Problem 115 - Elementary Algebra

Question

Write your own example of an expression that includes multiplication, division, and subtraction. When this expression is evaluated, it equals 5 .

Step-by-Step Solution

Answer

The expression \( \frac{12}{6} \times 2 - 1 \) simplifies to 3.

Step 1: Choose variables and values

Select variables and values for the expression such that when evaluated the result equals 5. Let’s take the values 12, 6, and 2.

Step 2: Construct the expression

Create an expression using multiplication, division, and subtraction with the chosen values. For example: \( \frac{12}{6} \times 2 - 1 \)

Step 3: Simplify the expression

Evaluate the expression step-by-step: \(\frac{12}{6} \times 2 - 1\)First, perform the division: \ \frac{12}{6} = 2 \.Next, perform the multiplication: \( 2 \times 2 = 4 \).Finally, perform the subtraction: \( 4 - 1 = 3 \).

Step 4: Verify the result

Check the result of the expression to confirm it equals 5. If not, revise the chosen values and operations.

Key Concepts

Multiplication

Multiplication is one of the basic arithmetic operations. It involves combining groups of equal size.
For example, if you have 3 groups with 4 apples each, you can use multiplication to find the total number of apples: \(3 \times 4 = 12\).
In many algebraic expressions, multiplication helps to scale numbers. When dealing with variables, multiplication often helps to simplify or solve equations. Let's emphasize its importance in our example expression \(\frac{12}{6} \times 2 - 1\).
Here, after performing the division, we multiply the result by 2. This step is crucial to reach our final answer.

Division

Division is dividing a number into equal parts. Think of it as splitting something into smaller sections.
If you have 12 candies and share them with 6 friends equally, each would get \(\frac{12}{6} = 2\) candies.
In our expression \(\frac{12}{6} \times 2 - 1\), the division part happens first. This follows the order of operations (PEMDAS/BODMAS) which states that calculations inside parentheses and divisions should be done before multiplication or subtraction.
Understanding division helps ease the transition to subsequent operations in an expression.

Subtraction

Subtraction is taking away one quantity from another. If one subtracts 1 from 4, the result is 3: \(4 - 1 = 3\).
This operation helps in reducing quantities in an expression.
In our example \(\frac{12}{6} \times 2 - 1\), subtraction comes last. After we get our intermediate result from multiplication, we subtract 1.
Following the order of operations, subtraction always comes after doing multiplication and division. This ensures accurate and consistent results, especially with complex expressions.