Evaluate The Expression:$\[ 7 \cdot 16 + 4 \cdot 5 \\]

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will evaluate the expression 7 * 16 + 4 * 5. We will break down the expression into smaller parts, apply the order of operations, and simplify it to a single value.

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

  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.

Breaking Down the Expression

The given expression is 7 * 16 + 4 * 5. We can break it down into two smaller expressions:

  1. 7 * 16
  2. 4 * 5

Evaluating the First Expression

To evaluate the first expression, 7 * 16, we need to multiply 7 and 16.

Multiplication is a commutative operation, which means that the order of the numbers being multiplied does not change the result. Therefore, we can write the expression as:

16 * 7

Now, we can multiply 16 and 7.

16 * 7 = 112

So, the value of the first expression is 112.

Evaluating the Second Expression

To evaluate the second expression, 4 * 5, we need to multiply 4 and 5.

Again, multiplication is a commutative operation, so we can write the expression as:

5 * 4

Now, we can multiply 5 and 4.

5 * 4 = 20

So, the value of the second expression is 20.

Combining the Results

Now that we have evaluated both expressions, we can combine the results to get the final value of the original expression.

7 * 16 + 4 * 5 = 112 + 20

Final Evaluation

To get the final value, we need to add 112 and 20.

112 + 20 = 132

Therefore, the value of the expression 7 * 16 + 4 * 5 is 132.

Conclusion

In this article, we evaluated the expression 7 * 16 + 4 * 5 by breaking it down into smaller parts, applying the order of operations, and simplifying it to a single value. We used the acronym PEMDAS to remember the order of operations and applied it to the given expression. The final value of the expression is 132.

Frequently Asked Questions

Q: What is the order of operations? A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS.

Q: How do I evaluate an expression? A: To evaluate an expression, you need to break it down into smaller parts, apply the order of operations, and simplify it to a single value.

Q: What is the value of the expression 7 * 16 + 4 * 5? A: The value of the expression 7 * 16 + 4 * 5 is 132.

Further Reading

  • If you want to learn more about the order of operations, you can check out the following resources:
  • Khan Academy: Order of Operations
  • Mathway: Order of Operations
  • If you want to practice evaluating expressions, you can try the following online tools:
  • Mathway: Expression Evaluator
  • Wolfram Alpha: Expression Evaluator

Introduction

In our previous article, we evaluated the expression 7 * 16 + 4 * 5 and simplified it to a single value. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

  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: How do I evaluate an expression?

A: To evaluate an expression, you need to follow these steps:

  1. Break down the expression into smaller parts.
  2. Apply the order of operations (PEMDAS).
  3. Simplify the expression to a single value.

Q: What is the difference between multiplication and addition?

A: Multiplication is a commutative operation, which means that the order of the numbers being multiplied does not change the result. For example, 2 * 3 = 3 * 2 = 6.

Addition, on the other hand, is not commutative. For example, 2 + 3 ≠ 3 + 2.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions. However, it's always a good idea to double-check your work and make sure that the calculator is set to the correct mode (e.g., decimal or fraction).

Q: How do I handle negative numbers in expressions?

A: When working with negative numbers, remember that multiplication and division can change the sign of the result. For example, (-2) * 3 = -6 and (-2) / 3 = -2/3.

Q: Can I use variables in expressions?

A: Yes, you can use variables in expressions. For example, if x = 2, then 2x = 4.

Q: How do I evaluate expressions with parentheses?

A: When evaluating expressions with parentheses, evaluate the expression inside the parentheses first. For example, (2 + 3) * 4 = (5) * 4 = 20.

Q: Can I use exponents in expressions?

A: Yes, you can use exponents in expressions. For example, 2^3 = 8 and 3^2 = 9.

Q: How do I handle fractions in expressions?

A: When working with fractions, remember that multiplication and division can change the fraction. For example, (1/2) * 3 = 3/2 and (1/2) / 3 = 1/6.

Conclusion

Evaluating expressions is an important skill in mathematics. By following the order of operations and simplifying expressions, you can solve a wide range of problems. Remember to double-check your work and use a calculator when necessary.

Frequently Asked Questions

Q: What is the order of operations? A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS.

Q: How do I evaluate an expression? A: To evaluate an expression, you need to break it down into smaller parts, apply the order of operations, and simplify it to a single value.

Q: What is the difference between multiplication and addition? A: Multiplication is a commutative operation, while addition is not.

Further Reading

  • If you want to learn more about evaluating expressions, you can check out the following resources:
  • Khan Academy: Evaluating Expressions
  • Mathway: Expression Evaluator
  • If you want to practice evaluating expressions, you can try the following online tools:
  • Mathway: Expression Evaluator
  • Wolfram Alpha: Expression Evaluator