Question

For Exercises \(1-74,\) simplify. $$15-5 \cdot 4$$

Short answer

Answer: -5

Step-by-step solution

Identify and Perform Multiplication First

According to the order of operations (PEMDAS), we need to perform the multiplication before the subtraction. In the given expression, the multiplication part is \(5 \cdot 4\). To perform the multiplication, multiply 5 by 4, which equals 20. The expression now becomes: $$15 - 20$$

Perform the Subtraction

Now, we perform the remaining operation, which is subtraction. Subtract 20 from 15: $$15 - 20 = -5$$ The simplified expression is: $$-5$$

Key concepts

Simplifying Expressions

Simplifying expressions involves breaking down a complex mathematical phrase into a simpler form. This process makes it easier to understand and solve an expression. You need to identify different parts of the expression and use mathematical operations systematically. In the exercise provided, the expression is simplified step-by-step by following the rules of order of operations. Simplifying an expression is like solving a puzzle, where each piece fits in place according to its rules.

PEMDAS

PEMDAS is an acronym that helps remember the order of operations in mathematics. It stands for:

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

Using PEMDAS ensures that everyone solves expressions the same way, avoiding confusion. Always handle operations inside the parentheses first, then exponents, followed by multiplication and division from left to right, and finally, addition and subtraction from left to right.
In our example, multiplication is done before subtraction according to these rules.

Multiplication

Multiplication, one of the fundamental operations, involves combining groups of equal sizes. In our expression, we see that multiplication is the operation that needs to be addressed first according to PEMDAS.
The multiplication part here is represented by \[5 \cdot 4 = 20\]which means you're adding 5 fours together. Recognizing multiplication in expressions is crucial as it impacts the final result significantly. Remember, whenever you see multiplication in any expression, it should be among the first operations you complete.

Subtraction

Subtraction is one of the basic arithmetic operations that involves removing one quantity from another.
In our simplified expression of \[15 - 20\],you subtract 20 from 15. This results in a negative number, which might be surprising, but it simply indicates that you're moving "below zero" on a number line. Understanding subtraction in expressions is key as it determines the sign and size of the final result. After simplifying all other operations, subtraction typically comes as one of the concluding steps to get your answer.