Problem 10 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 90-3 \cdot 5 $$

Step-by-Step Solution

Answer

The answer is 75.

Step 1 - Identify the order of operations

First, identify the order of operations. Remember PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 2 - Perform the multiplication

According to the order of operations, multiplication comes before subtraction. So, we need to solve the multiplication part first: \[3 \times 5 = 15\]

Step 3 - Perform the subtraction

Next, subtract the result of the multiplication from 90: \[90 - 15 = 75\]

Key Concepts

PEMDAS

When solving mathematical expressions, it's important to follow the Order of Operations. This is often remembered with the acronym PEMDAS, which stands for:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Following PEMDAS ensures that everyone solves the problem in the same way and gets the correct answer. Always handle operations inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Multiplication

Multiplication is one of the key arithmetic operations and is represented by the symbol \(.\cdot\). It involves finding the product of two numbers. For example, in the exercise \[90 - 3 \cdot 5\], we perform the multiplication before subtraction because of PEMDAS.

• The calculation for the multiplication part is simple: \[3 \times 5 = 15\]

It’s crucial to remember that multiplication is prioritized over addition and subtraction when following the order of operations.

Subtraction

Subtraction is used to find the difference between two numbers and is indicated by the minus sign (-). After completing any multiplication or division in an expression, you perform subtraction.
In the exercise \[90 - 3 \cdot 5\], after multiplying 3 and 5 to get 15, you subtract 15 from 90. The calculation looks like this:

• \[90 - 15 = 75\]

Subtraction is typically one of the last steps when you are following the order of operations (PEMDAS).

Arithmetic Operations

Arithmetic operations include basic mathematical procedures like addition, subtraction, multiplication, and division. These operations are the foundation of most math problems and are organized by PEMDAS.
Knowing how and when to use each operation is crucial. Here's a quick summary:

• Addition: combining numbers to get a sum.
• Subtraction: finding the difference between numbers.
• Multiplication: finding the product of numbers.
• Division: splitting a number into equal parts.

Mastering these operations allows you to tackle more complex math problems with confidence.