(c) 95 + 12 ÷ 12 + 10 95 + 12 \div 12 + 10 95 + 12 ÷ 12 + 10 (e) 10 + 13 − 12 ÷ 4 10 + 13 - 12 \div 4 10 + 13 − 12 ÷ 4 (e) 10 + ( − 14 ) × 4 10 + (-14) \times 4 10 + ( − 14 ) × 4 (f) 12 ( − 11 ) ÷ 3 ( − 6 12(-11) \div 3(-6 12 ( − 11 ) ÷ 3 ( − 6 ](g) 2 − 5 ÷ ( 15 ) ( − 2 2 - 5 \div (15)(-2 2 − 5 ÷ ( 15 ) ( − 2 ](4) 8 + 9 + 10 − ( 3 + 7 8 + 9 + 10 - (3 + 7 8 + 9 + 10 − ( 3 + 7 ](i) 8 ( − 11 ) ( − 3 ) ÷ 6 8(-11)(-3) \div 6 8 ( − 11 ) ( − 3 ) ÷ 6 (j) $11 + 9

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Solving mathematical expressions involves following the order of operations (PEMDAS) to evaluate the expression and find the final result. In this article, we will explore various mathematical expressions and learn how to solve them step by step.

Expression (c) $95 + 12 \div 12 + 10$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Divide 12 by 12: $12 \div 12 = 1$
2. Add 1 to 95: $95 + 1 = 96$
3. Add 10 to 96: $96 + 10 = 106$

Therefore, the final result of expression (c) is 106.

Expression (d) $10 + 13 - 12 \div 4$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Divide 12 by 4: $12 \div 4 = 3$
2. Subtract 3 from 13: $13 - 3 = 10$
3. Add 10 to 10: $10 + 10 = 20$

Therefore, the final result of expression (d) is 20.

Expression (e) $10 + (-14) \times 4$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Multiply -14 by 4: $-14 \times 4 = -56$
2. Add -56 to 10: $10 + (-56) = -46$

Therefore, the final result of expression (e) is -46.

Expression (f) $12(-11) \div 3(-6)$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Multiply 12 by -11: $12(-11) = -132$
2. Multiply 3 by -6: $3(-6) = -18$
3. Divide -132 by -18: $-132 \div -18 = 7.33$

Therefore, the final result of expression (f) is 7.33.

Expression (g) $2 - 5 \div (15)(-2)$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Multiply 15 by -2: $15(-2) = -30$
2. Divide 5 by -30: $5 \div -30 = -0.17$
3. Subtract -0.17 from 2: $2 - (-0.17) = 2.17$

Therefore, the final result of expression (g) is 2.17.

Expression (h) $8 + 9 + 10 - (3 + 7)$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Add 3 and 7: $3 + 7 = 10$
2. Subtract 10 from 27: $27 - 10 = 17$

Therefore, the final result of expression (h) is 17.

Expression (i) $8(-11)(-3) \div 6$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Multiply 8 by -11: $8(-11) = -88$
2. Multiply -88 by -3: $-88(-3) = 264$
3. Divide 264 by 6: $264 \div 6 = 44$

Therefore, the final result of expression (i) is 44.

Expression (j) $11 + 9$

To solve this expression, we need to follow the order of operations (PEMDAS).

1. Add 11 and 9: $11 + 9 = 20$

Therefore, the final result of expression (j) is 20.

Conclusion

Solving mathematical expressions involves following the order of operations (PEMDAS) to evaluate the expression and find the final result. In this article, we have explored various mathematical expressions and learned how to solve them step by step. By following the order of operations, we can ensure that we get the correct result for any mathematical expression.

Tips and Tricks

• Always follow the order of operations (PEMDAS) when solving mathematical expressions.
• Use parentheses to group numbers and operations when necessary.
• Simplify expressions by combining like terms.
• Check your work by plugging in numbers or using a calculator.

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not using parentheses to group numbers and operations.
• Not simplifying expressions by combining like terms.
• Not checking work by plugging in numbers or using a calculator.

Real-World Applications

Solving mathematical expressions is an essential skill in many real-world applications, including:

• Science and engineering: Mathematical expressions are used to model and solve problems in physics, chemistry, and other sciences.
• Finance: Mathematical expressions are used to calculate interest rates, investments, and other financial calculations.
• Computer programming: Mathematical expressions are used to write algorithms and solve problems in computer programming.
• Data analysis: Mathematical expressions are used to analyze and interpret data in statistics and data science.

Conclusion

In our previous article, we explored various mathematical expressions and learned how to solve them step by step. However, we know that practice makes perfect, and there's no better way to practice than by answering questions. In this article, we'll provide a Q&A guide to help you practice solving mathematical expressions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate expressions with parentheses?

A: When evaluating expressions with parentheses, you need to follow the order of operations (PEMDAS). Here's an example:

Expression: 2(3 + 4)

1. Evaluate the expression inside the parentheses: 3 + 4 = 7
2. Multiply 2 by 7: 2(7) = 14

Therefore, the final result of the expression is 14.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the result.

• Multiplication: When you multiply two numbers, you are adding a number a certain number of times. For example, 3 × 4 = 3 + 3 + 3 + 3 = 12
• Division: When you divide two numbers, you are finding the number of times one number fits into another. For example, 12 ÷ 3 = 4, because 3 fits into 12 four times.

Q: How do I evaluate expressions with exponents?

A: When evaluating expressions with exponents, you need to follow the order of operations (PEMDAS). Here's an example:

Expression: 2^3

1. Evaluate the exponent: 2^3 = 2 × 2 × 2 = 8

Therefore, the final result of the expression is 8.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different effects on the result.

• Addition: When you add two numbers, you are combining them to get a larger number. For example, 3 + 4 = 7
• Subtraction: When you subtract one number from another, you are finding the difference between them. For example, 7 - 3 = 4

Q: How do I evaluate expressions with multiple operations?

A: When evaluating expressions with multiple operations, you need to follow the order of operations (PEMDAS). Here's an example:

Expression: 2 + 3 × 4

1. Multiply 3 and 4: 3 × 4 = 12
2. Add 2 and 12: 2 + 12 = 14

Therefore, the final result of the expression is 14.

Q: What are some common mistakes to avoid when solving mathematical expressions?

A: Here are some common mistakes to avoid when solving mathematical expressions:

• Failing to follow the order of operations (PEMDAS)
• Not using parentheses to group numbers and operations
• Not simplifying expressions by combining like terms
• Not checking work by plugging in numbers or using a calculator

Q: How can I practice solving mathematical expressions?

A: Here are some ways to practice solving mathematical expressions:

• Use online resources, such as Khan Academy or Mathway, to practice solving expressions
• Work with a tutor or teacher to practice solving expressions
• Use a calculator to check your work and ensure accuracy
• Practice solving expressions with different levels of difficulty

Conclusion

Solving mathematical expressions is a fundamental skill that is used in many real-world applications. By following the order of operations (PEMDAS) and using parentheses to group numbers and operations, we can ensure that we get the correct result for any mathematical expression. With practice and patience, anyone can become proficient in solving mathematical expressions and apply this skill to real-world problems.