Evaluate The Following Expressions:a) ${ 81 \div 9\$} B) ${ 9 \times 11 - 6(-5)\$} C) ${ 9 + 12 \div 10 + 10\$} D) ${ 10 + 13 - 12 \div 4\$}

Introduction

Mathematical expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill that every student should possess. In this article, we will evaluate four different mathematical expressions, focusing on the order of operations and the correct application of mathematical rules. We will break down each expression into smaller parts, explaining the steps involved in evaluating them.

Expression a) $81 \div 9$

Evaluating the Expression

To evaluate the expression $81 \div 9$, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, there are no parentheses or exponents, so we can proceed to the next step.

Step 1: Divide 81 by 9

To evaluate the expression, we need to divide 81 by 9.

result = 81 / 9
print(result)

Step 2: Simplify the Result

The result of the division is 9.

Conclusion

The final answer to expression a) $81 \div 9$ is 9.

Expression b) $9 \times 11 - 6(-5)$

Evaluating the Expression

To evaluate the expression $9 \times 11 - 6(-5)$, we need to follow the order of operations. We will start by evaluating the multiplication and then the subtraction.

Step 1: Multiply 9 by 11

To evaluate the expression, we need to multiply 9 by 11.

result = 9 * 11
print(result)

Step 2: Multiply 6 by -5

Next, we need to multiply 6 by -5.

result = 6 * -5
print(result)

Step 3: Subtract the Result from the Previous Result

Now, we need to subtract the result of the multiplication of 6 by -5 from the result of the multiplication of 9 by 11.

result = 99 - (-30)
print(result)

Step 4: Simplify the Result

The result of the subtraction is 129.

Conclusion

The final answer to expression b) $9 \times 11 - 6(-5)$ is 129.

Expression c) $9 + 12 \div 10 + 10$

Evaluating the Expression

To evaluate the expression $9 + 12 \div 10 + 10$, we need to follow the order of operations. We will start by evaluating the division and then the addition.

Step 1: Divide 12 by 10

To evaluate the expression, we need to divide 12 by 10.

result = 12 / 10
print(result)

Step 2: Add 9 to the Result

Next, we need to add 9 to the result of the division.

result = 9 + 1.2
print(result)

Step 3: Add 10 to the Result

Now, we need to add 10 to the result of the previous addition.

result = 10.2 + 10
print(result)

Step 4: Simplify the Result

The result of the addition is 20.2.

Conclusion

The final answer to expression c) $9 + 12 \div 10 + 10$ is 20.2.

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

Evaluating the Expression

To evaluate the expression $10 + 13 - 12 \div 4$, we need to follow the order of operations. We will start by evaluating the division and then the addition and subtraction.

Step 1: Divide 12 by 4

To evaluate the expression, we need to divide 12 by 4.

result = 12 / 4
print(result)

Step 2: Add 10 and 13

Next, we need to add 10 and 13.

result = 10 + 13
print(result)

Step 3: Subtract the Result of the Division from the Result of the Addition

Now, we need to subtract the result of the division from the result of the addition.

result = 23 - 3
print(result)

Step 4: Simplify the Result

The result of the subtraction is 20.

Conclusion

The final answer to expression d) $10 + 13 - 12 \div 4$ is 20.

Conclusion

Introduction

In our previous article, we evaluated four different mathematical expressions, focusing on the order of operations and the correct application of mathematical rules. In this article, we will provide a Q&A guide to help you better understand the concepts and rules involved in evaluating mathematical expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve numbers. However, the key difference between the two is that multiplication involves repeated addition, while division involves sharing or grouping.

For example, 3 × 4 = 12, because 3 + 3 + 3 + 3 = 12. On the other hand, 12 ÷ 3 = 4, because 12 can be divided into 4 groups of 3.

Q: How do I evaluate expressions with parentheses?

A: When evaluating expressions with parentheses, you need to follow the order of operations. First, evaluate any expressions inside the parentheses, and then evaluate any operations outside the parentheses.

For example, consider the expression (2 + 3) × 4. To evaluate this expression, you need to follow the order of operations:

1. Evaluate the expression inside the parentheses: 2 + 3 = 5.
2. Multiply 5 by 4: 5 × 4 = 20.

Therefore, the final answer to the expression (2 + 3) × 4 is 20.

Q: What is the difference between an exponent and a power?

A: An exponent and a power are both mathematical operations that involve raising a number to a certain power. However, the key difference between the two is that an exponent is a small number that is raised to a certain power, while a power is the result of raising a number to a certain power.

For example, consider the expression 2^3. In this expression, 2 is the base and 3 is the exponent. To evaluate this expression, you need to raise 2 to the power of 3, which means multiplying 2 by itself 3 times: 2 × 2 × 2 = 8.

On the other hand, consider the expression 2^3 = 8. In this expression, 8 is the power and 2 is the base.

Q: How do I evaluate expressions with multiple operations?

A: When evaluating expressions with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses, and then evaluate any operations outside the parentheses.

For example, consider the expression 2 + 3 × 4. To evaluate this expression, you need to follow the order of operations:

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

Therefore, the final answer to the expression 2 + 3 × 4 is 14.

Q: What is the difference between a variable and a constant?

A: A variable and a constant are both mathematical expressions that involve numbers. However, the key difference between the two is that a variable is a letter or symbol that represents a value that can change, while a constant is a number that does not change.

For example, consider the expression x + 2. In this expression, x is a variable and 2 is a constant.

Conclusion

In this article, we provided a Q&A guide to help you better understand the concepts and rules involved in evaluating mathematical expressions. We covered topics such as the order of operations, multiplication and division, expressions with parentheses, exponents and powers, and multiple operations. By following the order of operations and applying the correct mathematical rules, you can simplify complex expressions and find the final answer.