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Chapter 0: Problem 59

Simplify each expression. $$ 6 \cdot 3-12 \div 4 $$

Short Answer

Expert verified
The simplified expression is 15.

Step by step solution

01

Identify the operations

First, identify all the operations in the expression. We have multiplication (\(6 \times 3\)) and division (\(12 \div 4\)).
02

Apply multiplication

Next, perform the multiplication operation: \(6 \times 3 = 18\). The expression now looks like this: \(18 - 12 \div 4\).
03

Apply division

Then, perform the division: \(12 \div 4 = 3\). The expression now looks like this: \(18 - 3\).
04

Perform subtraction

Finally, perform the subtraction: \(18 - 3 = 15\).

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Key Concepts

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

Order of Operations
In mathematics, the order of operations is very important for simplifying expressions correctly. To remember the correct order, you can use the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right). For our problem, we will follow these steps from left to right.

In the expression \(6 \cdot 3 - 12 \div 4\), there are no parentheses or exponents, so we move on to multiplication and division. Always perform these operations before addition and subtraction, working from left to right.
Multiplication
Multiplication is an important step in simplifying expressions. It entails combining equal groups. For example, in our expression \(6 \cdot 3\), you are combining six groups of three. This translates to \(6 \cdot 3 = 18\).

This step simplifies the expression to \(18 - 12 \div 4\), easing the process for the next operations. Always remember to perform multiplication before moving on to division, addition, or subtraction.
Division
After handling multiplication, the next step is often division. Division splits a number into equal parts. For instance, in \(12 \div 4\), you divide 12 into 4 equal parts, which gives you 3. Therefore, \(12 \div 4 = 3\).

Substituting back into our simplified expression, we now have \(18 - 3\). This makes our expression easier to manage as we move to the final step, subtraction.
Subtraction
Subtraction is the final step in our simplified expression. Subtraction removes a value from another, making it smaller. For example, when you have \(18 - 3\), you are taking away 3 from 18. This gives us \(18 - 3 = 15\).

By correctly following the steps of multiplication and division first, we simplify the expression adequately to use subtraction as the last step for the right answer. Thus, the simplified form of the expression \(6 \cdot 3 - 12 \div 4\) is 15.

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Most popular questions from this chapter

Residents of Linn County, Iowa, in the Cedar Rapids Community School District can use the expression $$(v \times 0.5485-4850) \div 1000 \times 31.44$$ to determine their property taxes, where \(v\) is assessed home value. (Source: The Gazette.)Use this expression to calculate, to the nearest dollar, the amount of property taxes that the owner of a home with each of the following values would pay. Follow the rules for order of operations. $$ \$ 200,000 $$

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{1}{6} $$

Find each square root. If it is not a real number, say so. $$ -\sqrt{900} $$

Evaluate each expression for \(w=4, x=-\frac{3}{4}, y=\frac{1}{2},\) and \(z=1.25 .\) $$ x y+y^{4} $$

Complete the table of fraction, decimal, and percent equivalents. $$\begin{array}{|c|c|c|}\hline \begin{array}{c}\text { Fraction in Lowest Terms } \\\\\text { (or Whole Number) }\end{array} & \text { Decimal } & \text { Percent } \\\\\hline \frac{1}{50} & & 2 \%\\\\\hline\end{array}$$
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