Problem 54 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 90-3 \cdot 5 \cdot 2^{2} $$

Step-by-Step Solution

Answer

30

Step 1: Evaluate the exponent

First, evaluate the exponent part of the expression. Here, it is important to follow the order of operations (PEMDAS/BODMAS). Calculate the exponent first: \[2^2 = 4\]

Step 2: Perform the multiplication

Next, substitute the value of the exponent and perform the multiplication: \[3 \times 5 \times 4\]Calculate step by step: \[3 \times 5 = 15\] and then, \[15 \times 4 = 60\]

Step 3: Perform the subtraction

Finally, subtract the result of the multiplication from 90: \[90 - 60 = 30\]

Key Concepts

Understanding PEMDAS

PEMDAS is a helpful acronym to remember the order of operations when solving mathematical expressions. It stands for:

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

Following PEMDAS ensures that you perform each mathematical operation in the correct order, which is crucial to getting the right answer. In our example, we start with exponents, followed by multiplication, and finally subtraction.

Working with Exponents

Exponents are a way to express repeated multiplication of the same number. For instance, 2^2 means multiplying 2 by itself, which equals 4. In the given exercise, we first need to evaluate the exponent:
2^2 = 4.
Sometimes, students mix up the order of operations, but always remember that exponents come before multiplication and subtraction. Practicing problems with exponents helps in mastering this step.

Multiplication and Subtraction

After handling any exponents, the next steps are multiplication and then subtraction, as per PEMDAS. Let's break down the given problem further:

• First, multiply 3 by 5 to get 15.
• Next, multiply the result (15) by 4. This gives us 60.
• Finally, subtract 60 from 90 to get 30.

Always resolve multiplication before subtraction to avoid wrong answers. Repeating exercises like this one will make you more comfortable with the order of operations.