9Y + 8 \)
- \( 20 = 0.5x + 5 \)
- \( a^2 + b^2 = c^2 \)

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Expressions} & \text{Formulae} & \text{Equations} \\
\hline
3x^2 + 2x + 5 & W = fd & 48 = 3x + 3 \\
4p + 9 & B = 24x^2 - 4 & 10 = 3x + 4 \\
ax^2 + bx + c & V = \pi r^2 h & 21 = 3x + 9 \\
3y + 10 & F = ma & 89 = 9Y + 8 \\
1.8x + 2.9y & & 20 = 0.5x + 5 \\
& & a^2 + b^2 = c^2 \\
\hline
\end{array}
}
\]