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Chapter 0: Problem 48

For exercises 1-80, evaluate. $$ 15 \div 3 \cdot 2 \cdot 4-6 $$

Short Answer

Expert verified
34

Step by step solution

01

- Division

Start by performing the division operation: \[ 15 \div 3 = 5 \]
02

- First Multiplication

Next, multiply the result by 2: \[ 5 \cdot 2 = 10 \]
03

- Second Multiplication

Then, multiply the result by 4: \[ 10 \cdot 4 = 40 \]
04

- Subtraction

Finally, subtract 6 from the result: \[ 40 - 6 = 34 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Division
Division is one of the core operations in mathematics. It essentially means splitting a number into equal parts. In the given exercise, we start with the division operation: \( 15 \div 3 \). This translates to '15 divided by 3'. When you divide 15 by 3, you are asking how many times 3 fits into 15. The answer is 5. So: \[ 15 \div 3 = 5 \]
Understanding how to perform division is crucial, as it often serves as the first step in many order of operations problems. Remember, division is distributive over addition and subtraction, which means we can't ignore it when enclosed within parentheses or as part of a complex expression.
Some quick tips for mastering division:
  • Practice with simple numbers to build confidence.
  • Use long division for larger numbers.
  • Understand the relationship between division and multiplication.
Mastering Multiplication
Next in our order of operations is multiplication. In our problem: \( 15 \div 3 \cdot 2 \cdot 4-6 \), after performing the division, we obtain 5. We then multiply 5 by 2. This is executed as follows: \[ 5 \cdot 2 = 10 \]
Once we have 10, we further multiply it by 4: \[ 10 \cdot 4 = 40 \]
Multiplication in mathematics involves scaling one number by another. Understanding multiplication is foundational as it comes up frequently in both simple and complex problems. Exercise tips for mastering multiplication include:
  • Memorize the multiplication tables for quick recall.
  • Break down larger numbers into smaller factors.
  • Use visual aids like grids and arrays.
Simplifying Subtraction
Finally, we arrive at the subtraction step in our exercise. After performing the previous operations, we have the result of 40. The last step is to subtract 6 from 40. Let's break it down: \[ 40 - 6 = 34 \]
Subtraction is the process of removing one quantity from another. It鈥檚 one of the simpler operations but requires accuracy, especially when working with larger numbers or complex expressions.
Some helpful tips for mastering subtraction are:
  • Always line up numbers by their place values.
  • Practice mental subtraction with round numbers first.
  • Use subtraction in real-world contexts to understand its practical applications.

By following these detailed steps and tips, you will have a strong grasp of performing operations by the order of operations. This ensures you can handle math exercises efficiently and accurately.

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Most popular questions from this chapter

For exercises 115-118, evaluate. On a scientific calculator, use the fraction key. For graphing calculators, use the Frac command to rewrite the decimal answer as a fraction. $$ \left(\frac{5}{34}\right)\left(\frac{8}{21}\right) $$

For exercises \(13-24\), rewrite the fraction as a decimal number. $$ \frac{4}{5} $$

$$ \text { Round } 0.0084 \text { to the nearest thousandth. } $$

$$ -0.6-0.8 $$

$$ \text { Find } 24 \% \text { of } 75 \text {. } $$
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