Evaluate 5 − 44 ⋅ ( − 0.75 ) − 18 ÷ 2 3 ⋅ 0.8 − 4 5 5 - 44 \cdot (-0.75) - 18 \div \frac{2}{3} \cdot 0.8 - \frac{4}{5} 5 − 44 ⋅ ( − 0.75 ) − 18 ÷ 3 2 ​ ⋅ 0.8 − 5 4 ​ .Enter The Correct Answer In The Box.

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Understanding the Expression

The given expression is a combination of addition, subtraction, multiplication, and division operations. To evaluate this expression, we need to follow the order of operations (PEMDAS):

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

Step 1: Evaluate Expressions Inside Parentheses

There are no expressions inside parentheses in the given expression.

Step 2: Evaluate Exponential Expressions

There are no exponential expressions in the given expression.

Step 3: Evaluate Multiplication and Division Operations

First, let's evaluate the multiplication and division operations from left to right:

  • 44⋅(−0.75)=−3344 \cdot (-0.75) = -33
  • 18÷23=18⋅32=2718 \div \frac{2}{3} = 18 \cdot \frac{3}{2} = 27
  • 27⋅0.8=21.627 \cdot 0.8 = 21.6

Step 4: Rewrite the Expression with the Results of Multiplication and Division Operations

Now, let's rewrite the expression with the results of the multiplication and division operations:

5−(−33)−21.6−455 - (-33) - 21.6 - \frac{4}{5}

Step 5: Evaluate the Expression

Next, let's evaluate the expression by following the order of operations:

  • 5−(−33)=5+33=385 - (-33) = 5 + 33 = 38
  • 38−21.6=16.438 - 21.6 = 16.4
  • 16.4−45=16.4−0.8=15.616.4 - \frac{4}{5} = 16.4 - 0.8 = 15.6

The final answer is: 15.6\boxed{15.6}

Frequently Asked Questions

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate 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 multiple operations?

A: To evaluate expressions with multiple operations, follow the order of operations (PEMDAS):

  1. Evaluate expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate multiplication and division operations from left to right.
  4. 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 operations that involve numbers, but they have different effects on the numbers. Multiplication involves adding a number a certain number of times, while division involves sharing a number into equal parts.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, follow these steps:

  1. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  2. Evaluate any multiplication and division operations involving the fraction.
  3. Finally, evaluate any addition and subtraction operations involving the fraction.

Q: What is the final answer to the expression 5−44⋅(−0.75)−18÷23⋅0.8−455 - 44 \cdot (-0.75) - 18 \div \frac{2}{3} \cdot 0.8 - \frac{4}{5}?

A: The final answer to the expression 5−44⋅(−0.75)−18÷23⋅0.8−455 - 44 \cdot (-0.75) - 18 \div \frac{2}{3} \cdot 0.8 - \frac{4}{5} is 15.6\boxed{15.6}.

Q: How do I check my work when evaluating expressions?

A: To check your work when evaluating expressions, follow these steps:

  1. Write down the expression and the steps you took to evaluate it.
  2. Check that you followed the order of operations (PEMDAS).
  3. Check that you performed the correct operations (addition, subtraction, multiplication, and division).
  4. Check that your final answer is reasonable and makes sense in the context of the problem.

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

A: Some common mistakes to avoid when evaluating expressions include:

  • Not following the order of operations (PEMDAS)
  • Performing operations in the wrong order
  • Making errors when multiplying or dividing numbers
  • Forgetting to simplify fractions
  • Not checking your work

By following these tips and avoiding common mistakes, you can become more confident and accurate when evaluating expressions.