Identify expressions and equations in this math worksheet.

To solve this problem, we need to identify whether each given statement is an expression or an equation. Here's the explanation and classification for each item:

Definitions:

1. Expression: A mathematical phrase that combines numbers, variables, and operators but does not contain an equals sign (=). It represents a value.
2. Equation: A mathematical statement that asserts the equality of two expressions. It contains an equals sign (=).

Step-by-Step Analysis:

1. 30 + 92
- This is a combination of numbers and an operator (+) without an equals sign.
- Classification: Expression

2. (44 ÷ 4) + 1
- This is a combination of numbers, operators (÷ and +), and parentheses, but no equals sign.
- Classification: Expression

3. (2 × 50) – 22 = 78
- This includes numbers, operators (×, –), parentheses, and an equals sign.
- Classification: Equation

4. 119 – 14 = 105
- This includes numbers, an operator (–), and an equals sign.
- Classification: Equation

5. 71 – 2 ÷ 13
- This is a combination of numbers, operators (– and ÷), but no equals sign.
- Classification: Expression

6. (100 + 37) – 73 = 64
- This includes numbers, operators (+, –), parentheses, and an equals sign.
- Classification: Equation

7. (68 ÷ 2) + 12
- This is a combination of numbers, operators (÷ and +), and parentheses, but no equals sign.
- Classification: Expression

8. (24 × 4) + 9 = 100 + 5
- This includes numbers, operators (×, +), parentheses, and an equals sign.
- Classification: Equation

9. 54 + (6 × 2)
- This is a combination of numbers, operators (+ and ×), and parentheses, but no equals sign.
- Classification: Expression

10. (313 – 10) × 6
- This is a combination of numbers, operators (– and ×), and parentheses, but no equals sign.
- Classification: Expression

11. (700 – 200) + 8 = 5 × 100 + 8
- This includes numbers, operators (–, +, ×), parentheses, and an equals sign.
- Classification: Equation

12. 293 ÷ 0.5 – 281
- This is a combination of numbers, operators (÷ and –), but no equals sign.
- Classification: Expression

13. (900 ÷ 90) + 72 – 7 = 65
- This includes numbers, operators (÷, +, –), parentheses, and an equals sign.
- Classification: Equation

14. Thrice the sum of 8 and 10
- This is a verbal description that translates to a mathematical phrase: \(3 \times (8 + 10)\), which is an expression.
- Classification: Expression

15. Double of 50 is 100
- This is a verbal statement that translates to \(2 \times 50 = 100\), which is an equation.
- Classification: Equation

16. 10 more than quarter of 8
- This is a verbal description that translates to a mathematical phrase: \(10 + \frac{1}{4} \times 8\), which is an expression.
- Classification: Expression

Final Classification:

- Expressions: 1, 2, 5, 7, 9, 10, 12, 14, 16
- Equations: 3, 4, 6, 8, 11, 13, 15

Solution Table:

| Statement | Expression | Equation |
|------------------------------------|------------|----------|
| 30 + 92 | ✓ | |
| (44 ÷ 4) + 1 | ✓ | |
| (2 × 50) – 22 = 78 | | ✓ |
| 119 – 14 = 105 | | ✓ |
| 71 – 2 ÷ 13 | ✓ | |
| (100 + 37) – 73 = 64 | | ✓ |
| (68 ÷ 2) + 12 | ✓ | |
| (24 × 4) + 9 = 100 + 5 | | ✓ |
| 54 + (6 × 2) | ✓ | |
| (313 – 10) × 6 | ✓ | |
| (700 – 200) + 8 = 5 × 100 + 8 | | ✓ |
| 293 ÷ 0.5 – 281 | ✓ | |
| (900 ÷ 90) + 72 – 7 = 65 | | ✓ |
| Thrice the sum of 8 and 10 | ✓ | |
| Double of 50 is 100 | | ✓ |
| 10 more than quarter of 8 | ✓ | |

Final Answer:

\boxed{
\begin{array}{|c|c|c|}
\hline
\text{Statement} & \text{Expression} & \text{Equation} \\
\hline
30 + 92 & \checkmark & \\
(44 \div 4) + 1 & \checkmark & \\
(2 \times 50) - 22 = 78 & & \checkmark \\
119 - 14 = 105 & & \checkmark \\
71 - 2 \div 13 & \checkmark & \\
(100 + 37) - 73 = 64 & & \checkmark \\
(68 \div 2) + 12 & \checkmark & \\
(24 \times 4) + 9 = 100 + 5 & & \checkmark \\
54 + (6 \times 2) & \checkmark & \\
(313 - 10) \times 6 & \checkmark & \\
(700 - 200) + 8 = 5 \times 100 + 8 & & \checkmark \\
293 \div 0.5 - 281 & \checkmark & \\
(900 \div 90) + 72 - 7 = 65 & & \checkmark \\
\text{Thrice the sum of 8 and 10} & \checkmark & \\
\text{Double of 50 is 100} & & \checkmark \\
10 \text{ more than quarter of 8} & \checkmark & \\
\hline
\end{array}
}